Medium run conclusions from Okun's Law and Expectations-Augmented Philips Curve

At least in the 3d edition, Blanchard writes:

  "In the medium run, the unemployment rate must be constant (my emphasis).
  The unemployment rate cannot be decreasing or increasing forever."

This is an inherent characteristic of the definition of the "medium run": that in it, some core magnitudes are constant. In some models, levels are constant (eg. aggregate consumption, aggregate capital stock, etc). In other models, growth rates are constant, and the model "has a steady-sate in growth rates". This means that levels grow indefinitely of course, but it is not wise (or useful, or meaningful) to project economic concepts to "infinite future".

Now for unemployment, it makes no sense to not be constant in equilibrium (at this simple level of exposition). In more sophisticated models, one could have the unemployment rate approaching asymptotically a constant (zero or not) without ever actually reaching it, but this is usually mathematical gadgetry with not much of economic intuition. (And in futuristic models, one could have unemployment approaching asymptotically unity, as machines and Artificial Intelligence take over all jobs).

Can this constant-by-conception-in-the-medium-run unemployment rate $u^* =const.$ be something else than the "natural rate of unemployment" $u_n$?

The natural rate of unemployment is  defined through the Phillips Curve, as that rate of unemployment at which realized inflation equals expected inflation (see previous chapters). Note that it is not assumed a priori that the natural rate of unemployment will be strictly positive -it could very well be zero. It is actual data that tells us that inflation stabilizes at strictly positive rates of unemployment. Then it is constant when inflation is a constant, and Blanchard discusses why inflation will also be a constant in the medium run. So it obtains that in the medium run $u_t = u_n =const.$.

Since the current unemployment rate stabilizes when inflation becomes constant, which happens in the medium run, the constants must coincide. If $u^* \neq u_n$ inflation will not be constant and we would violate another condition for the characterization of the medium run.

And Blanchard writes correctly

  "In the medium run the unemployment rate must be equal to the
  natural rate of unemployment".

So it does not assume what he wants to prove. The natural rate of unemployment is defined separately and with its own logic to be a constant, from the medium-run unemployment rate which is constant based on other arguments than those related to the natural rate of unemployment.

I hope this helps.


The currency is not as relevant as so many other more important factors.

Buying a better ship is a very important factor. If a better ship is chosen and it is Korean, then the buyer (and seller) will benefit from their comparative advantages. I.e. instead of making British workers produce inferior ship, they can produce something they are better at instead, sell that to Koreans, and buy a better ship from them.

Another factor is the fairness of trade. Is the trade fair? Are there any tariffs, subsidies, dumping, theft, currency manipulation, corruption, extortion, forced labor, etc. etc. going on? Maybe not in South Korea and UK, but generally international trade is never perfect.

National security. Are you buying a military ship? A tanker? Is the deal big enough to be abused for political purposes?

There are many more of course.

Currency element is just that one item the list that I highlighted.

That's why big deals like ships, which are more like into 10 billion pounds, usually require a lengthy public review process to go over all of these issues.

On the other hand, if we are talking about 10 pound soda bottles, then currency is about irrelevant for large to medium businesses that can fix exchange rates using Forex futures or swap contracts at virtually no cost. Different currencies is a problem for smaller businesses because accessing heavily regulated financial markets is pretty tough for them and they usually have to bear exchange rate risks and pay hefty commissions to the local banks.


Constant to the power of t in steady state

If the variables are constant, everything in the equation is time-invariant, while $a^t$ will still grow or fall over time (unless $a=1$). This is a contradiction and no steady state exists, unless $a=1$.


Why are ecology and economics seemingly disjunct topics?

I think you are right to say that an economy is always a subsystem of a larger ecosystem, but it needs not always be modeled as such.

It may be interesting to have a precise and elaborate model of the solar system taken in isolation, independently of its interactions with the rest of the galaxy, other galaxies, etc. In very much the same way, there are many good reasons to build a model of an economic system without accounting for how it fits in a more general ecosystem.

The same kind of question applies to many other topics. One could for instance ask "why partial equilibrium and not always general equilibrium?", "why small open economies instead of replicating the actual size structure of the global economy?", etc. I guess the only answer is that the smaller, less general models are considered useful in one way or another.

This is not to say that the opposite endeavours (the ecological economics attempts to model economic systems as part of an ecosystem) are worthless, quite the contrary. But there is only so much you can do and there is always a trade-off (in terms of estimability, tractability, additional assumptions, you name it ) to increasing the generality of a model.


Some thoughts:
Suppose there are two players $i,j$ and two numbers $1,2$. So type profiles are $\theta=(\theta_i,\theta_j) \in \{1,2\} \times \{1,2\}$, and let them be independet draws from the same distribution with $P(\theta_i=2)=p$ and $P(\theta_i=1)=1-p$ . On equilibrium path, this is a continuation game of any larger game because in the end there are always only two players left and in equilibrium they should be the ones with the highest types. This is the continuation game where the standing bid is so high that only the two highest possible numbers remain as plausible candidates.
Let $b$ be the current standing bid and solve backwards as player $i$:
First, $i$ overbids any $b\leq 1$ as challenging would mean losing for sure as for any $\theta, \theta_i+\theta_j\geq 2$.
Similarly, $i$ challenges any $b\geq 5$ as it means winning for sure as for any $\theta, \theta_i+\theta_j<5$ because 4 is the maximal sum.
$\theta_i=1$ challenges $b=4$ as $1+\theta_j\leq3<4$ to win for sure. $\theta_i=2$ challenges $b=4$ as overbidding to $b\geq5$ means player $j$ challenges the next round and wins. Challennging $b=4$ as $\theta_j=2$ means losing against type $\theta_j=2$, but winning against type $\theta_j=1$.
$\theta_i=1$ challenges $b= 3$ as overbidding means losing for sure as any type would challenge bid $b\geq 4$ for sure in the next round and the sum is at most 3.
$\theta_i=2$ overbids $b=3$ to 4 as challenging means losing for sure, given that $2+\theta_i\geq3=b$ for sure.
$\theta_i=2$ overbids $b=2$ as challenging means losing for sure, given that $2+\theta_i\geq3>b$ for sure.
$\theta_i=1$ overbids $b=2$ as challenging means losing for sure, given that $2+\theta_i\geq2=b$ for sure.
Hence, bidding 2 essentially means that the other one has the first move. You can construct multiple signaling equilibria here. Let's concentrate on the case in which nothing is inferred from such a move.
Consider the first round.
Suppose $p>1-p>\frac{1}{2}$.
As $\theta_i=1$, you could bid 4 in the first round. Both types must challenge, which means you lose against $\theta_j=2$ (sum is $3<4$) and lose against $\theta_j=1$ (sum is $2<4$). That is, you can only lose when bidding 4 as type 1 and you will never do this.
Alternatively, as $\theta_i=1$, you can bid $b=3$ in the first round, which means you lose against $\theta_j=1$ who challenges for sure (sum is $2<3$) and win against $\theta_j=2$ who would lose a challenge and loses from overbidding to 4, which you would challenge. Winning is more likely as you beat type 2 and $p>1-p$.
Alternatively, you can bid 2 in the first round, which means both types will overbid.
Type $\theta_j=1$ will bid 3 as bidding 4 or more means sure loss to them. You would challenge the 3 as type 1 and win (overbidding to 4 or more means sure loss to you).
That is you win at least with probability $1-p$.
What does type 2 do upon seeing $b=2$?
Given we assume no inference, they do the same as they would do if they started.
As $\theta_i=2$, you can bid 4 in the first round, which means you lose against $\theta_j=1$ (sum is $3<4$) and win against $\theta_j=2$ (sum is $4$). Both will optimally challenge you even if they learn your type - the high type knows they lost upon seeing 4, the low types knows they won. Thus winning is more likely, $p>1-p$.
Alternatively as $\theta_i=2$, you can bid 3 in the first round, which means you win against $\theta_j=1$ who challenges (sum is $3\geq3$, and them overbidding means you challenge in the next round and win) and lose against $\theta_j=2$ who overbids to 4 which you have to challenge and lose - $\theta_j=2$ would not challenge as this would mean sure loss to them. Thus losing is more likely, $p>1-p$.
Thus, back to type 1 bidding 2 in the first round. If $p>1-p$ and there was no inference, type $\theta_j=2$ bids 4 and you as $\theta_i=1$ win by challenging 4. But that would mean you always win as type $\theta_i=1$ when bidding 2. Then it must be that $j$ infers that you are type 1 when bidding 2. As a response, they would bid 3, which you can challenge or overbid and lose in any case. Hence, bidding 2 as type $\theta_i=1$ means, winning with probability $1-p$ and losing with probability $p$. Because $p>1-p$, this is worse than betting 3.
So $\theta_i=1$ bids 3 in the first round when $p>1-p$.
Now to type $\theta_i=2$ in the first round. Given the above, bidding 4 is better than bidding 3 given prior $p>1-p$. What about bidding 2?
Under the belief that type 1 bids 2, both player types would overbid to 3. Here, challenging would mean sure loss for type $\theta_i=2$. Hence, we overbid to 4 with the same outcome as bidding 4 in the first round. Under a belief that type 2 bids 2, a type 2 would overbid to 4 and win, and a type 3 would overbid to 3 and win challenge against 3 and also after a challenge against 4.
So $\theta_i=2$ bids 4 in the first round when $p>1-p$.
With $p<1-p$, type 1 would still not bid 4 in the first round, but also type 2 would not want to bid 4, instead they bid 3 and type 1 bids 2.


Effects of ACA individual mandate vs AHCA surcharge

Working off of Josh's answer let's do a case study based on a real world example. On Friday, before leaving for a 7 day cruise through the eastern Caribbean, I went to the Dr and got a prescription for Tramadol, a pain reliever to treat an injury. I went to all of the usual suspects, Walgreens, CVS, etc, and found that with my insurance, the cost for 15 50mg pills was 60 dollars. Using the app GoodRX, I was able to reduce this cost to 44 dollars. I decided to pass. Fast forward two days to find me sunning in the Dominican Republic but unable to enjoy myself because of the injury so I found the nearest pharmacy and was able to purchase a blister-pack of 20 50mg pills for 13 US  dollars without a prescription (Tramadol is not regulated like a narcotic as it is in America). These were not knock-offs but the actual meds. How could this be, I wondered. So I asked the pharmacist. He told me that drug manufacturers make all of their profits in America, marking up the same drugs that sell in other countries for reasonable prices to exorbitant prices and then offer modest discounts to insurers, not to mention the profits of the pharmacy. Why can one script be 90 bucks at Walgreens and only 4 bucks at Walmart?  The simple answer is greed and slothfulness. Drug companies and pharmacies rely upon the laziness of Americans and our willingness to get screwed and our eagerness to bitch about problems without the slightest intent on fixing them.

The moral of this story is that when it comes to managing health care costs, one of the major issues is the regulation of pricing. While I am an ardent believer in capitalism, we must limit the margins charged by drug manufacturers and suppliers alike. The government must modify Medicare Part D to include price controls and introduce these same controls into the ACA or we are doomed to ruination.


Is the study of the volunteer sector inappropriate for a labour economist?

I would agree that volunteered labor is a utility enhancing activity. Seen as a good, its price could be the opportunity cost, i.e. the wages foregone (for not working for pay). But then this is not really different from the concept of "leisure", since "leisure" in economics does not mean "fun and games", but rather "time spent not working for pay".

An interesting extension could be the potential value of volunteered labor as professional experience towards future employment for pay (in line with Arrow's "Learning by doing" efficiency concept). Then the issue becomes intertemporal, and also, income considerations arise: I want to volunteer, it generates utility directly for me, but also, I'd rather volunteer and build up professional experience that may lead to higher wages tomorrow, than try to work now and have lower pay due to smaller experience.


How to compute elasticity of substituion in general?

The formula you already have there is a general formula for elasticity of substitution, but I can see that it might be difficult to apply to your problem here given that $MU_{x_2}=1$. There is also another way how formula for elasticity of substitution can be expressed. You can use 'partial derivative formula' (e.g. see Sydsaeter et al. EMEA pp 430) which is the inelegant 'monstrosity' given below. For elasticity of substitution between $x_2$ and $x_1$ it will be given by:
$$\sigma_{x_2x_1} = \frac{−F_1^′F_2^′(x_1 F_1^′ + x_2 F_2^′)}{x_1x_2[(F_2^′)^2F_{11}^{''}
 − 2F_1^′F_2^′F_{12}^{''}+ (F_1^′)^2F_{22}^{''}]}, \text{ for }  F (x_1, x_2) = c$$
So in your case:
$$\sigma_{x_2x_1} = \frac{−x_1 (x_1^2 + x_2)}{x_1x_2[1^2\cdot 1
]}= \frac{-x_1^2-x_2}{x_2}$$
More specifically for $(x_1, x_2) = (1,1)$: $\sigma_{x_2x_1} = -2$


Why are there base years for GDP in current prices (or Nominal GDP)?

Updating of the base year is an indication of methodological changes in the way the national accounts are measured. This means two series with different base year (or reference year, as others call it) are strictly speaking not comparable over time.

Here is the official document from the Central Statistics Office informing about the changes. As the document states:

  1.3 The reason for changing the base year of the nation
  al accounts periodically is to
  take into account the structural changes which have
  been taking place in the economy
  and  to  depict  a  true  picture  of  the  economy  through
  macro  aggregates  like  Gross
  Domestic Product (GDP), National Income, consumption
   expenditure of Government and
  individuals, capital formation etc.

Also, as this article from the Reserve Bank of India states:

  II.1.1 In January 2015, the Central Statistics Office (CSO) released a new series on India’s national accounts. The distinguishing features of the new series are: (i) updating the base year from 2004-05 to 2011-12; (ii) improved coverage of corporate activity by (a) using the MCA 21 database1 of the Ministry of Corporate Affairs, (b) employing value-based indicators such as sales tax collections in conjunction with volume-based indicators such as industrial production, and (c) use of results from the latest surveys, including on activity in the unorganised sector; and (iii) methodological changes such as shifting from the ‘establishment’ to the ‘enterprise’ approach for estimating value added in mining and manufacturing.

If the base year is not updated when methodological changes are carried out, you would not be able to tell that the series before and after the update are not the same. Hence, changing the base year is a trivial way to tell the public they are different.

That is also the reason why the two series, even if in nominal prices, are different over the years.

A comprehensive and critical analysis of these methodological changes for India can be found in this recent paper.


Why are there so many migrants in the modern world?

Are current flows of migration bigger that they were in the past?

We tend to forget history because the numbers involved currently are smaller
relative to world population. For instance, the 8.8 million immigrants who came to the United States in 1901-1910 period is of similar magnitude to the 9.1 million immigrants who came in the 1991-2000 period, but both the U.S. and world populations were much larger than in 1901-1910.

Richard B. Freeman in a nice paper, entitled "People Flows in Globalization," reminds us about this fact.

Some countries indeed receive large inflows of migrants

The US, Russia and Germany are the biggest recipients of immigration (see Table 1 in the above paper). These flows have consequences for factor endowment and there is considerable and often heated controversy over their impacts on destination countries.

How Do Immigrants Affect Their Countries of Arrival?

Freeman examines this question (p.18 to 23) and reviews the empirics. In the basic model of immigration, immigrants reduce earnings of substitute factors and raise the earnings of complementary factors, where complements might include capital and some types of native-born labor. In the basic model, there is full employment but you may intuitively consider quantitative adjustments instead of price/wage adjustements by introducing frictions in the labor market. Note than in most advanced countries,
immigrants have higher unemployment rates and lower employment rates than native workers.

Related to this question a classical paper is "The Economics of Immigration," with theory and evidence by Georges Borjas in Journal of Economic Literature, December 1994. More recently, in 2015, Borjas published an interesting review on Immigration and Globalization. You mal also be intereted in reading his paper on how the collapse of the Soviet Union affects the productivity of American mathematicians.

Regarding policies Freeman  considers "radically economic policies" such
as auctioning immigration visas or charging sizeable fees and spending the funds on current residents to increase the economic incentive for advanced countries to accept greater immigration.


How does the fractional reserve banking system work?

The bank hasn't made £1080 out of nothing. Bob paid that money into the bank. It wasn't in the bank earlier, and it is in the bank now. Alice's account has been increased by £1000. And the bank has £80 extra that it earnt by lending to Bob.

It's helpful to distinguish the money that the bank holds, from the amount of money in the whole system, and from the amount of money the bank owns.

£1080 has left the rest of the system, and entered the bank.

The bank's own capital starts at £5000 and finishes at £5080 (ignoring any interest it's paid to Alice, and its operating costs).

Alice's account starts at £500, and finishes at £1500.

Bob's account starts and ends at £100.


Nash Equilibrium for n-shops Location Game

The following two claims hold in the general $n$-shop case.
Claim 1. In equilibrium a shop closest to an edge (0 or 1) cannot be alone.
Proof. Such a shop could gain customers by moving slightly inward.
Claim 2. In equilibrium at most two shops can be in any location.
Proof. Assume there is an equilibrium where there are three or more shops in a location. Denote the number of customers coming to this location from the left and right by $c_l$ and $c_r$ respectively. (In the 3-shop case $c_l + c_r = 1$.) All shops in the location have a payoff of $(c_l + c_r)/n$. By moving slightly to the left, a shop can attain a payoff that is arbitrarily close to $c_l$, and by moving slightly to the right a shop can attain a payoff that is arbitrarily close to $c_r$, therefore it can attain (almost) $\max(c_l;c_r)$. It is easy to show that if $n >2$ then
$$
\frac{c_l + c_r}{n} < \max(c_l;c_r).
$$

Using these two properties it is very easy to show that in the 3-shop case there is no pure Nash-equilibrium, so this is left as an exercise.
I happen to have a Desmos for this, if you'd like you can use it to validate the claims and reason about the proof.

Note: a mixed equilibrium does exist, see Shaked, A. (1982): Existence and Computation of Mixed Strategy Nash Equilibrium for 3-Firms Location Problem.

Interestingly, $n = 3$ is the only case without a pure equilibrium, $n \in \left\{2,4,5\right\}$ all have one, and for other $n$ values there are infinitely many equilibria. For a formal characterization one needs some additional properties, but no advanced mathematics. For a detailed discussion see
Eaton, B.C., and R.G. Lipsey (1975): The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition.


Two-player first-price auction with resale

Let's look at this with backward induction. Let $v_{i}$ be my valuation and $v_{-i}$ be your valuation. Suppose I've won the item. Then $v_{i} \geq v_{-i}$. If I sell you the item at price $v_{-i}$, then my utility is $v_{-i} - b_{i} \leq v_{i} - b_{i}$, where $b_{i}$ is my bid according to the symmetric equilibrium bidding strategy (which may not necessarily be $\beta$). Notice that I do not gain $v_{i}$ by selling you the item, as I do not possess it.

We see that I will never have incentive to sell you the item. So I should bid as if I'm not going to sell you the item. We have an equilibrium bidding strategy for this anyways, given by the first price auction.


Marginal Product of Capital in the Solow Model

According to your calculations MPK is not increasing in $K$. The Solow model assumes $0< \alpha < 1$, thus $\alpha - 1 < 0$ and $K^{\alpha - 1}$ is decreasing in $K$.


Are revealed preferences normative or positive notion?

However, I encountered an opinion that since all preferences derive from underlaying values they are all strictly normative and considering them positive even in the strict sense of revealed preference is a fallacy.

There's a logical inconsistency here which might help see why it's not a good way of looking at the issue.  What is the key element that is purportedly revealed by dividing the universe into "things normative" and "things positive"?  I would suggest that it is determinism - matters of a positive nature correlate by way of fully deterministic, structurally-modelable processes that are discoverable through repeated experiment.  Think physics - laws guide observables, observables reveal the laws, the laws can be used to predict future observables.  If a tree falls in a forest and no one is around to hear it, physics tells us that it still makes a sound.

Matters of a normative nature correlate only to the extent that a system of "norms" has been set up to enforce them.  Think ethics - morals guide behaviour, behaviour reveals morals, but can morals - absent a normative framework - be used to predict future behaviour?  No - because morals themselves can change, because agents are capable of deception, and because agents may not even have perfect knowledge of their own preferences. Crucially, morals alone are no guaranteed predictor of unexamined human behaviour.

So, I'd argue that your friend's opinion is logically inconsistent because it is a contradiction: in order for it to be true that all preferences derive from underlying values, it must be true that values influence behaviour in a deterministic way according to underlying laws that are, in principle, discoverable through experiment.  That's a pretty weighty claim, in my opinion not at all borne out by the preponderance of evidence - but if it were true, it would mean preferences are in fact positive!

Whether preferences are normative or positive then depends on the assumptions about the agent.  We usually want them to be positive so that we can math about them, and so we make a whole bunch of assumptions about homo economicus that - if true - support that assumption.  But of course, we know that homo economicus is a fiction. So we might suspect that our theory on preferences is at best a useful benchmark to provide context for understanding how people actually behave.


It is the transpose, in this case of the vector.


Listed property price v.s. transaction price

The listed price tells you something about the expectations of the vendor and their estate agent. It's a leading indicator, hinting at where the market may be going next.

The transaction price tells you something about the actual market during the period of the sale, in the period between the property going on the market and the date of exchange. It represents a real meeting of supply and demand - it is a market price. It only becomes available in the weeks or months after completion of the transaction, so the market will already have changed by the time one can get all the data.


Consider the incentive and participation constraints. That is, look at which buyer types would choose which option.

A buyer does not buy anything if
$$v_a < p_a \quad v_b < p_b \quad v_a +v_b < p_{ab}.$$
A buyer chooses only good $i \in \{a,b\}$ with $j\neq i$ if
$$v_i - p_i \geq 0 \quad v_i - p_i \geq v_i + v_j - p_{ab}.$$
Otherwise she chooses the bundle.
With the assumption of independent uniformly distributed values, it then requires some caution to derive the probabilities of each event.

Finally, you want to maximize your profit given by
\begin{align}
(1-p_a)(p_{ab}-p_a) p_a + (1-p_b)(p_{ab}-p_b) p_b + \\
\left( \frac{(p_a + p_b - p_{ab})^2}{2} + (1 - p_a) (1 + p_a - p_{ab}) + (1 - p_b) (1 + p_b - p_{ab}) \\
- (1 - p_a) (1 - p_b) \right) p_{ab},
\end{align}
which is super annoying, but Mathematica suggests that your solution is correct.


Marginal cost is always the same as the shadow price in the cost minimization problem
\begin{eqnarray*}
\min_x && w \cdot x \\
s.t. && f(x) = y.
\end{eqnarray*}
In optimum the shadow price (Lagrange multiplier) belonging to the condition $f(x) = y$ is the marginal cost.

However there are other optimization problems where the shadow price is something else, for example in the utility maximization problem

\begin{eqnarray*}
\max_{x,y} && U(x,y) \\
s.t. && p_x \cdot x + p_y \cdot y = m
\end{eqnarray*}

the shadow prices correspond to the marginal utility of money. (One could argue that this is the reciprocal of the marginal cost of producing more utility.)

Neither of these examples had anything to do with equilibrium, just individual optima.


Does RBC models pin down equilibrium output, amount of labor and capital without initial condition?

The stock of capital in the RBC model is a predetermined state variable, meaning that the capital $K_t$ available at time $t$ was determined at time $t-1$. Usually we have an accumulation relation of the form
$$K_t = I_{t-1}+(1-\delta)K_{t-1}$$
When solving an RBC model starting at time $t=0$, we must exogenously assume some initial capital stock $K_0>0$ to get the model started, since we don't explicitly consider what happened at time $t=-1$.

Labor, on the other hand, generally is not specified ahead of time. Instead, in many RBC models the household has an exogenous certain time endowment, perhaps normalized to 1, and then "leisure" $L_t=1-N_t$ is the amount of time remaining after "labor" $N_t$. Leisure then enters into the utility function just like consumption. (An equivalent and common alternative is to directly put labor $N_t$ as a "bad" into the utility function.)

The basic contrast is that capital is a stock while labor is a flow. We can choose the level of investment flow $I_t$ in each period, and the stock $K_t$ (which we can no longer control once we've reached time $t$) reflects the accumulation of past investment flows $$K_t = \sum_{s=0}^\infty (1-\delta)^s I_{t-s-1}$$
Meanwhile, labor $N_t$ is a flow that the household can choose optimally at time $t$.

Things becomes more complicated in a model with either (A) human capital or (B) search frictions. With (A) human capital, the effective supply of labor is partly a stock, since it reflects past flow investments in human capital; whereas with (B), the number of ongoing employer-employee relationship is a stock that reflects accumulated matches. Neither of these are present in the baseline RBC model, however.

Instead, the baseline RBC model is essentially the Ramsey growth model augmented with a stochastic process for TFP and endogenous labor supply. In this model, capital $K_t$ is the only endogenous linkage between periods.


Car prices haven't changed in 20 years, no inflation?

Inflation is measured against a basket of goods. It's a symptom of what's going on in markets. Some products go up in price over time. Some go down in time. Some stay the same price, but change their specification.

So it's looking down the wrong end of the microscope, to ask why inflation hasn't affected car prices. Car prices are part of inflation. Changes in car prices affect inflation.

The causal link the other way is very very weak. Inflation puts pressure on wages. If this causes wages to rise, then the cost curve shifts, and equilibrium prices change. But for cars, wage costs are a very small part of total car manufacturing cost. And the market for labourers in the industry has shrinking demand and over-supply, so upward pressures are very weak.

The inflation experienced by car manufacturers is very different to the inflation experienced by the public. We've been through a global financial crisis and a super-cycle in commodities. A general-public inflation measure is a very poor measure of input-cost inflation for car manufacturers.


Why do bonds pay back the entire principal at maturity instead of paying it off gradually?

They just issue new debt to roll over the principal anyway. Unlike individuals, they do not have a fixed life span.
Trading amortising bonds in the secondary market is a pain, since you then need to keep track of the amortising schedule when pricing them. (This point was discussed in comments. The calculations for amortising bonds in 2018 are straightforward, but not in the era before digital computers, and that is when bond market conventions were developed.) Vanilla bonds with the same maturity and coupon are effectively identical, but this is not true for two amortisers with different maturity dates. Although this does not appear to be an issue now; trading conventions were largely determined in the pre-digital computer age. For example, the principal amount on a bond is used in for default recovery purposes; that is equal to the face value of a bullet bond, but has to be determined for an amortising bond, which is an awkward calculation to be done on the fly without access to digital computing technology.
One added note is that straight amortising bonds have a very low duration relative to a bullet principal payment. Many investors want to get as much duration as possible for a given investment amount.


Cheap money makes it worthwhile doing stupid things.


What are good advanced textbooks to learn mathematics for economist?

In my honest opinion the best book in this regard is fundamental methods of mathematical economics by Chiang and Wainwright.
It starts at the very basics and then goes all the way up to dynamic optimisation, also covering linear algebra, matrices, advanced calculus  topics such as implicit functions and equation solving at all levels.
Combined with a fine and clear step by step writing style and lots of examples and exercises I find it really a good book.


Why is the marginal utility of money assumed to be constant in Marshallian Theory of Consumer Behaviour

Marshallian Theory is notoriously about computing consumer surplus (and then welfare changes).

But it would be nonsensical to perform such calculations if at the level of one individual, the unit of valuation of surplus, i.e. the marginal utility of money (or the utility of one extra euro), were changing before and after changes in, say, prices. Also, what sense would it make to compute surplus (pleonastically) over many individuals if each of them had a different marginal utility of money?

In these two "within-individual" and "between-individual" cases, not having a constant marginal utility of money would be like summing objects with different units... Hence this assumption.


Controling the level of hours worked in the multiplicative formulation of KPR

Continuing on my comment, if both parameters are set strictly higher than unity, then we can get all the range, indicatively:

This is why I asked how important for the work at hand is to constrain them in the $(0,1)$ interval instead.

This won't be the first time when a mathematical functional form has some inherent restrictions that do not allow it to reflect the whole spectrum of possible human behavior.


Are there any examples for $u(x_1, x_2) = \max\{x_1, x_2\}$ in real word?

One way to think about this utility function is "I can only use one of these two goods, and I will use the one that I have more of"

Some examples:

Choosing between two sets of equally-valued but non-matching dishware. Once you have one set, the other one is useless to you.
If your budget constraint is such that you can only have one kind of platform of some kind, then "items to be used with that platform" works. As commented above, Android apps and iPhone apps, or multi-platform video games, or DVDs vs Blu-Rays.
If you were an opportunistic politician deciding whether to pander to group A or group B, knowing that whichever group you pick the other will hate you, then "number of voters in group A" and "number of voters in group B" would go into your utility function as max(A, B).


Which of Arrow's four desirable properties' is violated in this scenario?

Note that an alternative being highest-ranked by an agent involves comparisons with all other alternatives, which raises doubts that your method satisfies independence of irrelevant alternatives. Indeed, it does not.  Independence off irrelevant alternatives is actually the only property that is violated.

Here are two profiles, only the preferences of the first two agents matter in them, so I will not specify the preferences of the other agents. I only assume the other agents preferences are the same in both profiles.

Agent 1, Profile $1$: $a\succ b\succ c\succ d$

Agent 2, Profile $1$: $b\succ a\succ c\succ d$

In Profile 1, the social ranking of $a$ and $b$ is $a\succ b$.

Agent 1, Profile $2$: $c\succ a\succ b\succ d$

Agent 2, Profile $2$: $b\succ a\succ c\succ d$

In Profile 2, the social ranking of $a$ and $b$ is $b\succ a$.

Since the relative ranking of $a$ and $b$ is the same in both profiles, independence of irrelevant alternatives is violated.


How to interpret illigal foreign currency (cash) transfers in terms of Balance of payments

This answer starta out with how illegal transactions are normally treated in the national accounts. Transactions that are just attempts to evade currency controls are a special case, discussed later.

If the illegal transaction was somehow measured, there would be two entries: the entry for the illegal good/service on the trade account, and the cash flow in the capital account. That is, they are interpreted in the same way as legal activities. Therefore, in response to:

  Is such operation capital inflow or outflow

Currency leaving the country is a capital outflow, and a capital inflow if the currency was coming into the country.

  why is it so?

To keep the published balance of payments balanced.

The problem is: how do we measure these flows? In particular, we generally have no idea where non-electronic currency (e.g., $100 dollars bills) is being held.

If illegal activities were disguised as something else ("money laundering"), the cash flows should end up in whatever accounts the activity was disguised to be.

Countries tend to only include illegal transactions in the national accounts if the statisticians believe that they have a way of tracking them. For example, Statistics Canada was able to estimate the extent of tobacco smuggling (to avoid taxes) based on the disruption in other data. The underground economy behaves differently in each country, and so attempts to measure its effects varies across countries.

To what extent illegal transactions are just a measure to evade currency controls (and not for trafficking in illegal goods) they would once again show up in the form that the transaction was registered. One typical way this is done is to adjust invoices in trade, so that the amount of money exchanged is greater than the true value of the goods. This shows up in the national accounts as an excessively large imports/exports (depending on the direction of the flow).


Why does marginal cost (derivative of total cost) differ from variable cost at each level?

For $Q_1 = 1, Q_2 =2$, you calculate

$$TC(Q_2) - TC(Q_1)=7$$
which is the additional (incremental) cost to produce the second unit of output, and then you compare this to

$$\frac {dTC}{dQ} |_{Q=Q_2} = 12$$

which is marginal cost when you are already at production level $Q_2$. From this observation alone, the two are not comparable.

As for practical value: assume marginal revenue is a straight line at $P=8$. What to do? The "marginal cost equals marginal revenue" leads to  $3Q^2 \leq 8 \implies Q^*= \sqrt {8/3} \approx 1.633$. What's the problem with that?

Well, the product we are examining may not be divisible so much as to make incremental cost adequately close to marginal cost. This not-sufficient divisibility  may force us to resort to integer-value calculus, and use the concept of incremental cost instead : produce the highest quantity for which incremental cost is lower or equal to incremental revenue - and we will obtain the correct answer $Q^* =2$.

Note: "sufficient divisibility" is not a strictly "physical constraint" but is judged also on economic considerations. If we are contemplating producing, say, cars to the range of hundreds of thousands, then, even if each car costs say 20 thousand euros, the pains and computational inconvenience of integer-valued calculus may not worth the small reduction in profits if (by using marginal calculus) we end up producing one unit more than optimal given indivisibility.


Is this a valid or legitimate way of comparing countries on traits and characteristics?

I have no idea whether there are formal rules, but you can emulate physical scientists and look at the units.

Dividing solar power by population is reasonable, as you get megawatts per capita. Those refer to real quantities.

However, you are dividing by GDP (in a roundabout fashion). The units of GDP are (currency unit)/(year). Since megawatts are a real quantity, and thus no currency value, the resulting ratio is (megawatts)(years)/(currency unit). This does not appear to correspond to anything.

You could try to fit a model that predicts solar capacity as a function of wealth and population, and the model calculations should implicitly correct the units.


Where does the Euler equation get its name from?

It appears, like a lot of other math economics uses, this one was lifted from fluid dynamics. From Wikipedia:

  The Euler equations first appeared in published form in Euler's article "Principes généraux du mouvement des fluides", published in Mémoires de l'Academie des Sciences de Berlin in 1757 (in this article Euler actually published only the general form of the continuity equation and the momentum equation;[3] the energy balance equation would be obtained a century later). They were among the first partial differential equations to be written down.


Are there any non-paywalled reputable economics journals?

Theoretical Economics (TE) and Quantitative Economics are two open access, peer reviewed journals. The former I know is of very good quality, arguably the top "field journal" in microeconomic theory.


Premises on which the Efficient Market Hypothesis is built upon

The efficient market hypothesis does not require everyone being omniscient. It works through the supply/demand and price mechanism.

For example, imagine that you have private information that a company X is doing bad (without being a manager or other person banned from insider trading). If company X is doing bad then sooner or later it’s stock price will have to go down, so if you own it’s stock you would sell it now while the price is still high or if you don’t own the stock you would short sell it.

However, as you start selling the stock you are pushing the price down. Since it’s profitable for you to sell or short sell as long as the market price is above the actual value of the company, you would do that so much that the price would eventually be driven to the point where the price is exactly equal it’s value.

The central assumption of the efficient market hypothesis is the perfect market assumption. In a perfect market there are no transactions costs, information is costless, investors are rational. In the real world however, these assumptions do not completely hold and the market is not fully efficient.

This being said, there is evidence that despite these imperfections markets are efficient to a certain extent as prices do adjust in response to new information. In fact it’s astonishingly hard to beat the market, and difficult to find deviations from the efficient market hypothesis empirically but now we know they exist.


While calcluating GNP, the overall income of a citizen working abroad is considered or only his/her remittances?

GNI (Gross National Income) is the current description of what used to be called GNP.  It is GDP (Gross Domestic Product) plus net primary income from abroad (primary income receivable from the rest of the world less primary income payable to the rest of the world)

Assuming this individual is a long-term resident (1 year or more) in Country B, than none of this counts as Country A's GNI (Gross National Income is the current description of what used to be called GNP).  The earnings count in Country B's GDP (as part of the income measure) and GNI, while the remittance is part of Country A's secondary income from Country B and affects the Balance of Payments current accounts of the two countries.  See chapter 12 of the IMF Balance of Payments manual.  Something similar happens with the self-employed

If however this individual is a short-term resident (less than a year) or a cross-border worker, employee compensation counts as primary income and so is part of Country A's GNI though Country B's GDP (as part of the income measure).   Any goods or services this individual pays for in Country B is counted as a export from Country B to Country A. See chapter 11 of the IMF Balance of Payments manual. For short-term self-employed migrants, income counts as an export of services from Country B to Country A, and so counts in Country A's GDP and GNI, but again anything spent in Country B counts as trade the other way

Measuring these flows and making these distinctions are difficult for national statistical services, especially for migrant workers who do not know how long they will be staying in another country


Income effect $-\frac{\partial x_i}{\partial m} x_i$ or $\frac{\partial x_i}{\partial m}x_i$?

The income effect is defined as $\mathbf{-\frac{\partial x_i}{\partial m}x_i}$.

Let $x_i$ be a normal good; that is, a good whose Marshallian demand increases with an increase in income $\left(\frac{\partial x_i}{\partial m} > 0\right)$. Even if there was no substitution effect $\left(\frac{\partial h_i}{\partial p_i} = 0\right)$ from an increase in own-price, the amount of $x_i$ consumed would still be reduced as the consumer is effectively poorer. Hence the net income effect in this case is negative, which necessitates the negative sign since $x_i$ is non-negative. Analogous logic holds if $x_i$ is an inferior good instead.

This interpretation is consistent with Nicholson & Snyder (p. 156).


Where to find series of capital-output ratio for the US?

Capital to output ratio can be calculated using the BLS productivity measures data.
Capital to output ratio is simply K/Y.  Capital (K) is usually called either capital input or capital services and output which would be called real value added output.

Which can be found here:  https://www.bls.gov/mfp/mprdload.htm   under 1987–2019 Major Sector Multifactor Productivity.

https://www.bls.gov/mfp/special_requests/mfptable.xlsx

Or the World Bank group- Capital-Output ratio (NKY)
https://datacatalog.worldbank.org/dataset/capital-fundamentalism-economic-development-and-economic-growth/resource/babcd99a-16a3-4bef


How dominant assurance contract fix free rider problem?

It was established in the comments that the source of this claim is Tabarrok: The private provision of public goods via dominant assurance
contracts via Wikipedia.

Tabarrok writes

  assume that a plain is flooding and that a dike must be built to hold back the river. It
  is known with certainty that the flood will be averted if the dike reaches 6ft.
  If the dike doesn’t reach 6ft then the river overflows and the builder’s efforts
  are wasted. Assume that the agent’s choice is binary, he can help to build the
  dike or not.  [...]
  note that the game really consists of two distinct elements [...] Consider column one; the problem in this column is not free
  riding. [...] The problem in column one is that the agent doesn’t want to waste his effort
  in building a dike which won’t hold the river. Each agent lacks “assurance”
  that the others will contribute in the event that he contributes.
  The problem in column 2 is quite different. In column two each agent
  assumes that the public good will be provided regardless of his actions. Each
  agent, therefore, wishes to “free ride” on the others.  [...]
  The assurance problem can be overcome via an assurance contract.

[emphasis by me]

So assurance contracts are not claimed to overcome the free riding problem.


History of Macroeconomic Measurements before GDP

Maybe the earliest economic quantities to be measured are the number of people in a tribe or nation as a measure of economic and military potential. Roman (Roman king Servius Tullius) and ancient Israeli censuses (Prophet Moses duing the Egyptian Exodus) were said to have been conducted in the 6th and 13th centuries before the common era (Wikipedia -- Census).

William Petty's (mercantilist, 1623-1687) political arithmetic is often considered the first work related to economic measurement and econometrics and crudely and innovatively estimated the population, national income and national
wealth for Ireland and England. François Quesnay (physiocract) is often regarded as his fellow pioneer and his Tableau Economique (1759), is often considered a forerunner of the modern national income and product accounts (Hillinger (2007)).

For more precise economic estimates, measures of national production of pig iron goes back in the USA and the UK at least as far as 1870.

  Productivity Change in British Pig Iron, 1870-1939 Donald N.
  McCloskey The Quarterly Journal of Economics Vol. 82, No. 2 (May,
  1968), pp. 281-296


Is wealth created when money is transferred from a wealthy country to a less wealthy country?

No purchasing power is not created from thin air. When you convert money through PPP (expressed usually in terms of local currency to USD) you are getting information about what is the purchasing power of US dollar that would get you the same basket of goods under the law of one price. This is not the same as making currency conversion with exchange rate which generally tells you not much about what would be the actual purchasing power of different currency.
Moreover, it is generally agreed by international trade economists that one of the major reasons why you will find discrepancies between exchange rate and purchasing power parity is the Balassa-Samuelson effect (See Krugman et al. International Trade Theory and Policy). This is because according to Balassa-Samuelson theory the price level in a country depends on productivity mainly in the tradable sector (mostly consisting of goods) because tradable and non-tradable sector (mostly consisting of services) compete for the same workers. This in turn means that if productivity in tradable sector increases it will increase wages not just in tradable sector but also in non-tradable sector.
This is the reason why hairdresser with exactly the same level of skill will get much higher wage in US than in India. However, this in turn leads to violation of law of one price as then also prices in non-tradable sector will be generally higher in US (e.g. haircut in US will be much more expensive than haircut in India).
Beside Balassa-Samuelsson effect, divergence between PPP and market exchange rate can be also due to transaction costs (which lead to failure of one price), differentiated goods (beef produced under strict EU health regulations is not the same beef as beef produced in some developing economy), fixed investment costs  that can also lead to deviations of law of one price and various composition issues when constructing price indecies (see Marrewijk International Economics: theory application and policy 2nd ed pp 471).
As a consequence of this there you will observe divergence between PPP and market exchange rate, but that is not the same as saying that some purchasing power was created out of nothing as they measure different things.


How does exchange rate change with respect to interests?

If by “greater”, you mean higher number It depends on how you quote exchange rate. Under American system the exchange rate between USD and euro would be given by $S=EUR/USD$ under European system the exchange rate would be quoted other way around as $S=USD/EUR$. So under American system if the USD appreciates due to higher interest rates the $S$ would actually get lower while under the European system appreciation would actually lead to greater/higher exchange rate $S$.

Otherwise, ceteris paribus, higher interest rate has to lead to appreciation under the standard exchange rate model since the exchange rate is given in standard monetary model of exchange rates:

$$S=ln(p)-ln(p_f)= ln(m)-ln(m_f) -(ln(y)-ln(y_f))+\lambda(i-i_f) $$ (where $p$ is price level, $m$ money supply, $y$, real GDP i interest rate and $f$ denotes foreign sector - also I assume that $ ln(L(i)) \approx \lambda i$so the exchange rate should appreciate when interest rates $i$ increases and nothing else change.


I am not exactly sure what you mean by "block price" and I don't know the bucket buddy. However, I feel like you are talking about what microeconomists term bundling, the practice of selling two (or more) different goods together in one package.

Interestingly, bundling can be profitable even without any production-cost related efficiency arguments. It can serve as a tool to sort consumer types and thus can be used to price-discriminate.

The classical paper on bundling by a monopolist is McAfee, McMillan and Whinston (1989). For an introductory treatment of the topic read, e.g., Belleflamme and Peitz, Chapter 11 - or the corresponding chapter of basically any other textbook on industrial organization or microeconomics.


How is momentum justified as a common risk factor?

The Jegadeesh and Titman (1993) paper is usually considered Original Source, though I'm sure you could find something earlier that looks similar if you looked hard enough.

I don't think there is a satisfactory explanation. Momentum is not correlated with macroeconomic variables, it does not seem to reflect persistent exposure to other (known) sources of risk, and is driven almost entirely by the 7 to 12 months before stocks are chosen as part of a momentum portfolio. This all makes it extremely difficult to put a solid theoretical model to it that doesn't have a behavioral aspect.

Recently (mid 2009), there was a momentum crash in the market. Daniel and Moskowitz argue that momentum has rare "panics" periods like this, where crashes occur for momentum. So during normal periods investors may be being compensated for this risk. The question becomes "what are these crashes caused by?" The authors make the case that following a period of declining stock values, momentum portfolios will be long a lot of low market beta stocks, and short a lot of high beta stocks. If there is a sudden rebound in the market, momentum strategies will experience a crash. So this is at least suggestive of a direction for more formal modeling, but they ultimately suggest a behavioral interpretation may be necessary as well.

If you have not seen it, Jegadeesh and Titman (2011) review the evidence for momentum in more detail, and explore behavioral explanations for momentum, of which I have little knowledge.


Confusion regarding remedying negative externalities of consumption through taxation

Your reasoning is basically correct. In fact, when I teach externalities to my students, I draw something very much like your diagram 1.

The textbook is confusing because the MSC and MSB curves are supposed to show the social benefits and costs of this particular activity. Taxes and subsidies can't possibly change these costs/benefits because they don't change the fundamental real effects of the activity (one unit of smoke is equally disgusting, regardless of whether it is taxed or not). The tax just means that in addition to this cost, some money is changing hands. But that's not really a social cost because the money will end up belonging to someone.

I don't think it's too helpful to start thinking about the idea "that a tax will also cause an increase in MSC (effects on employment of tobacco farmers etc.)"

Those workers sell their labour in a labour market with a price mechanism. Unless we think there is some market failure in that labour market, the market achieves allocative efficiency. We don't usually talk about externalities when people loose out from price increase or quantity falls in a well-functioning market because those things are efficient and there isn't a very strong case for intervention.


Definition: Extractive Goods (Comtrades HS-Categorization)

I know this is a little late, (just joined this forum two hours ago) but if it is still relevant. You should look at the Australian Department of Foreign Affairs and Trade TRIEC system (Google "DFAT TRIEC") It is an established system and useful for high level groupings. You might try to use their groupings and hopefully be able to answer the questions from the analysis.


If an ordinal-scaled utility function is defined via strictly increasing transformation, how can it represent a case of indifference?

I think you are most confused about what is meant by “defined in terms of strictly increasing transformations” or being “informationally equivalent.

You should think it in the following way, a utility function represents someone’s preferences if the function gives a higher/lower/equal value from bundle a than from bundle b if that person prefers more/less/the same bundle a than bundle b. Suppose that such function is $u(x)$, then you can ask, is there a unique function with such properties (I.e. that represents the person’s preferences) and the answer is NO. Any strictly increasing monotonic transformation of $u(x)$, say $f(u(x))$ is also a function describing the preferences of the person. Hence we say that these two are valid representations, and are equivalent (or informationally equivalent).

Note that whenever you are comparing two bundles you can use any one of the possible representations, and the “strictly increasing monotonic transformation” part is just to check if two functions are equivalent representations of preferences.


Pareto optimal and Walrasian equilibrium

We have two Consumers 1 and 2, and two goods 1 and 2 pure exchange economy. The following utility functions can be used to represent their preferences:

$u_1(x_{11}, x_{12}) = x_{11}$
$u_2(x_{21}, x_{22}) = x_{22}$

Equilibrium price vector $(p_1, p_2=1)$ and allocation $((x_{11}, x_{12}), (x_{21}, x_{22}))$ satisfy the following:

Optimality Conditions (Allocation must solve the utility maximization problem of the two consumers, i.e. it must lie on their demand functions)

$(x_{11}, x_{12}) = \left(\frac{50p_1 + 50}{p_1}, 0\right) $
$(x_{21}, x_{22}) = \left(0, 50p_1 + 50\right)$

Market Clearing Conditions

$x_{11} + x_{21} = 100$
$x_{12} + x_{22} = 100$

Solving the above gives price vector $(p_1, p_2) = (1, 1)$ that supports the allocation $((x_{11}, x_{12}), (x_{21}, x_{22})) = ((100, 0), (0, 100))$ in equilibrium. This allocation is the only competitive equilibrium. It is also the only Pareto efficient allocation in this economy.


Mathematics of the income and substitution effects

The (Hicks-) substitution effect is by definition the change in consumption of X induced by a change of the relative prices, holding utility fixed. Thus, the original budget line is "rolled along" its indifference curve until it has the same slope (same relative prices) as the actual budget constraint after the price change. This determines $e'$. You can think of the tangent to $e'$ as a hypothetical budget constraint that compensates you for the lost utility resulting from the increasing price of $X$ by adding income until you can just afford a bundle with the same utility as the original bundle $e$. In total, the change from $e$ to $e^*$ is then separated into a change from $e$ to $e'$, (rolling the budget line along the indifference curve: relative price change, holding utility constant = substitution effect) and a change from $e'$ to $e^*$ (parallel shift of budget line: income change, holding relative prices constant = income effect).


Perfect Competition and costs of production question

Welcome to Economics SE. We ask that when asking about homework questions that you show your work so we can see what you need help with. The site is not meant to be a free homework solving machine.

Remember that a firm's profit is revenue minus costs, where costs can be fixed (200) or variable (manipulation of the marginal costs).

$$\Pi(q) = pq - c_f - c(q)$$

where $p$ is price, $c_f$ is fixed costs, and $c(q)$ is the cost with respect to $q$. We don't necessarily need to expression the variable costs as a function in this case.

So using the information we have, we know that for producing one unit of the good, our profits are:

$$\Pi(1) = 300 \cdot 1 - 200 - 270 = -170$$

For two goods, we have

$$\Pi(2) = 300 \cdot 2 - 200 - (270+210) = -80$$

And so on...

So you do this calculation for all the quantities and you see which one maximizes profits. That will also allow you to answer part b. As for part c, you have to see if there is a way for profits to be above 0 for some quantity produced.


Which currency do we consider when talking about trade balance ?

My reading of the Marshall-Lerner condition is that it assumes the price of exports is constant in the domestic currency and the price of imports is constant in the foreign currency.  Analysis is conventionally done in the domestic currency

But, initially after devaluation, volumes are assumed to stay the same (short-term inelasticity) and measured in the domestic currency the values of exports stays the same while the value of imports rises, leading to a deterioration in the measured trade balance; this is the immediate cost effect of devaluation. If you were to measure in the foreign currency, the short-term value of exports would fall while the short-term value of imports would stay the same, again leading to a deterioration in the measured trade balance


What is the most general definition of “the core” in game theory?

We can talk of the core for any arbitrary game. To explain how let me compare it directly to how we define non-cooperative games. In a standard non-cooperative game we define Players, $I$, action sets for each player, $A_i$ for each $i\in I$ and payoff functions that map any profile of actions to payoffs $u_i: A\rightarrow \mathbb{R}$, where $A=\prod_{i\in I} A_i$. Finally the solution concept, for example, Nash equilibrium, correlated equilibrium or rationalizability is a condition on these objects that we think are a good prediction of what will happen. For instance, Nash equilibrium predicts that every player is best responding to a correct belief about what other players are doing.

The  Core is another solution concept, however, the language developed so far is not sufficient, because the idea of the core is that it predicts that no group of people (or coalition) will have a profitable deviation. It is clear that now the unit of analysis are groups of people, so the "agents" in this setup are the elements of $P(I)$, the power set of $I$, which contains all possible groups of people, so you will need to define the action sets for each of these groups. A natural way could be that if $C\in P(I)$ then $A_C=\prod_{i\in I\cap C} A_i$, i.e. the coalition $C$ can choose the actions of all its players. It is clearly not the only possibility, maybe you want to allow for players to have some autonomy within the coalition, but let's say you define action sets that way.

You will also have to define payoff functions for each possible coalition. Again a natural way could be to define $u_C=\sum_{i\in iI\cap C} u_i$, i.e. the sum of utilities of players in the coalition. Note that your assumption on this coalition utility will necessarily come with some assumptions of how you substitute between players' utilities within the coalition.

Finally, you will have to define which coalitions are possible to co-exist. For example, can players belong to multiple coalitions or not? Again a natural way would be to rule out this possibility so that in equilibrium each player must belong to only one coalition, i.e. $C\cap C'=\emptyset$. This language will allow you to define that the core will be a situation where all players belong to a coalition, each coalition chooses an action for each of their players and there is no subset of players that will rather separate from their current coalition to form another one and choose a  different profile of actions.

Hopefully, I  have made clear that I needed to make several assumptions just to be able to define the core. Especially if I want to have some counterpart with the original non-cooperative game I started with. This is cumbersome.

I think this is why, to some extent, the way some of the literature developed was by not subordinating the definition of core (intrinsically a cooperative solution concept) to the terminology of a non-cooperative game. One way to do it is by directly defining a payoff function for each player from being part of a coalition $V_i(C)$ for each player where $C\in P(I)$ (this notation has implicit that being in a coalition can probably imply different actions on your part). The core is then a partition of players (each player belongs to a coalition, say $i\in C_i^*$) such that there is no coalition $C'\in P(I)$ such that for all $i\in C'$, you have $V_i(C')\geq V_i(C_i^*)$ and with strict inequality for some $i\in C'$.

Clearly, this last formulation has fewer assumptions than my first formulation. However, it is also clear that it does have assumptions. The main ones (at least for me) is that suffices to know what coalition you belong to figuree out your payoff (i.e. no externalities between coalitions). And the other important assumption is that players can only belong to one coalition. This is restrictive in many situations, for example, politicians that belong to multiple interest groups, etc.

Depending on what you are willing to assume about the nature of cooperation and deviations from cooperation, you will get a different-looking definition of core, but the general principle is the same. The core is the prediction that captures that no subgroup of players has incentives to coordinate and improve their condition. So the concept is not bound to specific kinds of games, but I think that there is no consensus on how to apply it universally to all kinds of games.


Government Ownership vs Private Ownership

Yes, there are lots. Several state-owned energy companies succeed in international competitive markets, for example.

EDF is majority-owned by the French State, and is a successful competitor in energy markets in other countries; e.g. GB electricity retail.

DONG is majority-owned by the Danish State, and is a successful competitor in energy markets in other countries; e.g. UK offshore windfarm installation.


Can we add well-being into macro model as an endogenous variable?

One can model anything, that's why it is a model. The real question is what the value of such a model would be.

More to the point, I think this would be a very hard thing to do sensibly because how are we going to measure well-being? It encompasses way more factors than our economic models typically capture, such as social relations, health and mental state. Even if we include all of those, the relation between all those variables among each other and well-being is often unknown. We could theorize about it, but actually finding out what the relations are would be very hard to do.

For example suppose I model well-being as a combination of health, income and social relationships. That would mean that my macro-economic model would have to contain some kind of measure how social relationships evolve. Moreover, not only are increases in my income going to improve my well-being directly, but it is also going to affect my health (positively up to a point probably) and social relationships (those I guess could go both ways depending on income inequality or the possibility to be generous or visit friends and relatives).

If one really wants to capture well-being there are so many variables affecting that, that the model essentially becomes a black box. We don't know what's driving the results anymore.

What has been done, is trying to measure these things in retrospect. There are various macro-economic/social indicators and indices that try to capture how well-being has evolved over time. These retrospective studies are then used to judge what has gone well and what has not (the latter is also a hard thing to do because we typically have no good counterfactuals)


I believe the single most commonly used metric for contagion is a sharp increase in the correlation of returns in various countries, either within a country (e.g., the correlation of daily returns in the markets for stocks, bonds, and commodities) or across countries (e.g, the correlation of daily returns in the stock markets in Europe, North and South America, Asia, etc).

While correlation is an easily understood measure, and while it's true that pairwise correlations do tend to rise during crisis periods, using correlations in this manner is not without pitfalls. In particular, sampling correlation coefficients will rise during periods of heightened market volatility (and this is a major difference to, say, regression coefficients), irrespective of whether there's a real crisis or not. For more on these pitfalls see, e.g.,

Forbes and Rigobon, 2002, "No Contagion, Only Interdependence: Measuring Stock Market Comovements", Journal of Finance, vol. 57, pp. 2223-2281.

and

Loretan and English, Evaluating changes in correlations during periods of high market volatility, BIS Quarterly Review, 2000, June, pp. 29-36.


One thing to consider, is that it looks like you may have a unit root, though not necessarily.
An example of a unit root would be the stochastic process $y_k=y_{k−1}+\epsilon_{k−1}$, where the error term is mean-zero.
Unit roots can cause problems. For one, they are not stationary processes. Using OLS relies on stationarity. A violation can lead to a 'spurious regression': invalid estimates but with a high R-squared.
However, these problems are solvable. The first step is to run a unit-root test, of which there are many.
I suggest looking elsewhere for further material on this, e.g. here. There is lots out there and a full treatment would be outside the scope of one answer.


Why utility rather than expected utility in Cochrane's "Asset Pricing"?

As mentioned in the comments this comes down to stylistic choices, since as you correctly pointed out:
$$u(c_t)+\beta E_t[u(c_{t+1})]=E_t[u(c_t)+\beta u(c_{t+1})]$$
However, in principle both expressions are correct. The first expression states that the $U_t(c_t, c_{t+1})$ is a composite function of present utility of consumption $u_t(c_t)$ and expected utility of future consumption $E_t(u_{t+1}(c_{t+1}))$, whereas the second expression is directly expected utility of present and future consumption. When we condition on presently known information those two are equivalent here.
The notation that Cochrane uses is not used everywhere  but there does not seem anything wrong with it either from mathematical perspective or economically.


Estimating the second derivative of function from optimizers

The first order condition of the maximization problem is
\begin{equation}
f'(x)-s=0\iff f'(x)=s
\end{equation}

We can then replace $x$ by $x(s)$ because this is the optimal value given $s$. Since this is true for every $s$, we can differentiate with respect to $s$ which yields
\begin{equation}
f''(x(s))x'(s)=1
\end{equation}

Which can be rewrite as
\begin{equation}
f''(x(s))=\frac{1}{x'(s)}
\end{equation}

Then $x'(s)$ can be estimated by finite differences which would give $f''(x)$.


Reference request about econometric analysis of Environmental Kuznets curve

There is a very good review article by Richard Carson in the review of environmental economics and policy, which (perhaps unfortunately) shows that much of the empirical evidence for an environmental Kuznet's curve is weak at best.


Probit with panel data - assumptions violated with endogenous covariate?

Yes it does. According to the Verbeeks guide to modern econometrics (pp418) standard panel fixed effects binary model assumes that error has “a symmetric distribution with distribution function $F(.)$, i.i.d. across individuals and time and independent of all $x_{is}$” [with the model being  $y_{it}^*=x_{it}’ \beta+ \alpha_i+u_{it}$].

Just a two pages later Verbeek also writes about Random effects probit model $y_{it}^*=x_{it}’ \beta +\epsilon_{it}$ that $\epsilon_{it}$ should also besides other things be independent of $x$.

Now both of the above panel models are technically static since no lags are involved but I don’t see any reason why this assumption could be relaxed just by making model dynamic. In fact there is a such thing as panel IV logit/probit, probably people would not invest time into development of those if this assumption could be relaxed by just adding lags.


Adverse selection in competitive markets- labor market

Suppose that $r'(\theta)>0$. The following figure should make clear that saying $r(\theta)\leq w$ is equivalent to saying that $\theta\leq r^{-1}(w)$ (where $r^{-1}(\cdot)$ is the inverse of $r$):

So we can rephrase your question as 'why should $E(\theta|\theta<r^{-1}(w))$ be non-linear?'

Let's calculate this expectation (assuming that $\theta$ is distributed on support $[\underline{\theta},\overline{\theta}]$ according to CDF $F$):

$$E(\theta|\theta<r^{-1}(w))=\frac{1}{F[r^{-1}(w)]}\int_\underline{\theta}^{r^{-1}(w)}\!\theta F'(\theta)d\theta.$$

For $E(\theta|\theta<r^{-1}(w))$ to be linear in $w$ we would need $\partial E(\theta|\theta<r^{-1}(w))/\partial w$ to be constant.

Differentiating with respect to $w$ we have
$$\frac{\partial E(\theta|\theta<r^{-1}(w))}{\partial w}=\frac{F'[r^{-1}(w)]\frac{\partial r^{-1}(w)}{\partial w}\left[F[r^{-1}(w)]r^{-1}(w)-\int_\underline{\theta}^{r^{-1}(w)}\!\theta F'(\theta)d\theta\right]}{F[r^{-1}(w)]^2}$$

The above expression isn't the prettiest thing to look at, but a quick glance should convince you that it will only be constant under very special circumstances. For example, even if we take a highly linear environment like $r(\theta)=\theta$, $F(\theta)=\theta$, we have
$$\frac{\partial E(\theta|\theta<r^{-1}(w))}{\partial w}=\frac{w^2+\underline{\theta}^2}{2w^2},$$
so $E(\theta|\theta<r^{-1}(w))$ is non-linear.


Why does the US have public debt if they make more than that annually?

The names “United States” or “US” refer to different entities here. With regards to the debt, they’re referring to the government of the country. With regards to the GDP, they’re referring to all the businesses of the country. So the government owes several trillions of dollars to those who have purchased treasury bonds, and the businesses of the country produce (every year) an even larger amount of money in profits. But the government only taxes a portion of those profits, and so it would take far longer than just a few years, to pay off all of the debt — and also (at least recently) the government keeps spending more than it collects in taxes, so it is simply getting further and further into debt.

A similar situation is going on with the world as a whole. When talking about the debt of various countries, what people are really discussing are the debts of the various governments of those countries. Basically, the governments of the world owe large sums of money to the businesses (and individuals) of the world. They also tax those businesses (and individuals) every year, and use those taxes to pay back (some of) the debts. But when (say) England owes money to the US and the US owes money to China, there’s no way to really “cancel out” the debt and just say that England owes China, because it’s the government of England who owes money to citizens in the US, and it’s the government of the US who owes money to the citizens of China, and so forth. Sometimes governments owe other governments money, but it’s often simpler to just keep track of the debts rather than try to cancel them out.


Not sure what level of answer you're expecting, but here's an intuition. In equilibrium, countries should have balanced trade. That is, imports equals to exports.

If a country consistently exports more than it imports, the demand for its currency should make the currency appreciate (relative to other currencies). The country's currency would appreciate until its exports are not as competitive, driving down the trade balance and current account.

Likewise, if a country's CA is negative, then the low demand for that country's currency would make the currency depreciate, and it would be able to export more.

By looking at the country's current account, you could "estimate" if the currency is overvalued (should depreciate in the future... if CA is negative) or undervalued (should appreciate in the future... if CA is positive).

This is just the gist of the argument. More considerations need to be put in each country's characteristics such as demography, development status, etc. The IMF (with much criticisms from some of its member countries) issues what's called the External Balance Assessment (EBA) which serves as a "benchmark" of whether it thinks a given currency is over/undervalued. To be sure, some argue that this is somewhat political as the USTR sometimes point to this as a basis for putting some countries on the "watchlist" for being a currency manipulator. Be sure to read the list of caveats and disclaimers of the EBA though.


Νominal money could be seen as a "conserved quantity" in a similar/analogous sense that we have in physics, under some qualifications and restrictions.

I stress that we are talking about the nominal value of money, which is an indisputable quantity and legal tender (the concept of "real" value is an estimated value and hence subject to disagreements etc.)

Then if we exclude
1) The central bank/government with the authority of the law
2) The commercial banking system as regards Transactions that have to do with taking or repaying loans
3) Actions that just destroy the physical carrier (say, burn the paper bill)

...then transactions do not alter the amount of nominal money, and in that sense, the nominal value/amount of money is conserved.

We exclude 1) because the central bank / government have the power by law to create new money (and destroy existing money, for example "cutting zeros" after a hyperinflation episode).

We exclude 2) because commercial banks create money under the "fractional reserve banking" system, while money is destroyed whenever a loan is repaid (the part that has to do with the principal, not the interest). The OP should ask a different question if the OP wants to know about that.

We exclude 3) because we can argue that these are not "normal economic transactions".

So the system in which nominal money can be considered a "conserved quantity" is a subset of a real world economic system.


Is it true that the U.S has to run a chronic trade deficit with the rest of the world as a price to pay for being the world's reserve currency?

This is an excellent question and I will do my best to give you a well thought out answer.

Many observers believe the U.S. dollar (USD) will lose its status as the world's reserve currency. In fact, I got pushback from another forum regarding finance about this. These doomsday dollar folks cite agreements between China and Iran on settling trade in their own currencies rather than US dollars as evidence that the end of the dollar as a reserve currency is near.

You can actually find documentation from the IMF on what are some of the worlds currency that are being held in reserve by the planets nations: Currency Composition of Official Foreign Exchange Reservers (COFER)

Back in 2013 the U.S. trade deficit shrank to $34 billion and it was presented as good news. But if we don't run a trade deficit, that would lead to problems for us, in particular, on U.S. corporate profits. The financial media does not talk about this because it does not understand the connection between our trade deficit and our currency being the world's reserve currency which creates a dynamic that was coined in thee 60s, known as Triffins' Paradox, based on the observations of Belgian-American economist, Robert Triffin.

It was Robert Triffin who pointed out that the country whose currency foreign nations wish to hold (the global reserve currency) must be willing to supply the world with an extra supply of its currency to fulfill world demand for this 'reserve' currency (foreign exchange reserves) and thus cause a trade deficit.

So there always has to be a fundamental imbalance in the balance of payments. Depending on the goal at any given period, it may require an overall flow of dollars out of the United States, while at other periods of time, it may require an overall flow of dollars in to the United States, but net currency inflows and outflows cannot both happen at once.

How sound is this? You will have to look at it for yourself as we have been doing this for almost a quarter of a century now. So we have all been living it since the day we were born. A better question would be, how sound is it for the U.S. to maintain its dollar as the world reserve currency and run a trade surplus. That's a new one, that's one we haven't tried.

This leads us to your last question.

Just like we invoked Triffin's Paradox to explain our current situation, for this new one we can invoke Hobson's Choice.

If you run trade surpluses, you cannot supply the global economy with the currency flows it needs for trade, reserves, payment of debt denominated in the reserve currency and credit expansion, so yes it would lead to the end of the USD as a global reserve currency.

If we no longer possess a global reserve currency, we can't print money and have it accepted as payment. (The euro and yen are quasi-reserve currencies based on the size of the European Union and Japanese economies, but neither acts as the primary reserve and as a result both are vulnerable to currency crises, despite the conventional wisdom that both are on the same footing as the U.S. dollar.)

So trade surpluses on our part are impossible as we hold the global reserve currency.


There are two reasons I can think of for this effect.

The more economic reason is that commodity prices are usually pro-cyclical. In economic booms those commodity producing countries and their currencies do quite well (their currency goes up and hence USD goes down). And vice versa, in uncertain economic times, there is not as much demand for commodities, and hence less demand for currencies of commodity producing countries (USD goes up and price of commodity declines).
Another reason is more due to unit of account. Many of these commodities are traded in dollars even though the end users are global. If USD went up 1% against all currencies, however the main suppliers and end users of a commodity (say copper) are mostly in Chile and China respectively, then conceivably the cost of copper denominated in Chilean Peso might not have changed at all. This could happen because the Chilean supplier would be willing to sell their copper at 1% lower in USD terms and still get the same profit in Chilean Pesos terms. Therefore, in certain cases it is just a matter of perspective.


Derivation of the elasticity of substitution of a general production function with labor-augmenting technological progress

You have that in  equilibrium each factor is paid its marginal product, so
$$\tag1\frac{w_i}{p_i}=B_if'(l_i)$$ and $$\tag2\frac{r_i}{p_i}=f(l_i)-K_if'(l_i)\frac{B_iL_i}{K_i^2}=f(l_i)-l_if'(l_i)$$ so deviding (2) by (1) we have:

$$\tag3\frac{r_i}{w_i}=\frac{f(l_i)-l_if'(l_i)}{B_if'(l_i)}.$$

Take the derivative of $r_i/w_i$ with respect to $l_i$:
$$\tag4\frac{d(r_i/w_i)}{d(l_i)}=\frac{(f'(l_i)-(f'(l_i)+l_if''(l_i)))B_if'(l_i)-B_if''(l_i)(f(l_i)-l_if'(l_i))}{(B_if'(l_i))^2}=-\frac{f''(l_i)f(l_i)}{B_i(f'(l_i))^2}$$

Note that $l_i=\frac{B_i}{(K_i/L_i)}$ so
$$\tag5\frac{d(l_i)}{d(K_i/L_i)}=-\frac{B_i}{(K_i/L_i)^2}=\frac{l_i}{(K_i/L_i)}.$$ Using the chain rule ans substituting (4) and (5) we have:
$$\frac{d(r_i/w_i)}{d(K_i/L_i)}=\frac{d(r_i/w_i)}{d(l_i)}\frac{d(l_i)}{d(K_i/L_i)}=\frac{l_if''(l_i)f(l_i)}{(K_i/L_i)B_i(f'(l_i))^2}$$ and by the inverse function theorem we get:
$$\tag 6\frac{d(K_i/L_i)}{d(r_i/w_i)}=\frac{(K_i/L_i)B_i(f'(l_i))^2}{l_if''(l_i)f(l_i)}$$

Finally by multiplying (3) and (6) and dividing  by  $(K_i/L_i)$ we conclude that

$$\sigma_i=\frac{d(K_i/L_i)}{d(r_i/w_i)}\frac{r_i/w_i}{K_i/L_i}=\frac{(K_i/L_i)B_i(f'(l_i))^2}{l_if''(l_i)f(l_i)}\cdot\frac{f(l_i)-l_if'(l_i)}{(K_i/L_i)B_if'(l_i)}=\frac{f'(l_i)(f(l_i)-l_if'(l_i))}{l_if''(l_i)f(l_i)}=\frac{f(l_i)}{l_if''(l_i)}\left[1-\frac{l_if'(l_i)}{f(l_i)}\right]$$

as desired. $Q.E.D.$


But it is, there is just a simple oversight in your calculations:
We can indeed write identically

$$\eta_{\lambda, J} = \frac{\partial \lambda}{\partial \theta}\frac{\partial \theta}{\partial J} \cdot \frac{J}{\lambda} \\
\implies \eta_{\lambda, J}= \left\{\frac{\partial \lambda}{\partial \theta} \frac{\theta}{\lambda}\right\}\left\{\frac{\partial \theta}{\partial J} \cdot \frac{J}{\lambda}\right\} \frac{\lambda}{\theta} $$

But the term in the second curly brackets is not equal to $\eta_{\theta, J}$.
We have to re-arrange to get

$$\eta_{\lambda, J}= \left\{\frac{\partial \lambda}{\partial \theta} \frac{\theta}{\lambda}\right\}\cdot \left\{\frac{\partial \theta}{\partial J} \cdot \frac{J}{\theta}\right\} \frac{\lambda}{\lambda} $$

The fraction in the end now cancels and so
$$\eta_{\lambda, J}= \eta_{\lambda, \theta} \cdot\eta_{\theta, J} $$


The ADEFA website does have information on sales, disaggregated by company, market (internal/export), and for very year since 1959. For example:

This data is here. Disaggregation by company and market is here.

ADEFA does not provide data on profits thought. As you can see from the latter link, all companies are multinationals with subsidiaries in Argentina (e.g. Toyota Argentina S.A. where "S.A." stands for Sociedad Anónima, meaning PLC). As such, they provide annual statements to the local tax authorities, including profits. They should also publish annual reports to their investors (e.g. Toyota 2014 here; see profits in page 8). And official government organisations also make these statement public (e.g. here). In other words, all the data must be available online. You just need to google something like "name of company memoria anual 20XX", where memoria anual stands for annual financial report, for year 20XX.

Whether the data is systematically available free of charge, I doubt it. Normally consultancy companies, investment banks and other financial firms produce compilations and analysis of this data for their clients (know this from first hand, when worked at Deutsche Bank). Unless you have access to one of those, you will have to compile the data yourself. At least there are just a few car companies, so this should not take you long.

PS: beware of over/under reported utilities due to transfer pricing though.


For the case of two goods, give an example of preferences that are represnted by a continuous utility function that allows for fat indifference curves

$$u(x, y) = 2$$
is a simple example of a continuous utility function with thick indifference curve.

\begin{eqnarray*} u(x, y)= \begin{cases} x & x < 1 \\ 1  & 1 \leq x < 2 \\ x - 1 & x \geq 2 \end{cases} \end{eqnarray*}

is another continuous utility function with thick indifference curve for $u=1$.


Soft Question: Economic measurement in a post-industrial economy

Your friend is right that GDP and similar measures are flawed—or, at least, incomplete. But this isn't exactly news to economists!

For example, Richard Easterlin was arguing in the 1970s that GDP is a poor measure of national well-being. The specific issues with GDP that you point out in your question (failure to account for the value of innovations or for free products, etc.) are so well-known that they now make it into tutorials aimed at high school students. For a more recent take on the issue, here is a discussion paper on the topic of technology and GDP measurement (the author also has a book on the topic of GDP as a measure).

To be a little bit more concrete about how economists know the measure is flawed, let's look at how economic theory helps us to set objectives and guides us in measuring our performance in a simple example.

Economics as a body of knowledge suggests variables of interest to a policymaker. Suppose, for the sake of illustration, we are concerned only with maximising peoples' material well-being. We know that we can get a measure of material welfare by computing the area bounded by the general equilibrium demand curve and supply function. So, in an ideal world, we would just measure this total surplus and pursue policies that increase it. For a variety of reasons, this quantity is difficult to measure—especially at the aggregate level over time.

The 'next best' alternative is to use the economic model to tell us what variables influence this surplus, and then try to measure those variables instead. Obvious examples of such variables are income (which expands demand possibilities) and technology (which expands production possibilities). Broadly speaking, if income is going up and technology is improving then the surplus (which is what we are actually interested in) should also be increasing.

It is important to keep an eye on both variables because the theory tells us that surplus can rise as income falls if, for example, technology is improving fast enough (just think about the extreme case where technology is so good that we can produce everything costlessly; then price and income would be zero, but surplus from consumption would nevertheless be very high).

With this framework in mind, it is very natural to look at GDP and say: "This is a measure of income, which is a part of the picture. But it is missing another component (technology) that we know, from theory, is also important."

If measures like GDP are known to be so flawed, why are they used? It is important to understand that no serious economist cares about GDP per se. Instead, economists stress the importance of a portfolio of policies that work together to improve overall well-being of the populace. There are many factors that weigh on well-being. These include income and productivity (which will show up in GDP), but also technological innovation, environmental improvement, improved health outcomes, reduced inequality, and so on.

Given these objectives, some way is needed to measure the efficacy of policy. Because the agenda is multi-faceted, we need enough indicators to measure the various dimensions we are interested in. GDP is useful because it is a widely-available measure of one part of what economists are interested in (material wellbeing). But this should not be confused with a situation where GDP is the objective in its own right. Nor should it be thought that economists have no interest in improving upon this measure.

The monomaniacal fixation with GDP is really a trait of the media and politics rather than practicing economists.


Won’t paying wages to temporarily unemployed due to Coronavirus result in inflation?

Not by itself. The inflation generally depends on the following monetary relation:

$$ MV =PY$$

Where M is money supply, V velocity of money (how much one buck is used in economy), P is the price level (change in which is inflation), and Y is a real output.

Now solving for P so we can focus on inflation gives us:

$$P=\frac{MV}{Y}$$

Hence price level (and consequently) increases when money supply increases, velocity of money increases or output decreases.

Now let’s analyze giving money to those unemployed.

Is it newly created money? If not then money supply won’t increase. If yes then it would increase inflation rate.
Redistribution generally does not affect velocity of money much so we can skip that.
Does this change the output Y? Well not by much those people are already unemployed. If anything it could increase Y as unemployed have probably high marginal propensity to consume so in short run redistribution from a richer person with lower marginal propensity to consume will increase Y. Especially if this spending was not paid out of higher taxes but from debt.

So a priori as long as it’s not financed through printing new money it should not really have effect on inflation. Inflation is ultimately a monetary phenomenon.

Also, yes it’s a redistribution mechanism like most of the things that UK government does. Any policy that uses government funds as a transfer to others, or fund non-public good services (like NHS for example) is a redistributive measure.


Is a universal basic income possible in the United States?

This is a good question. To be concrete, I think it's easier to pick a single number - this is arbitrary, but I'll go with the figure of $10,000 offered in the proposal by Charles Murray (one of the most prominent conservative supporters of a universal basic income). I'll assume that this is offered to every adult in the US age 18 and over, expanding slightly on Murray's 21 and over proposal.

This would be about 85% of the average poverty level for a single individual, just above 50% of the poverty level for a single parent with two children, and (at $20,000) about 85% of the poverty level for a family of four with two parents and two children.

The direct budgetary cost of this program, of course, is easy to calculate: it is the number of Americans age 18 and over, times \$10,000. There are about 245 million American adults currently, making this cost \$2.45 trillion. This compares to total federal government expenditures that are currently about \$4 trillion. (See this NIPA table for some figures.) Remarkably, the sum of "government social benefits" and "grants-in-aid to state and local governments" (the latter of which is almost entirely grants for social programs like Medicaid) is currently about \$2.4 trillion. Hence, to a first approximation, we could say that the federal government could afford the $10,000 UBI given its current budget if it eliminated all other existing transfers.

How plausible is this? Not very. More than 75% of the federal government's transfer spending is on three programs: Social Security, Medicare, and Medicaid. This spending is overwhelmingly concentrated on the elderly, with some also on the disabled (SSDI and Medicaid) and children (Medicaid). Taking away these programs and replacing them with the basic income, which is distributed evenly throughout the adult population, would surely leave these groups receiving far less in total than they currently do. This would be politically near-impossible to push through, and any sudden change would be dubious on policy and moral grounds too. (Even if one doesn't like the distribution of transfer spending embedded in these programs, millions of people have planned their lives around it.)

This is just one case of a basic point - which is that unless one plans to achieve massive savings through improved administrative efficiency or improved work incentives, any reallocation of the existing transfer pie will involve offsetting winners and losers. Since existing transfer recipients (aged, disabled, poor children, etc.) are targeted for a reason, such a shift may be quite painful. Moreover, any improvements in administrative efficiency are unlikely to be large enough to save much money; the more likely source of savings would be improved incentives, particularly relative to the dysfunctional disability system and perhaps current overspending on health care. But I haven't seen a case made that these would be anywhere near large enough to make a UBI work within the current budget without large losses to some existing party.

On a more positive note, I should mention that the headline cost of the UBI may not be quite as bad as it looks. Since the current tax-and-transfer system embeds very large implicit marginal taxes on some beneficiaries, it would be possible to replace these with higher explicit marginal taxes to claw some of grant back, without incurring additional distortions at the margin. That said, these high marginal taxes are heavily concentrated in certain segments of the population (e.g. single parents with children). The US tax-and-transfer system currently makes heavy use of tagging, which saves money at the expense of potentially perverse social incentives (conservatives have complained about incentives for low-income parents to avoid marriage for years). Doing away with tagging could limit these particular bad incentives and concentrated high marginal rates, but necessitate moderately higher marginal rates throughout the population.

Finally, if it is not realistic to eliminate existing transfers, we can think about how difficult it would be to establish a UBI through increased taxation. If (given the substantial existing transfers to the elderly) we limited the \$10,000 to adults below age 65, we are down to a population of about 200 million and cost of \$2 trillion. Since personal consumption expenditures are currently about \$12 trillion, (unrealistically) assuming a constant tax base these \$2 trillion could be raised through a 24% VAT with 70% coverage. This would be quite high, but not totally out of line with international norms. Furthermore, since current GDP is about \$17.5 trillion, and additional \$2 trillion in transfer spending (again unrealistically assuming constant GDP) would increase the US's overall tax intake as a share of GDP by 11.5 percentage points. This would make the US similar to the typical European country, still below states like Denmark, Sweden, and France with the highest taxation.


Do real life economists and financial analysts actually use calculus in their jobs?

Yes, whether you do research and you need to study a new model and characterize optimal behavior, or if you are studying data and you are estimating any model that is not linear you use calculus on a regular basis.

Even though computers are very powerful and can save the time and energy of doing calculations (including finding derivatives), often times having a firm knowledge of the maths behind what the computer is doing can save tons of time and improve the performance of algorithms.

That being said, it is also true that many economists can get by only knowing the minimum of calculus, since a lot of the tools that the market values the most from economists require, instead,  a firm grasp of probability, statistics and good economic intuition.


Can vaccine distribution and appointment setting up be considered game theory?

Having spent time with a few eager students of game theory myself, I sense that the "real" question you might have wanted to ask was:

What is the best way to motivate people to get inoculated, given that they have varying attitudes towards the vaccine or vaccination in general.*

To answer that question from a normative perspective, i.e. assuming everyone is rational in the economic sense, we actually need the theory not of games but of mechanism design. Game theory's primary concern is to predict the outcome(s) of some given strategic interaction, regardless of whether those outcomes are desirable (e.g. mutual defection is the predicted, albeit inefficient, outcome in Prisoner's Dilemma). On the contrary, the goal of mechanism design is to implement some desirable outcome via a strategic interaction; that is, to come up with a suitable game whose equilibrium is the outcome desired by the mechanism designer. See Dixit et al. (5th ed, ch. 14-15) for an easy introduction, or Tadelis (2013, ch.14) for a more rigorous treatment at an advanced undergraduate level.
Of particular relevance here is a special case of mechanism design called information design, where the designer (e.g. a government or public health authority) uses a suitable information revelation strategy (e.g. when and what data to publish) to persuade the public to get inoculated, given that they hold a variety of initial beliefs about the efficacy of the vaccine and will rationally update their beliefs based on information released by the designer. Information design is still at the forefront of economic research, so the linked JEL paper, which I consider above the undergraduate level, is probably as introductory a summary on this topic as you can get for now.
There is also a positive approach to address the above question. By positive I mean the  approach is founded on the acknowledgement that people are not perfectly rational and are predisposed to act in a certain way when appropriately primed. A prominent example is the nudge theory, which draws on insights from psychology and economic experiments to frame choice problems in such a way that people are more likely to pick the option favored by the so-called "choice architect" (the behavioral economic counterpart of a mechanism designer).
Lastly, although there is behavioral game theory as such, I feel that it's not as relevant to your question because much of the literature is devoted to explaining the gaps between actual play and predicted play of some canonical games.

*I'm not quite sure what you mean by "appointment setting" beyond its logistic aspect, so I will ignore it.