What I believe you mean is that a production function has Constant Returns to Scale.

i.e. $$f(\lambda K, \lambda L)= \lambda f(K, L) $$

Where $\lambda \ge 0$

Thus in your case where $K=3$ and $L=6$

$$f(3,6)=3 \times f(1,2)$$

and since ${f_{max}(1,2)=4}$  (i.e. $f(1,2) \le4$) the maximum product a firm can produce using $K=3$ and $L=6$ would be

$$3 \times f(1,2)= 3 \times 4 =12$$

Hope this helps!


Is debt servicing in the structural or cyclical budget balance?

The IMF methodology to determine the structural balance is given here: link to article.

I would summarise the methodology as: the sensitivity of budget components to the deviation of actual output from potential is estimated, as well as that deviation (the output gap). Taken together, that gives an estimate of the effect of the cycle on the budget balance.

It is unclear what estimates for their sensitivity of interest payments is, but since bond payments are contractually fixed, they are invariant to the state of the cycle. Only newly-issued debt costs are affected by current interest rates.

The only way that interest payments would be considered non-structural is that a steady-state interest rate is calculated, and this deviation from actual is used to determine the effect of the cycle. Based on the IMF document, this was not done in their methodology (on page 7, the author states that the only expenditure adjusted was  unemployment benefits). Realistically speaking, such an adjustment would be complex (how much are 10-year bond yields affected by current conditions?), and the effect is small in most countries (since the bulk of outstanding debt has long duration in most countries).


Understanding the gradient of the social cost curve in a market failure/ negative externalities diagram

It simply depends on the shape of the marginal external damages. If the total damages are linear in output, then the marginal damages are constant, and the gradient of the marginal social cost is the same as that of the marginal private cost.

If the total damages are quadratic (or some other form with increasing marginal damages), the marginal social cost has a steeper slope than the marginal private cost.

In a simple example: if the marginal private costs are $MPC(Q)=70+2Q$, where $Q$ is quantity produced and total damages are $D(Q)=50Q$, then marginal external damages are $MED=50$ and the marginal social costs of production would be:

$MSC=MPC+MED=70+2Q+50=120+2Q$

If in contrast the damage function would be $D(Q)=50Q+2Q^2$, then marginal external damages would be $MED=50+4Q$ and the marginal social costs of production:

$MSC=MPC+MED=120+6Q$

As you can see the latter has a steeper slope than the original MPC, whereas the former does not.


Considering that modern economies rarely experience recessions due to supply shocks (such as spiking oil prices), we should look at this from the perspective of a demand shock, a decrease in spending. This should not have too significant of an impact on the supply of exports. The supply for these depends on foreign demand, theoretically unaffected by the recession in this country thus far. Some firms may produce both for export and for domestic demand, and some of these might need to shut down if prices drop below a certain level, but this should not occur on a large scale. The fall in domestic demand may even be largely compensated for by foreign demand, with a slight fall in price. The "high wages" would be no different from before the recession, and they would eventually fall as the economy comes back to potential output.

In contrast, net imports will definitely fall if aggregate demand does. Considering that spending on these is tied to, well, the same factors influencing aggregate demand, anything which might have induced a contraction of spending on domestic goods would similarly decrease demand for imports.

Given an at worst moderately impacted supply of exports and a massively impacted demand for imports, the net export of the recessionary country would certainly fall (though this may be more ambiguous if there is expansionary monetary policy to counteract the recession, but this might work in the same direction). The major trade partner would, of course, see its net export move in the opposite direction, importing at similar levels and exporting less. The key thing here is that the target country's demand for imports would not be modified.


The book is right. The proper way to go about this is of course to work out the theory and the math before plugging in any specific numbers. Fixing the quantity produced, we have
$$ \bar Q = L^bK^a \implies K = (\bar Q)^{1/a}L^{-b/a}$$

Then, since capital is on the vertical axis

$$\frac {dK}{dL} = -\frac{b}{a}(\bar Q)^{1/a}L^{(-b/a)-1} $$

Note that we do not differentiate $\bar Q$ since we want it to be fixed, for different combinations of inputs.

Inserting the production function expression

$$\frac {dK}{dL}= -\frac{b}{a}[L^bK^a]^{1/a}L^{(-b/a)-1}$$

$$\implies \frac {dK}{dL}= -\frac{b}{a}\frac{K}{L}$$

Then, plug in the specific numbers: $b=1/3, a=3/4, K = 40, L = 20$ so

$$\frac {dK}{dL} = -\frac{1/3}{3/4}\frac{40}{20} = -\frac{4}{9}\cdot 2 = -\frac{8}{9}$$


How exactly can blockchain technology be used to make a supply chain more efficient?

I am an economist and I am skeptical that the value will be large, remember that the planet has a 65 trillion dollar economy and so while a billion dollars is a lot of money to me, it isn't a lot of money in the big scheme of things.

On the surface, blockchain appears to improve accountability and reduce fraud.  I said on the surface because very few large scale blockchain frauds have happened yet.  Also, the most inefficient components of the world economy usually depend upon graft and those systems are resistant to implementing processes that improve accountability.

I do think that adding blockchain will improve system integrity, but I am wondering how the mafia will get to the outside nodes to degrade the information quality before it enters the process.  Consider a WalMart buys a set of goods numbered X0001 through X0050 and they are physically delivered.  Imagine that the shipping container is surreptitiously intercepted and a general manifest marking X0001 through X0050 as received goes through the process rather than the time consuming manual process of scanning each good.  The blockchain is defeated.

Now let us imagine that the packaging for each good is given a RFID with a unique encryption.  This is costly.  The mafia hires hackers to break into the system from the source and determine the encryption system itself.

Learning from this, they hire amazing network security, so the mafia hires a janitor to bug the place and steal documents.

Blockchain is nothing more than a distributed information recording system.  It is resistant to system destruction, facilitates verification and validation, and improves accountability but we have seen very few large scale failures.  Consider this, the Internet is resistant to system destruction, facilitates verification and validation of actors and nearly guarantees signal propagation as long as enough underlying communication systems survive.

The Internet's value has been heavily located in porn and cat videos.  Fraud is rampant and it is an open system, largely.  So is blockchain.  Open systems, like public highways, still depend upon policing and monitoring.

Although blockchain is proposing to replace centralized systems, as the Internet did for the postal service and BBS, it isn't clear that it will be of GREAT value for strong centralized systems.  Instead, the gains will probably be in poor centralized systems such as the international wire system.  It is aged, outmoded and outdated and hasn't seen real improvements in my lifetime.  It hasn't changed greatly since its 19th-century antecedents.  The same is true for the ACH system because Congress refuses to allocate the money.  On the other hand, the Swedish or British systems are great.

My guess is that its greatest value will be in exposing graft.  For example, if you could continuously track a container in a port in Ghana, then you could track what workers actually did what work and you would be able to expose clearly the pattern of bribes which speed up or slow down the harbor.  That is, you could if the customs and dock workers use the tools as intended.

Blockchain just decentralizes signal.  It is a human system and it will be implemented as part of greater human systems.  I think roving bandits like hackers and stationary bandits like customs workers haven't had a real chance to attack it yet.

If I were working in blockchain, I would be working on the inputs to the system and not the system itself.  The money is still in preventing GIGO.


Who exploits comparative advantage in international trade?

It's fine to make a supposition that it costs Colombia twice as much to make cars as coffee, and Japan twice as much to make coffee as cars.  It's also fine to express these ratios in terms of the respective local currencies.

The apparent problem you describe only arises because you go beyond the above and express the costs in terms of a common currency (\$).  But in a situation of autarky, there is no way in which the exchange rates needed to convert prices in other currencies to \$ could be determined. Thus your supposition is incoherent.

The way in which comparative advantage would be exploited, given the ratios you describe and given free trade, is that the rate of exchange of Colombian to Japanese currency would adjust to a level at which, in both countries, Colombian coffee is cheaper than Japanese, and Japanese cars are cheaper than Colombian. The Colombian car business will then be able to benefit from comparative advantage while not needing to look beyond the relative prices of locally produced and imported cars.

Addendum:  If, in the past, two countries both used gold as a currency, this would not, given autarky, be equivalent to a common currency. Even if the gold were physically the same, it might just happen (eg for geological reasons) to be scarcer and therefore more valuable in one country than the other.  In the absence of international trade and of payment in gold for traded goods, there would be no mechanism to equalize the value of gold in the two countries.  It would therefore be feasible that the cost, in terms of their respective gold currencies, of producing every good would be higher in one country than the other.  Given free trade, however, the value of gold in the two countries would be equalized at a level at which some goods would be cheaper in one country and some in the other.  The mechanism for equalization would be that people and businesses in the more expensive (and therefore more gold-abundant) country,  taking their own rational decisions and without any need for central control, would import goods from the cheaper country, paying in gold and therefore causing an outflow of gold to the cheaper country.


Stata code for linear regression that controls for state effects

Here's a guess about what has gone wrong, since what you wrote down will get you a different error message.

I would bet dollars to donuts that you left out the the reg (short for regress) from:

xi: reg sust_all form_type_dum EDUCPAY HAZARDPAY SHIFTPAY SKILLPAY MILPAY COLLBARG RESPAY CHIEFMAX  OPBUDGET OPBUDGEST POPULATION i.STATE, robust

Also, unless your version of Stata is ancient, you don't need xi:, so just type:

reg sust_all form_type_dum EDUCPAY HAZARDPAY SHIFTPAY SKILLPAY MILPAY COLLBARG RESPAY CHIEFMAX  OPBUDGET OPBUDGEST POPULATION i.STATE, robust

Stata will handle the state FEs for you.


Labor theory of value examples and exercises

Check these slides, which includes a fairly introductory analysis to the LTV, including some trivial examples and calculations.

Another introduction can be found here (part one) and here (part two).

Yet, this is the best I am aware of. It is an attempt to explain the theory to "undergraduates" using a simple example. Worth reading!


References where fewer rules resulted in better governance

I think in the literature of uncertainty I once read that increasing the number of laws increases the potential source of uncertainty. However, it was probably more related to investment than to working performance. However, if you are interested "Measuring economic policy uncertainty" by Baker, Bloom and David (2013) might be a good start.


Do assets without rental income streams appreciate relative to assets with rental income streams?

I believe he assumes that there is no arbitrage and also that there are no pricing bubbles. So two assets that have the same price today would have the same net present value.

Let $P_t$ denote the price of an asset in year $t$, $d_t$ the dividend (or rental income or cashflow) you get from said asset in year $t$ and let $r$ denote the interest rate (which I assume to be constant for simplicity's sake). Then the price of the asset today is
$$
P_1 = \frac{d_1}{1+r} + \frac{P_2}{1+r}.
$$
Using iteration
$$
P_1 = \sum_{t=1}^{n - 1} \frac{d_t}{(1+r)^t} + \frac{P_n}{(1+r)^{n-1}}.
$$
If you compare two assets with
$$
P_1^A = P_1^B
$$
where
$$
\forall t: \ d_t^A > 0, \ d_t^B = 0,
$$
then or all $t>1$ you will get:
$$
P_t^B > P_t^A.
$$
This is somewhat paradoxical, as a there is no clear reason why $P_t^B$ should be positive if it never pays dividends. You could assume that it has not yet payed any dividends but will start doing so soon.

However I think Landsburg's main argument is that $d_t>0$ holds for the house
as well, not just the stock.


What determines the rate of interest on national debt for a country?

The first thing to recognise is that an interest rate is a price because the interest rate tells you how much the borrower has to pay in return for receiving a loan.

The borrower would obviously like to pay as little as possible for the money s/he wants to borrow. But how little s/he can get away with paying depends upon how willing people are to lend their money. Here are some examples of how willingness to lend affects interest rates.

If the borrower already borrowed a lot of money and looks to be in danger of defaulting (i.e. not being able to pay everyone back) then lenders will be less willing to give him/her their money for fear for losing it. The borrower will therefore have to agree to pay a higher interest rate in order to induce people to be willing to lend.
If times are hard (i.e. in a recession) and money is short then it again becomes more likely that the borrower will be unable to repay their loan. Again, the borrower must be prepared to pay a higher interest rate to compensate lenders for this risk, otherwise they will refuse to lend.
People have lots of choices about where to put their money: government bonds (from many different governments), the stock market, savings accounts, pensions, real estate investment, corporate bonds, commodities, etc. The better is the return they get on alternative assets, the less willing a lender will be to give you their money. You then have to be prepared to pay more to induce lenders to give up all those lucrative alternatives. So borrowers will pay higher interest rates when returns in general are higher.
Not only the returns on other assets, but also their volatility matters. In times of uncertainty, assets like stocks or commodities are likely to be more volatile so that the return investors get on them becomes more risky. Since lending to certain actors (e.g. the government) is relatively safe by comparison, people will be more willing to lend money to these actors during uncertain times. Thus, the interest rate will tend to be lower during times of volatility and higher when alternative assets are experiencing relatively smooth growth.
If inflation is high then money loses its value quickly. I am going to be reluctant to give someone my money for five years if, by the time I get it back, it is worthless—I'd rather spend the money now while it's still worth something. Thus, to induce people to lend, the borrower will have to pay higher interest when inflation is higher.

Note that this reasoning applies to borrowing more generally (i.e. also by consumers or firms) as well as to government borrowing.


What does the following mean: "supply has positive elasticity”?

Price elasticity of supply is: $\frac{dQ_s}{dp}\frac{p}{Q_s}$. Because supply slopes upward $\frac{dQ_s}{dp}>0$. $Q_s$ and $p$ are also positive so    $\frac{dQ_s}{dp}\frac{p}{Q_s}>0$.


How does US (its economy, banks, industry) profit from dollar being the "standard currency"?

Some major benefits include:

Seigniorage on currency acts as a source of government revenue, allowing for lower taxes and higher spending. One paper (Neumann (1992)) puts this at about \$15 billion a year.
Lower borrowing costs on public and private debts due to greater demand for financial assets denominated in the currency, particularly credit risk-free assets. A McKinsey report (An exorbitant privilege? Implications of reserve currencies for competitiveness (2009)) estimates that this lowered the "...US borrowing rate by 50 to 60 basis points in recent years, generating a financial benefit of $90 billion".
Because households consume many non-tradable goods and services and earn income denominated in local currency, households naturally have hedges on the fluctuation of local currency. Increasing the scope of dollar denominated goods and assets increases the strength of this hedge, reducing currency risk in consumption, trade and finance. For example, Euro-ization is thought to have increased GDP on in the Eurozone by 0.4 percent per year (about 40 billion Euros) from the reduction of transaction and hedging costs (Emerson, Gros, Italianer, Pisani-Ferry, and Reichenbach(1992)).
More liquid capital markets, because there are many more buyers and sellers of dollar denominated assets.
Deeper capital markets, because liquid and cheap capital encourages the raising of capital

You many also be interested in the book Exorbitant Privilege (Eichengreen (2012)) which includes an extensive discussion of this topic.


Why is it that poverty incidence is high in the agricultural sector?

Well I think that agriculture poverty is there because farmer can't store its product and sell that when prices are good as his product is perishable. With this he has to remain busy throughout the year either harvesting or in production and has no control over markets.


Continuation value versus utility in asset pricing

The term "continuation value" is usually used to refer to an aggregation of utility in future periods. In the case of $U_t = u(C_t) + \beta E_t[u(C_{t+1})]$,
$u_t$ is the flow of utility per period and $U_t$ is an aggregate of $u_t$ over all time periods $t$ and $t+1$. The quantity $\beta E_t[u(C_{t+1})]$ is the expected discounted continuation value and is in the same units as $u(C_t)$.
Recursive utility works similarly. The difference is that utility over multiple time periods can't be easily aggregated. In the expected utility case, it's aggregated using a weighted sum of expectations. To see this, I'll show how you can write an expected utility function in recursive form. This should make the continuation value used in discussions of recursive utility easier to understand.
Again, let $u_t$ be the flow of utility per period. Suppose that
$U_t$ is an aggregate of $u_t$ over all time periods from time $t$ into the future.
Sometimes $u_t$ is referred to as the "per-period utility function". An economic actor making decisions in time $t$ maximizes $U_t$, where $u_\tau$ for $\tau = t, t+1, t+2,...$ are simply the components that make up $U_t$.
Consider the case of CRRA utility:
$$
U_0 \equiv E_0 \sum_{t=0}^\infty \beta^t \frac{C_t^{1-\gamma}}{1-\gamma}.
$$
Let $u_t = \frac{C_t^{1-\gamma}}{1-\gamma}$ and let
$$
U_t = E_t \sum_{\tau=t}^\infty \beta^{\tau-t} \frac{C_\tau^{1-\gamma}}{1-\gamma}.
$$
Then,
$$
U_t =
E_t \sum_{\tau=t}^\infty \beta^{\tau-t} u_\tau
$$
and we can represent utility here recursively,
$$
U_t = u_t + \beta U_{t+1}.
$$
In the expected utility case of CRRA, $U_t$ is simply a weighted sum of future per-period utility. Epstein-Zin utility is a case in which $U_t$ is an aggregate of future per-period utility, but it cannot be expressed as a simple weighted sum.
Rather, $U_t=((1-\beta)C_t^{1-\rho}+\beta (\mathcal{R}_t(U_{t+1}))^{1-\rho})^{1/(1-\rho)}$,
where $\mathcal R$ is a "certainty equivalent" operator.


Group contamination in Regression Discontinuity

Are you looking for general references on Diff-in-Diff (DiD) and Regression Discontinuity (RD)?

If yes, a good starting reference at the undergraduate level is probably

J.  Angrist  and  J.S.  Pischke, Mastering' Metrics: The Path from Cause to  Effect, Princeton University Press, 2014. Look at chapters 4 and 5 for RD and DiD.

If who want to dig deeper:

J. Angrist and J.S. Pischke, Mostly Harmless Econometrics, Princeton University Press, 2009, chapters 5 and 6.

For recent references on RD

C. Carpenter and C. Dobkin, “The Effect of Alcohol Consumption on Mortality: Regression Discontinuity Evidence from the MLDA, American Economic Journal: Applied Economics 1 (2009), 164-182.
A. Abdulkadiroglu, et al., “The Elite Illusion: Achievement Effects at Boston and New York Exam Schools,” Econometrica, 2014.

On Did:

D. Card and A. Krueger, “Minimum Wages and Employment: A Case Study of the Fast Food Industry in New Jersey and Pennsylvania,” American Economic Review 90 (1994), 1397- 420.
D. Card, “Using Regional Variation to Measure the Effect of the Federal Wage,” Industrial and Labor Relations Review (1992) 46, 22-37.
C. Carpenter and C. Dobkin, “The Minimum Legal Drinking Age and Public Health,” The Journal of Economic Perspectives 25 (2011), 133-156.

Considering your example, I guess that it could be a contribution to show that a small increase in benefit per capita may increase fertility. Is the benefit permanent? If not, I doubt that people will have a strong incentive to get another child. Moreover, it takes time to get a new child! So, there is a time dimension issue. They cannot claim the benefit if they don't have the child! If your design allow for this, you can exploit the time dimension in case some families respond to the incentive.


First of all, this is not a Tobit-type estimator. A Tobit estimator is a maximum-likelihood estimator, which is based on a full specification of the error distribution. You have only the median specified, so it can't be an MLE.

What can we do? To begin with, note that, for a random variable $Z$, the median of $\max(c,Z)$ is $\max(c, \mathrm{med}(Z))$, which can be proved by using the definition of the median.

Thus, for your problem, you have
$$\mathrm{med}(y|X) = \max(c, f(X,\theta))$$
under the assumption that $\mathrm{med}(\epsilon|X)=0$. A natural extremum estimator would be the minimizer of
$$\frac{1}{n} \sum_{i=1}^n |y_i - \max(c, f(X_i,\theta)) |.$$
You defined the median as the minimizer of $E(|Z-e|-|Z|)$, but this is the same as the minimizer of $E|Z-e|$ without $-|Z|$, so I dropped the "$-|y_i|$" from the objective function.

This is a generalization of Powell (1984), Least absolute deviations estimator for the censored regression model, Journal of Econometrics, 25, 303-325. See the paper for more details including consistency. https://web.stanford.edu/~doubleh/eco273/powell1984.pdf


Find the optimal labor supply when labor utility is linear

I guess you mean that the condition $-\beta +\lambda w =0$ does not include labor. But you have the profit maximizing wage relation that includes labor and wage, and so combining, you can obtain an expression that includes the marginal product of labor, and the multiplier lambda, which can be expressed in terms of the other decision variables.

Ok, I see you got lost in running around your equations.

Profits are zero since the firm is a price taker and the production function is homogeneous of degree one (constant returns to scale).

$$ \frac{\alpha}{1-\alpha}n_2 w = k q \implies n_2\frac{\beta}{\lambda} = \frac{1-\alpha}{\alpha} kq$$

Since $\lambda = 1/c_1p_1$, $q=p_1$ and $k = \bar y -c_1$we get

$$n_2\beta c_1p_1 = \frac{1-\alpha}{\alpha} (\bar y -c_1)p_1$$

$$\implies n_2 = \frac{1-\alpha}{\alpha\beta } \left(\frac{\bar y}{c_1} -1\right)$$.

Now, go back to the budget constraint

$$c_1 p_1 + c_2 p_2 = p_1 ( \bar y - x ) + qx + wn_2 + \pi$$

Inserting the various optimal conditions, you should arrive at

$$c_1 = \frac {\bar y}{1+\alpha \beta}$$

which leads to $n_2 = 1-\alpha$.


Why did the rate of money supply growth accelerate from 1993-96 in the United States?

So long as the growth rate of the monetary base is greater than the growth rate of M2, the ratio of M2 over the base (velocity) will decrease. (The numerator of M2/MB is growing less slowly than the denominator.)

That is what happened during (most of) the period shown. It was only in 1996 that M2 was growing faster than the base, which would increase velocity.

Your question is effectively attempting to characterise the second time derivative (acceleration) of M2 in terms of the acceleration of the monetary base and velocity. In my answer to another question, I give the relationship for acceleration in the money supply, and it is related to the acceleration in the monetary base and the acceleration of velocity. The data shows the level of velocity, which is not enough to characterise the relationship.


revealed preference given an uncertain environment?

Revealed preference theory is essentially about the observable empirical content of theories. Now if we look at the classical model of utility maximization, if there is a fixed function $f:X\to O$ and a utility function $u:O\to\mathbb{R}$, utility maximization amounts to maximizing with respect to the utility function $v:X\to\mathbb{R}$ given by $v(x)=u\big(f(x)\big)$ for all $x\in X$. There is nothing new here.

If $f$ can change or is uncertain, you are looking at a form of changing preferences or uncertain preferences. Since revealed preference theory is about the observable empirical content of theories, you need some theory about changing preferences or uncertain preferences. The task is then to identify the empirical content of the theory. For this to be an interesting exercise, there needs to be some relation between different decision problems. One example is the work of Gul and Pesendorfer on the empirical implications of the Strotz multiple self model of changing preferences with consistent planning in

  Gul, Faruk, and Wolfgang Pesendorfer. "The revealed preference theory of changing tastes." The Review of Economic Studies 72.2 (2005): 429-448.


Having a lower inflation rate is not the same as having lower overall prices?

The inflation rate is the rate of change in the price level.

A lower - but positive - inflation rate (say from 3% to 2%) still results in higher prices -this is typically called disinflation, and highlights the fact that lower inflation doesn’t necessarily mean lower prices.

A negative inflation rate print (like -1%) implies the price level did actually decrease - typically referred to as deflation.


Where does the current debate stand on passive vs active monetary policy?

I would like to think so, Monetary policy has changed since the creation of the Federal Reserve. There is a big difference in business cycle frequency and magnitude since post World War II, see attached image.

image source: McGee, Robert T.. Applied Financial Macroeconomics and Investment Strategy (Global Financial Markets) (p. 18). Palgrave Macmillan US. Kindle Edition.

This can be attributed to demographics, technology and other secular influences. However, I like to think this is also do to the Fed learning from the past and is slowly getting better and controlling there mandates. Some argue that we where headed towards another depression in 2008, but the Fed offsetting the money multiplier with QE to keep money supply relatively stable.

Of course there are plenty that would disagree with me, but I don't claim to be a economist, I am a investor.. Then again most economist are busy disagreeing with each other to bother arguing with me.

Cheers,
Aaron


Walras Law in a production economy with fixed costs

Partial answer:
for simplicity let $P_c =1$.
The budget constraint: $c= wn + \Pi$
Simplify (plug in $\Pi$): $c= F(n)- fc$
Goods clearing: $c = F(n)$
The household's budget constraint is inconsistent w/ goods market clearing.
The firm pays a fixed cost that doesn't go to anyone. In a "true GE model" all payments have to go to someone in the economy.
One solution is to rewrite the goods market clearing condition:
$c= F(n)- fc$
IE: some of the output good is consumed by the household, and some by the firm...
Alternatively, a common approach in economics is to assume one factor (say capital) is fixed in the short run ($k=\bar{k}$) and rented from households. In this case $fc= r\times\bar{k}$:
\begin{align*}
\Pi
&=
\max_{n^D, k^D} \left\{ P_c F(n^D) - w\times n^D - r\times k^D \right\} \text{ s.t. } k^D = \bar{k} \tag{short-run}
\end{align*}
The household's problem is then:
\begin{align*}
\max_{c,n^S, k^S} U(c,n^S) \text{ s.t. } P_c c = w\times n^S + r\times k^S + \Pi
\end{align*}
GE: prices $(P_c,w,r)$ & allocations $(n^D,k^D,c,n^S,k^S)$ all optimize & markets clear:
1 (Labor) $n^D=n^S$
2 (Goods) $c=F(n^D)$
3 (Capital) $k^D=k^S$
Now the household's constraint is no longer inconsistent w/ Goods market clearing.
\begin{align*}
P_c c
&=
w\times n^S + r\times k^S + \Pi
\\ &=
w\times n^S + r\times k^S + (P_c F(n^D) - w\times n^D - r\times k^D)
\\ &=
P_c F(n^D) \tag{k, n clear}
\\
c &= F(n^D)
\end{align*}
It appears there is no good way of modeling fixed costs in GE w/o having some household in the economy endowed w/ & rent out the factor that is fixed.


What I don't understand is why we discount the profits in year one but
  don't consider inflation in year one. This seems inconsistent to me.
  Why do we discount the real profit in the first year and not the
  nominal profit, or if we assume nominal profits in year one are the
  same as real profit, why do we discount in year one?

As you said, the firm

  expects profit in the first year to be $60,000, and they expect real profits to remain at that level over the next five years.

They are expecting both real and nominal profits (because they do not explicitly state only one or the other) to be \$60,000 for year one but they need to calculate NPV for $T_0$, thus they need to discount the \$60,000 for a single year (and the others for an additional year).

We're realizing the profit as income starting in $T_1$, and realizing the initial capital expenditure at time $T_0$.

$T_0$----------$T_1$--------$T_2$--------$T_3$--------$T_4$--------$T_5$
-200000 + 60000 + 60000 + 60000 + 60000 + 60000 Real
-200000 + 60000 + 62400 + 64896 + 67492 + 70192 Nominal
-200000 + 54054 + 50645 + 47451 + 47451 + 41655 Nominal Discounted

Calculated in Python:

>>> -200000 + sum(60000 * (1.04**i) / (1.11**(i+1)) for i in range(5))
38264.90224378838

As to the reason the authors of the question gave these conditions, I presume that they want to ensure that you can quickly arrive at the correct calculations based on seemingly trivial but important details. I recall a similar trick in a corporate finance final, where a careful reading of the question indicated that a speedy reading of the question (one that I initially made and expected most of my peers would make) would result in an off-by-one time period mistake.


It's unclear how market equilibrium is reached in case of overproduction

You are basically asking a dynamic question on the basis of a static model, although this often done for convenience. In a real static model, over production is impossible.

You answered the first part of your question yourself: In the short run the Q2-Q'goods got sold off at a lower price. For the long run: recall that the supply curve is also the industry's marginal cost curve. If producers lower their prices below P2, some of them will start to operate at less than max profit and either go out of business or reduce production, to operate at max profit level again. In the long run we thus move along the supply curve, downwards to point E.


Compustat Annual is used in Gabaix and Landier (2008). A famous stylized fact is the power-law distribution (by Gabaix again) of firm sizes. But power-law claims have been criticized as resulting from poor measurement.


Did I calculate the expected value and the variance correctly?

He who formulated the exercise is wrong, and this is why I am posting a full answer to a homework question.
This is a classic example where manipulating recursive relations can lead to different representations that may appear "different" and with different properties.

$$\Delta Y_t \equiv Y_{t}-Y_{t-1} =  \mu + Y_{t-1} + \varepsilon_{t} - \mu - Y_{t-2} - \varepsilon_{t-1}$$

$$\implies \Delta Y_t = \Delta Y_{t-1} - \Delta \varepsilon_{t} \tag{1}$$

At the same time

$$Y_t = \mu + Y_{t-1} + \varepsilon _t \implies \Delta Y_t = \mu +\varepsilon _t \tag{2}$$

The right hand side of Eqs. $(1)$ and $(2)$ represent the same process.

In any case, neither of these are $MA(1)$.

Moving forward, which one to choose?

A soft adoption of Occam's razor indicates that eq. $(2)$ is the simplest. A bit more specifically, we note that the manipulation resulting in $(1)$ hasn't "saved" us from the existence of a unit root and non-stationarity in a clear way.

Both therefore suggest to adopt $(2)$, that says that  $\{\Delta Y_t\}_t$ is the sum of constant and a $WN$ process.


What is the best way to estimate a demand curve?

The approach you use has various problems.

Yes you need more than 16 observations. In most parametric models (including OLS) as a rule of thumb you need at least 25-30 observations per independent regressor (see Newbold et al statistics for business and economics for example).
You can use a linear model but you should not assume demand is a linear function of price. OLS is a model that is linear in its parameters but that does not mean necessarily that the relationship between two variables should be modeled in a linear way.

For example, a more realistic assumption about demand would be given by the following function:
$$q = a p^{\beta_1} x^{\beta_2}$$
where, $q$ is quantity, and $x$ some control variable, which is not linear but after taking logs of both sides this demand can be modeled by OLS because OLS needs to be just linear in parameters (here $\beta_1$ and $\beta_2$):
$$q = \ln (a) + \beta_1 \ln (p) + \beta_2 \ln (x) + e$$

Another problem is that you don't include any control variables. You should include several of them - anything you think can affect quantity demanded aside from price should be ideally controlled for (and remember you should expand your sample to always have at least 25-30 observations per independent regressor in a parametric model).

Even though demand is estimated with models that employ regressions, using just simple OLS is inappropriate. Supply-Demand is an endogenous system. Price affects quantity demanded and quantity demanded affects price at the same time and the same holds for supply.

Hence you cannot simply run two independent OLS and then equate them to determine equilibrium price. You should  model this as an endogenous system where both supply and demand are modeled at the same time. There are also further issues that I did not explore here but these are already quite severe and will lead to biased coefficients and/or wrong inference.
Writing a tutorial for estimating supply and demand relationship is completely beyond the scope of Stack Exchange, and what is the best way might vary from case to case, but if you want to see an example of how to properly estimate supply-demand relationship it can be found in this paper from MacKay & Miller (2018).


The Envelope theorem is a general mathematics result says that you can differentiate a value function with respect to a variable without implicitly differentiating the maximum argument variable.

Example: $V(p_x,p_y,w)=U(x(p_x,p_y,w), y(p_x,p_y,w))+\lambda(p_x,p_y,w)[w-p_x-p_y]$

If I want to see how utility at its optimal level changes when wealth changes, I can simply differentiate this equation with respect to wealth explicitly:

$V_3=\lambda$ - so the marginal utility of wealth is simply the Lagrange multiplier.

As you can see I did not differentiate anything else, even though wealth does appear in U. This is simply because if you did do that, those terms would drop out =0 as a result of the FOC

The relationship between indirect utility and expenditure is from the 'duality' between the two. The reason why $V(p,e(p,u))=w$ stems from the fact that the optimal arguments for both will be equivalent when the value of utility achieved in the utility max problem is the same utility level that we set as $U=\bar u$ in the expenditure minimization problem.

If you do the FOC for both utility max and expenditure min you get the tangency conditions:

$p_x/p_y=MRS$ in both cases. So if the target level $\bar u$ is what we achieve in the utility max problem, then the marshallian and hicksian demands will be the same. Then the value function for the expenditure min is:

$e(p_x,p_y,\bar u)=p_xh_x+p_yh_y=p_xx+p_yy=w$ and since $\bar u=V$

$e(p_x,p_y,V)=w$

Similarly,
$V(p_x,p_y,w)=U(x,y)=U(h_x,h_y)=\bar u$ and since $w=e$

$V(p_x,p_y,e)=u$

You can find a lot more by searching for 'utility duality'.


Does finding real income adjust for inflation?

Indeed deflating nominal income using CPI does get rid of the effect of inflation. I think you're just getting confused by the phrasing.

I assume you are referring to the following sentence on pg. 6:

  We  have  shown  that  the  net  result  of  her  raise  and  inflation  was  an  increase of 7.9% in real income.

Let me rephrase this sentence: we have shown that after raising her salary by 10% and then adjusting for inflation, the net effect is that her real income increased by 7.9%.


Why doesnt Law of Diminishing Marginal Utility not affect price effect?

This may just be a semantic misunderstanding. The Law of Diminishing Marginal Utility (LDMU) does "affect" the price in the sense that it is responsible for the convexity of preferences, which in turn guarantees a well-defined price effect. The formulation "price effect = income effect + substitution effect" is just a short way of saying that the change in consumption following a change in the price of a good can be decomposed into two different (consumption changing) effects called income effect and substitution effect. The LDMU itself is not a change in consumption and therefore not part of this identity; it is more like a prerequisite to be able to establish this identity in a unique way.

(PS: The LDMU only makes sense for cardinal utility functions which have long ago been replaced by ordinal ones, at least in deterministic contexts. It should be replaced by the Law of Diminishing Marginal Rate of Substitution. What I said above holds analogously then.)


How can the replacement level fertility be 2.1 everywhere in the world?

Your claim that the replacement level fertility is "universally taken as 2.1" is false.

World Resources Institute:

  This rate is roughly 2.1 children per woman for most countries, although it may modestly vary with mortality rates.

Craig (1994):

  In developed countries, replacement level fertility can be taken as requiring an average of 2.1 children per woman. In countries with high infant and child mortality rates, however, the average number of births may need to be much higher.

2.1 is simply a very crude and made-up figure. It's just 2 (replace the parents) plus a little more (arbitrarily assumed to be 0.1) to account for mortality.

Where a writer is unable or unwilling to obtain better estimates, she will often simply use this 2.1 figure. But this does not mean she believes that the true replacement level fertility in her context is precisely 2.1.


IS-LM-BP Model: How will income and interest rate change if government expenditure is increased?

Yes, the diagram represented in the question is correct. Assuming imperfect capital mobility (with the BP curve steeper than the LM curve), an increase in G will:

Move the IS curve to the right.
At this point (B), there will be a BOP deficit because the point is below the BP curve.
Thus, the domestic currency will depreciate.
Exports will rise, imports will decrease and thus net exports will rise.
This will have two effects: (a) this will shift the IS curve further to the right (because net exports have risen, and so Y has risen) and (b) this will shift the BP curve to the right (because net exports have risen, improving the current account balance).
The new equilibrium is at C.

I found a better diagram illustrating this (the diagram includes two cases: one with the BP flatter than the LM and one steeper; the points and movements marked with an asterik (*) are the ones concerned with the case of BP being steeper than the LM). (Image Courtesy of Polinomics: http://policonomics.com/is-lm-bp/)


For starters, the original article. Banks et. al (1997) discuss its assumptions. This survey might also be helpful.


Is there some background/explanation why the Fed discontinued publishing their M3 indicator, circa 2006?

https://www.federalreserve.gov/releases/h6/discm3.htm:

  M3 does not appear to convey any additional information about economic activity that is not already embodied in M2 and has not played a role in the monetary policy process for many years. Consequently, the Board judged that the costs of collecting the underlying data and publishing M3 outweigh the benefits.


Banking Regulatory Frameworks, between the 1973 collapse of Bretton Woods and the introduction of the Basel Accords in 1988?

I found two of two papers discussing this period, the second at length.

  Throughout the 1970s, the capital position of many banking
  institutions declined significantly. To address this decline, in
  December 1981, the bank regulators issued explicit minimum capital
  standards for banks and bank holding companies. These standards
  required banks to hold capital at least equal in amount to a fixed
  percentage of their assets. While these standards have been given
  credit for increasing bank capital ratios, the 1980s saw an increase
  in both the number and cost of bank failures. A weakness of the
  minimum capital standards is that they failed to take into account the
  risk in a bank's portfolio of assets; high-risk assets required the
  same amount of capital as low-risk assets.

Risk-based capital, portfolio risk, and bank capital: A simultaneous equations approach by K Jacques and P Nigro (1997)

  In 1972 the Fed capital standard was revised again. Asset risk was
  separated into “credit risk” and “market risk” components. In
  addition, banks were required to maintain a higher capital ratio to
  meet the test of capital sufficiency. Further, the Fed reintroduced
  both the capital to total asset and capital to total deposit ratios.
  This time, however, the former ratio was based on total assets less
  cash plus U.S. government securities, a rough “risk asset” adjustment.
  In practice, bankers and analysts used the FDIC and Fed standards more
  than those of the OCC.

  None of the agencies established a firm minimum capital ratio.
  Instead, the capital positions of banking institutions were evaluated
  on an individual bank basis. Particular attention was directed toward
  smaller banks whose loan portfolios were not as diversified and whose
  shareholders were fewer in number than those of larger institutions.
  It was reasoned that small or “community banks” might have a hard time
  raising capital in times of difficulty and therefore should be more
  highly capitalized at the start than larger institutions. Table 1
  shows the banking industry’s capital-asset ratios from 1960 to 1980.
  The table shows that there was a steady downward drift in the ratio,
  which can be explained by a number of factors. Chief among these would
  be the attractiveness of increased leverage in banking and reliance on
  other techniques to manage balance sheets, e.g., liability management.

  In late 1981 the three Federal bank regulatory agencies announced a
  new coordinated policy related to bank capital. The policy established
  a new definition of bank capital and set guidelines to be used in
  evaluating capital adequacy. The new definition of bank capital
  included two components: primary and secondary capital.

  Primary capital consisted of common stock, perpetual preferred stock,
  surplus, undivided profits, mandatory convertible instruments (debt
  that must be convertible into stock or repaid with proceeds from the
  sale of equity), reserves for loan losses, and other capital reserves.
  These items were treated as permanent forms of capital because they
  were not subject to redemption or retirement. Secondary capital
  consisted of nonpermanent forms of equity such as limited-life or
  redeemable preferred stock and bank subordinated debt. These items
  were deemed nonpermanent since they were subject to redemption or
  retirement.

  In addition to the new definition of capital, the agencies also set a
  minimum acceptable level for primary capital and established three
  zones for classifying institutions according to the adequacy of their
  total capital.

International risk-based capital standard: History and explanation by MC Alfriend (1988)

In the United States it isn't just Basel that is changing. FDICIA act of 1991 is also an important regulatory change for regulatory capital standards. My understanding is that Basel I only worried about credit risk but FDICIA introduced capital requirements for interest rate risk as well, perhaps in response to the contemporaneous savings and loan crisis where many thrifts failed as a result of losses from interest rate exposures.


Straffin, P. D. (1993): Game Theory and Strategy. How is the security level on p. 103 calculated?

Suppose Colin plays A with probability c and B with probability 1-c, while Rose plays A with probability r and B with probability 1-r. Then Rose's payoff is

$2rc+4(1-r)c+10r(1-c)+0(1-r)(1-c)$

Rose's security level is calculated by taking the max-mini payoff: that is, for each value of r, find the minimum payoff over all c, then find the maximum such value.

So, first, we can simplify the above expression:

$2rc+4c-4rc+10r-10rc = 4c+10r-12rc$

As a function of c, this is a line with intercept $10r$ and slope $4-12r$.

Case I: $r = \frac13$, this line is a constant $10r$. Plug $r =\frac13$ in and you get $\frac{10}3$

Case II: $r > \frac13$, then it's negatively sloped, and the minimum occurs at $c = 1$, with a payoff of $4-2r$. Since $r > \frac13$, we have that the payoff is less than $4-2/3 = \frac{10}3$.

Case II: $r < \frac13$, then it's positively sloped, and the minimum occurs at $c = 0$, with a payoff of $10r$. Since $r < \frac13$, the payoff is less than $\frac{10}3$.

In other words, if Rose plays A $\frac13$ of the time, then she gets an average of $\frac{10}3$ regardless of what Colin does. If she plays A less than $\frac13$ of the time, then if Colin plays B, then she gets 10 less than $\frac13$ of the time and 0 the rest of the time, getting her less than  $\frac{10}3$. If she plays A more than $\frac13$ of the time, then if Colin plays A, she gets 2 more than $\frac13$ of the time and 4 the rest of the time, getting her less than $\frac{10}3$.

So Rose can guarantee herself $\frac{10}3$ by playing A $\frac13$ of the time, and every other strategy has a possibility of giving her less than that. Thus, $\frac{10}3$ is her security level.

The reason BA should be played at least $\frac13$ of the time is that if BA is played  $\frac13$ of the time  and AB is played  $\frac23$ of the time, then Colin's payoff is  $8*\frac13+ 5*\frac23 =  \frac83 +  \frac{10}3 = \frac{18}3=6$, which is his security level. If BA is played less than  $\frac13$ of the time, then his payoff goes below his security level, so he would be better off not cooperating.


Wooldridge's Microeconomics book vs Cameron and Trivedi's textbook

Both books are very good, and they are not competitive but rather complementary. I would say that compared to $CT$, $W$ is a more "traditional" econometrics book, while $CT$ includes whole chapters in broader underlying statistical issues. At the same time, $CT$  are relatively more concerned with the dirty reality of doing applied econometrics with real-world data sets, and how this feeds back to the theoretical models.

Regarding your choice, it matters what each instructor does with each book. Ask them.

Learn which chapters are covered in each class and compare, to see if they cover the same subjects or not... there must be a reason why there exist two available classes.


Is population growth irrelevant with respect to per capita GDP growth

Indeed, there is branch of literature about semi-endogenous models (Jones, 1995, Segerstrom 1999 etc.). They were basically arguing that there was a scale effect in endogenous growth models, which means that when population increases, by default, growth increases (it is due to the fact that there would be more researcher in society, this is the scale effect.) and this branch of literature shows that growth rate at the long run is equal to the growth rate of population, which is an exogenous term. It is why they called it as "semi-endogenous".

This was challenging endogenous models but the empirical literature states that that the semi-endogenous model does not fit to data.

Some empirical references are :

Ha and Howitt (2007)

http://onlinelibrary.wiley.com/doi/10.1111/j.1538-4616.2007.00045.x/full

and

Madsen (2008)

http://link.springer.com/article/10.1007/s10887-007-9024-0


The marginal cost is the cost added of producing an additional unit of product. In this case the company is paying a factory in China \$3 per unit to produce the product. Assuming you have no other variable costs (i.e. costs that vary with level of output) then the cost of producing an additional unit is indeed $3.


Does immiserizing growth exist outside of theory?

The concept of immiserizing growth describes a situation where a mainly exporter country that grows, finds itself worse-off because the terms of trade (relative prices) change too much against it.

Immiserizing growth has generated some theoretical interest in the past, and various situations have been determined under which such a phenomenon may arise, enhancing the original contributions by
Johnson, Harry G. 1955. "Economic Expansion and International Trade," Manchester School 23, pp. 95-112
and
Bhagwati, Jagdish. 1958. "Immiserizing Growth: A Geometrical Note," Review of Economic Studies 25, (June), pp. 201-205.

I do not know of any real-world example though. On the contrary some studies have been conducted which have estimated the critical values for the variables of a real-world economy, in order for it to face the possibility of immiserizing growth-and these thresholds are not observed in practice.

As an example, Ramon Lopez (1991), in "Microeconomic Distortions: Static Losses and their Effect on the Efficiency of Investment", studying the economy of Chile for the period 1974-1989, estimated that, under full employment, the critical tariff rate for the prospect of immiserizing growth to arise would be $185$%, while with unemployment, it would be $260$%, which are too high compared to observed tariff rates.

The real concern about International Trade is its distributional effects inside each country, i.e. whether it creates "misery" for part of the population, while benefiting some other part. This is also "immiserizing growth" (for some of the citizens) but not in the sense meant by the scholars that originally coined the term.


Why do stocks that don’t pay any dividends change price when the company does better?

Even if a company pays no dividends, its price will usually reflect its "fundamentals" or "how well it's doing". This is because:
If the price is too low (relative to any metric, be it earnings, growth, etc.), then anyone can profitably launch a takeover/acquisition bid.
Example. A company has 1B shares each priced at \$1 (so market cap is \$1B), pays no dividends, and earns \$100B (profits) per year. Then one could buy up all 1B shares for \$1B, own the company entirely, and enjoy \$99B in profits in just the first year alone.
(Second and third paragraphs are identical to another answer I gave.)


This is from the end of the first chapter in the book Public Finance in Canada 4th edition by Harvy Rosen.

This book is  a primer for welfare economics. The book states gives a list of:

Journal of Public Economics
Canadian Tax Journal
National Tax Journal
Public Finance
Public Finance Quarterly
International Tax and Public Finance
Journal of Public Economic Theory
Economics of Governance

Also remember most general interest economic journals also publish articles that deal with welfare economics/public finance issues.

Hope this list helps


Term for rapid economic growth when starting over or in a new place

With a bit of humor, you could use the Schumpeterian term "creative destruction" -the humor relates to the fact that Schumpeter used the term to describe an inherent structural feature of capitalism, not historical/natural accidents/disasters.

Apart from that tongue-in-cheek proposal, I am not aware of a compact term to express what you describe. A common way could be a "vintage theory of capital" approach, where it is recognized that "old and new" capital coexists with different levels of technology embodied in it, and so in a sense "averaging" the actual technological/efficiency level used in the economy. Then what you describe amounts to an abrupt loss of "old" capital which may lower the output level but creates a positive discontinuity in the actual average technology level used in the economy, creating abrupt and higer growth rates.

You can broaden the concept of capital to also include "human capital" and maybe also "institutional capital" (and so "technology" will then refer also to "knowhow/experience" and "transactional technology" as well).


If a weak preference relation is complete and transitive, why is the strict preference relation negatively transitive?

I think your confusion here stems from misinterpreting negative transitivity to mean "not transitive". But that's not what it means. It is perfectly possible for a binary relation to be both transitive and negatively transitive, as is the case here with the strict preference relation.

Definition 1. A binary relation $\mathcal{R}$ is transitive if: $$x \mathcal{R} y \text{ and } y \mathcal{R} z \implies x \mathcal{R} z.$$

Definition 2. A binary relation $\mathcal{R}$ is negatively transitive if: $$x \not\mathcal{R} y \text{ and } y \not\mathcal{R} z \implies x \not\mathcal{R} z.$$

(Those are forward slashes over the $\mathcal{R}$'s meaning "not". The LaTeX "not" here isn't quite working as well as I'd like.)

The strict preference relation $\succ$ is both transitive and negatively transitive.

It is transitive because $(x \succ y \text{ and } y \succ z)$ implies $x \succ z.$
It is negatively transitive because $(x \not\succ y \text{ and } y \not\succ z)$  is equivalent to $(y \succsim x \text{ and } z \succsim y)$, which, by the transitivity of $\succsim$, implies $z \succsim x$ or $x \not\succ z$.


Non-viable Industry with demand curve above supply curve

If we consider that no one wants an infinite number of any material thing other people can supply and that there are only a finite number of people/firms, the demand function should be bounded. That means that eventually the price people are willing to pay for one extra unit of the good will be zero, and assuming non-negative production costs at this point the supply curve will not be under the demand curve. So the situation you describe can only exist in theory.
However you can have examples where for large quantities the demand function is over the supply function, e.g., the market for ordinary air. People desperately need air (up to a limit), yet it can be supplied at zero cost (it is freely available, again up to a limit).


How to derive the Indirect Utility Function from the Marshallian Demand Function?

Recovering the utility function given Marshallian demands only is called the 'Integrability problem'.

In general, it is quite difficult. However, there are some conditions under which it is possible. Kim Border has some notes on this topic on his website.


What is the long run equilibrium in layman's terms?

Long-run equilibrium is a theoretical construct. One may argue that an economy never really gets a chance to actually reach it. So it is best to explain it in a hypothetical setting:
Imagine an economy with fixed population and all markets in equilibrium. By all markets I mean the money market (no excess money, no shortage of money), goods market (no pilling of goods in factories, no shortage either - producers' plans for production are unchanging) and labor market (whoever wants to be employed at the going wage-rates is employed). Now, strictly speaking, one more market, bonds market, is left, but by the famous Walras law, when $n-1$ out of $n$ markets are in equilibrium, so will be the $n^{th}$ one.
You can say that the economy is currently in long-term equilibrium. It is producing at full capacity. So let's give it a demand-side shock. It could be a monetary shock by the central bank, or by government by increasing/decreasing spending, external shock due change in export demand, etc. Basically, a shock which shifts the aggregate demand curve.
Now we have a disequilibrium. Not all goods that are produced could be sold (or not enough are produced). There is more money circulating in the economy than required (or not enough money to meet the need of increasing transactions). What do we do now?
Usual option: In the immediate aftermath, we should produce less (or more) to meet the new demand. To do this workers are fired (or more are hired at higher wages) changing the labor market equilibrium as well.
Alternatively, we could also just slash (or increase) prices so that demand is balanced again. But there are problems with this. It is almost impossible to do this in a synchronized way everywhere. On the top of if, producers would also want to simultaneously cut wages (or workers will demand higher wages due to higher prices - that producers may not be immediately agree to). This alternative option, as per macroeconomic literature, is not smooth. It faces rigidities and happens slowly. As your book points out, if, hypothetically, it did happen then there would be no change in employment or output levels.
This is what distinguishes short-run and long-run equilibrium in macroeconomics. The usual option is the one that creates a short-run equilibrium where the prices and wages are yet to be adjusted to reach the long-run equilibrium.


Burden of debt; Internal or external financing?

Q1 : If you define external debt as "forex debt" context.
If the debt repayment amount for every period are greater than a country import/export amount, then it will influence the exchange rate.  Subsequently affect goods price.

For internal debt (e.g. money borrow within the country, using various financial tools or creative derivative ).
On positive side, if the debt spending bring in long term production or/and cost saving benefit, it will be reduce the debt burden, increase income. As it suppose to get the debt payoff from the positive benefit.

On negative side, internal debt can be wasted, or lead to speculative activities. In such case, the problem can be many folds, depends on the magnitude of of the debt. For "smaller scale", creditor or so call "investor" lost their money. E.g. Enron, Worldcomm scandal.
For the worst snowball case, the effect is much dire and difficult to assess. E.g. the worst private sector debt, you can check out example of subprime mortgage crisis. For country level, you can check out the Greek government-debt crisis.

Q2 : Under perfect world production context (no production of unwanted goods, goods/finance speculation/corruption), as long as the production income are more than the debt, there will be no ill effect from borrowing.

Note : In each economic question, context is always required, no matter how you apply famous/infamous economist that apply math formula. Because human society keep adapting and exploiting the system.


How does domestic demand affect the domestic currency's value

What effect is stronger in response to domestically motivated economic
  growth? Is it the depreciating effect of imports or the appreciating
  effect of new entrants or am I missing something entirely?

There's no general answer to that. It depends on the particulars of each economy. Some factors are:

Whether imports outweigh exports or viceversa;
Whether the tax reduction is coupled with spending cuts, tariffs,
foreign debt, etc.;
Taxpayers' general propensity to save the additional "disposable"
income could influence the exchange rate in either direction,
depending on where they deposit their savings.


Why can Iceland setup and maintain a single-payer system but Vermont can't?

From what Wikipedia tells me on the Vermont case, the Vermont government feared increases in costs and taxes from such a reform. In the end, it boils down to what people/voters/decision-makers are willing to pay for a health care system they believe to be good for the people. Scandinavian countries provide lots of top-class public services (health care, child care, education) but also collect the highest tax rates in the world. Apparently, political will and public opinion in Iceland were willing to accept the price attached, which was not the case in Vermont. Beyond, it is possible that the move from the previous system was less drastic in Iceland, requiring fewer things to change.


Since 1980, in which years has the US debt-to-GDP declined and why?

The time series for the debt-to-GDP ratio are available on the FRED wesbite: link to debt-to-GDP chart. I will let the reader download the data, rather than list the years here.

As for why it falls, it requires a good macroeconomic model. The reason being is that we need to explain both the fiscal deficit and the rate of nominal GDP growth.

Policymakers do not directly control the deficit. Faster growth means a greater tax take, less social spending. Meanwhile, capital gains taxes are determined by the hard-to-forecast changes in stock prices.

Nominal GDP (the denominator) can grow as a result of faster inflation, or faster real growth. The precise determinants of this have bee the subject of economic debates for decades. I obviously cannot answer it here.

One factor to keep in mind that the existing level of the ratio matters a lot. If nominal GDP growth is 5%:

you need a fiscal deficit of 5% of GDP to keep the ratio unchanged if the starting level is 100%,
you only need a deficit of 2.5% if the starting level is 50% of GDP.

If you look at the chart, the biggest fall in the ratio after 1980 was during the late 1990s. There was a brief fiscal surplus, and growth was relatively strong. There was a technology boom, along with the tech stock bull market/bubble that generated a lot of capital gains taxes. (The Clinton administration raised taxes earlier, which was also a factor in the surplus.)

(In a comment, you asked about the 2000s. During that period, the ratio rose, but that can be partly traced to the increased defense spending that happened. Once again, there’s too many moving parts in the budget and economic growth to give a simple explanation of how the ratio moved.)


In the case of Apple at least, the answer is yes: this article dated August 31 2019 talks about the impact of the latest round of tariffs on Apple products produced in China.

  Apple, the largest U.S. technology company by market cap, has its products assembled in China by Foxconn and then ships them to consumers all over the world. The Apple Airpods, Apple Watch and accompanying Apple Watch bands and the Apple Homepod are all products subject to the higher tariffs beginning Sunday. The iPhone doesn’t appear to be impacted this round, but could be subject to tariffs that begin Dec. 15.

https://techcrunch.com/2019/08/31/apple-products-under-pricing-pressure-as-new-15-tariffs-drop-sunday/


When does the Divine Equilibrium refinement coincide with that of Perfect Sequential Equilibrium?

Some input:

In Cho, I. K., & Kreps, D. M. (1987). Signaling games and stable equilibria. The Quarterly Journal of Economics, 179-221, Banks & Sobel's Divine (and Universally Divine) equilibrium concepts are presented in Section IV.4 as a stand-alone concept.
On the other hand Grossman & Perry's Perfect Sequential Equilibrium concept is just mentioned in Section IV.5 which has the title "Never a weak best response".

In the Banks, J. S., & Sobel, J. (1987). Equilibrium selection in signaling games. Econometrica, 647-661. paper on Divine Equilibrium, page 654 (near the end of Section 3), we read "(...) This condition is more restrictive than universal divinity because (...)" , "this condition" being "never a weak best response".

So it appears that Perfect Sequential Equilibrium (PSE) is a stronger equilibrium filtering criterion than Divine Equilibrium. This accords with

Theorem 2 of Banks & Sobel : Every signaling game has a divine equilibrium
to be contrasted with Section 4. of the Grossman, S. J., & Perry, M. (1986). Perfect sequential equilibrium. Journal of economic theory, 39(1), 97-119. paper introducing PSE, where they show by means of an example that a Perfect Sequential Equilibrium may fail to exit.

A paper that applies both concepts is Beggs, A. W. (1992). The licensing of patents under asymmetric information. International Journal of Industrial Organization, 10(2), 171-191.. In Section 3.2 a result is derived by an appeal to the PSE concept. Then the authors note that, given an additional condition, they could obtain the same result by an appeal to Divinity. This agains shows that PSE, when it exists, is stronger than Divine equilibrium. Here too an example is offered for a case when the PSE does not exist.


Concavity of Cobb-Douglass Utility Function on Non-Open set

I assume the notation $\mathbb R^2_+$ refers to $[0,\infty)^2$.

Note that the set on which a function is defined need not be the same set on which a function is differentiable. In particular, it's typical that differentiability requirements are imposed on open sets (see e.g. the fundamental theorem of calculus). This is because defining differentiability on boundary points requires extra care that's usually unnecessary for the issue at hand (such as defining concavity of a function via the Hessian matrix).

The Cobb-Douglas function is defined on $\mathbb R^2_+=[0,\infty)^2$, (continuous also on that domain), and differentiable on $(0,\infty)^2$, which is open and convex.


There is no general principle. It depends on preferences. Especially the degree of risk aversion, i.e. the preference toward risk.

As you mention, there is a trade-off. If there would be a dominant factor, as your title asks, then there would be no trade-off, as the best decision would always be clear.


Which are some proven methods to compare alternative economic theories?

There is one theoretically sound methodology to do what you are asking.  When you have multiple models to compare, the only choice is Bayesian model selection and Bayesian model averaging.

Bayesian methods have several properties that you would want.  Any statistic created is intrinsically "admissible," and "coherent."  The disadvantage, which does not exist for Frequentist methods, is that it is built on inductive reasoning rather than deductive reasoning.  An article on this can be found at https://plato.stanford.edu/entries/induction-problem/

Induction only allows you to test models you have, but cannot test models you do not have and so will always be incomplete.  If you reject a Frequentist null hypothesis, then you reject all theories except the null.  The problem with this happens when the model is complex and cannot be turned into a pure binary hypothesis.  It is worse when more than one model rejects its null.  If that happens then, Frequentist theory is silent on what to do.

A statistic is admissible if there is no less risky way to create it and it is coherent if you could place a fair gamble on it.  The idea of a parameter is more flexible in Bayesian thinking than Frequentist.  A model is a parameter in Bayesian thinking.  As it is a parameter, you can construct a probability statement around it.  Bayes theorem naturally rewards better fitting models, while penalizing models for more structure.  It is a natural Occam's razor with a mathematical interpretation.  It also simply sets aside Friedman's defense as unnecessary.

One of the better axiomatic constructions for Bayesian statistics is Cox's.  You can find it at

  Richard T. Cox. The Algebra of Probable Inference. 1961. Johns Hopkins University Press. Baltimore, MD

It assigns "plausibilities" to logical assertions.  Usually as odds or probabilities.  Surprisingly, it is worth reading.  If you are doing model or theory comparison, then, more so, this is the case.


Expected inflation in the real interest rate equation

Your formula isn't quite right. If $r$ is the nominal interest rate, and $\pi$ is the inflation rate, the real interest rate is $\frac {1+r}{1+\pi}-1$. The formula $r-\pi$ is approximation for small rates. (Note: for all of this, I'm using "rate" to mean the multiplicative factor minus one. So if the balance is multiplied by 1.2, the rate is 0.2.)
The inflation should be over the period over which the interest rate is being calculated. It's like to like: the real interest rate at a particular time is given by the nominal interest rate at that time compared to the inflation at that time.
The fact that you think you are wondering whether you should use the future inflation suggests that you may be confusing the spot inflation rate with the Consumer Price Index. You can get the real interest rate by taking the total nominal interest times the ratio between the CPI at the end of the period to the CPI at the beginning. That is, if $r$ is the total nominal interest, $CPI_i$ is the starting CPI, and $CPI_f$ is the final CPI, then the total real interest is $(1+r) \frac {CPI_f}{CPI_i}-1$.


What are the economic benefits of SLAPP in file sharing/piracy?

Background

Since the marginal cost of distribution for a creative work such as a song is now essentially zero, the efficient thing to do would be to provide all songs to listeners at a price of zero (i.e. to allow piracy). However, this neglects the fact that producing creative works involves a fixed up-front cost (e.g. studio recording time, or simply the artist's time composing the work) that cannot be covered if the price is zero. Moreover, it is efficient for producers of 'good' songs (i.e. those that create value in excess of the production cost) to incur the fixed cost, and for producers of bad songs not to do so.

The way that society mostly addresses this issue is through the grant of intellectual property (specifically, copyright) protection. The trade-off made is that artists are allowed to act as monopolist suppliers (with all of the attendant inefficiencies) because the resulting profits will give them an incentive to produce in the first place. The fact that a seller's rewards are tied to their monopoly profits means that the most popular artists should, in principle, have the biggest incentive to create.

Efficiency effect of piracy

If one buys the idea that we need IP protection to induce the production of creative work then tolerating widespread piracy is a bad idea because it takes away the profit that is supposed to provide artists with the incentive to create. Whilst each individual instance of piracy might be efficient, the overall effect of reducing the number of works produced might not. It is then necessary to ensure that enough people do not pirate enough of the time to keep the rewards from production at a sufficient level.

People should be expected to pirate if the benefits from doing do (free consumption of creative works) exceed the costs (determined by likelihood of being prosecuted and the penalty when prosecuted). An obvious way to stop people from pirating is to increase this cost by prosecuting more people—even if you don't really care that much about winning. Indeed, the main objective is not to win the case and get what, to the RIAA is pocket change; rather, the objective is to scare people enough that they start buying rather than pirating music. [n.b. The RIAA would have to win at least some of the cases, otherwise the threat would be completely empty. As Densep notes in a comment, this raises the issue of whether we can really call these cases SLAPPs or not].

If the result is that artists earn more money and respond by producing more creative works then this can indeed be efficient.

Some tangential remarks

The last qualifier (if the result is that artists earn more money and respond by producing more creative works then this can indeed be efficient) is non-trivial. There is some debate about how elastic the supply of creative works really is to the rate of piracy and whether this effect is big enough to offset the efficiency gains that come from consuming creative goods at marginal cost (i.e. zero).

My sense is also that there is a consensus among economists that the existing degree of copyright protection (typically something like the entire life of the author plus an additional seventy years) is far more generous than the level necessary to induce efficient levels of creative goods production.

Lastly, there are other ways of providing an incentive to create. For example, instead of granting an intellectual monopoly, the state can insist that all creative works are freely available and instead reward artists with a lump-sum prize. This avoids the monopoly distortion, but has a couple of drawbacks: (i) the prize would have to be funded somehow (e.g. from taxation, which is itself distortionary); (ii) it would be necessary to find a way to ensure that prizes are only given to reward the right kinds of music. The advantage of the intellectual property approach is that the market automatically rewards popular songs more.


It seems that there is already some prior work on theory of gamification from game theory perspective. For example, Easley & Ghosh (2016), provide theory on optimal badge design even explicitly mentioning sites like StackOverflow and their paper seems to be highly cited.  Hamari, Huotari & Tolvanen (2015) have article titled "Gamification and economics" which offers a survey of uses of gamification in various economic concepts. The paper itself does not seem to offer any novel models but it offers a literature review with a chapter specifically focusing on game theory.


Do credit cards create more printed money

One initial point: you refer to "printed money", which would normally be restricted to currency in circulation (notes and coins); the parts of the money supply that are electronic are literally not printed.

Borrowing on a credit card creates a credit card receivable, which is not normally considered part of most money supply figures. However, if it were part of a securitisation, it might eventually show up as part of the wider money supply aggregates (M3). (The securitisation ends up funded by a money market fund, and money market funds are typically part of "wide" money supply definitions.)

Are we collectively shooting ourselves in the foot as a result of this fabricated money?

If you think the only objective policy is to preserve the value of the currency unit, perhaps. The relationship between money supply growth and inflation is debatable, but it is seems safe to say that extremely rapid borrowing by the non-financial sector is associated with higher inflation.  However, if the objective is to enhance output and employment, not really.

Credit cards are just another form of credit. The growth of modern capitalist economies is associated with credit expansion. It may be possible to have a growing economy without credit growth, but it would be very difficult. Investment could only be funded by profits, and it would be difficult to offset the withdrawal of financial assets from circulation by the savings desires of households. Without credit, the only mechanism to recirculate savings to the business sector is via equity injections. In practice, direct equity investment is not a significant source of funding for the business sector. That is, stopping credit growth chokes off funding for businesses in practice.

In other words, we can say that society faces a trade-off between monetary stability and growth; the exact nature of that trade-off is somewhat fuzzy.


What does the Fed do with their profits?

Fed sends its net profits to the US treasury. Fed keeps portion of the money it earns to cover its operating expenses but everything above that is necessary for it's functioning and dividends to member banks is remitted back to the treasury see the explainer by Fed St Louis here.

For example, according to ABA Banking journal the Fed net revenue in 2018 was $\$55.5$ billion, from which $\$54.9$ billion was payed directly to the US treasury.  The dividend payments according the source totaled $\$714$ million, rest was all used to cover various operating costs.


Top 10% authors in the field of Cognitive & Behavioural Economics

https://ideas.repec.org/top/top.cbe.html

Ernst Fehr, Institut für Volkswirtschaftslehre, Wirtschaftswissenschaftliche Fakutät, Universität Zürich, Zürich, Switzerland
Urs Fischbacher, Fachbereich Wirtschaftswissenschaften, Universität Konstanz, Konstanz, Germany
Robert Sugden, School of Economics, University of East Anglia, Norwich, United Kingdom
Andrew Schotter, Department of Economics, New York University (NYU), New York City, New York (USA)
Peter P. Wakker, Econometrisch Instituut, Faculteit der Economische Wetenschappen, Erasmus Universiteit Rotterdam, Rotterdam, Netherlands
...

And the other 140 economists.


What would the consequences of an economy-wide 500EUR/tonne carbon tax be?

My sense is that €500 / t CO2 is on the low side. It would change behaviour but it would not substantially alter the economy.

Here are some sample calculations how the tax would affect prices in the transport, food and electricity. This is of course before producers and consumers have adapted their behaviour.

Plane trip London-Paris return 0.244 t CO2 = tax €122 (244% of ~€50 lowest available fare)
Eurostar London-Paris return 0.022 t CO2 = tax €11 (18% of €66 lowest available price)
(Source1, Source2)

Carbon intensity of food consumption in Germany (Source)
1.9763 t x 1.2 (20% carbon intensity of last mile as per report) = 2.372 t
2.372 t / year x €500 = tax €1,186 / year
The proposed tax would add 27% to the average consumer spending on food in Germany of €4.320 / year (Source)

Carbon intensity of electricity generation in EU: 300 g CO2eq / kWh = 0.0003 t / kWh (Source)
Tax / kWh @ €500 t CO2: 0.0003 x €500 = €0.15 / kWh

Average price of domestic electricity in EU: €0.22, of which €0.09 taxes (Source)
The €500 / t CO2 tax would increase the electricity price in Finland (€0.17 incl taxes) to about the level in Denmark (€0.30 incl taxes): €0.17+ €0.15 = €0.32.

In sum, while the tax would likely change behaviour the proposed level appears to be in the range of other existing taxes for many products (VAT in EU is 17-27%). Arguably credits would have to be given to some households for them to be able to effort this new tax on basic necessities (these are typically VAT exempt today). That said, certain carbon-intense sectors that are not currently taxed at all would experience an important impact. Aviation is an obvious one. It would be important to identify them and their potential substitutes to determine the qualitative impact that the proposed tax would have.


Find a separating perfect Bayesian equilibrium

$BA'$ doesn't work because $A'$ is not a best response to $X$, which is a best response to $B$.


A study of  Gopi Shah Goda, Matthew Levy, Colleen Flaherty Manchester, Aaron Sojourner, and Joshua Tasoff (2015) The Role of Time Preferences and Exponential-Growth Bias in Retirement Savings showed that in the US the most important cognitive bias is the exponential growth bias.
Exponential growth bias is bias that occurs because people intuitively do not understand exponential growth. So when people save they think about growth intuitively in linear way.
I don't know if there is a study that says it affects younger people more, but I think it would make sense since more time difference between present and future also means a larger difference between exponential and linear growth.


Recovering from large government debt without currency devaluation

By one estimate (here is another) , as a result of WWII, the United Kingdom saw a debt of more than 200 percent of GDP. They never defaulted on their debt after reaching that level. I believe they never did anything radical, just systematically growing government spending more slowly than national income, thus gradually eroding the debt as a fraction of GDP.

The paper Sustainability of High Public Debt: What the Historical Record Shows may also be of interest.

  The paper looks into the debt histories of three European countries,
  Britain, France, and Germany, to study three questions. First, are
  there historical parallels to the accumulation of high debt in
  peacetime that has taken place in the past decades? The answer to this
  is mostly in the negative. National debt was high during long periods
  but usually related to wars or their financial aftermath. Second, how
  were large debts reduced, and that were the factors determining
  decision-making? Recent research has emphasized the role of social
  conflict in this context. We find that although this may play a role,
  the dominant effect may have come from international financial
  relations. Third, what are the macroeconomic effects of budget
  stabilization, and does it pay off for a country to repudiate or
  inflate away its debt? The short-run evidence is mixed, as the success
  of debt default has varied considerably. In the long run, however,
  stabilizing the budget pays off, as there seem to be no lasting
  adverse effects of fiscal austerity on a nation's growth performance.


The question as posed doesn't make sense to me. An increase in the market interest rate will reduce the price of current bond holdings precisely because they become less attractive since there are now more profitable alternatives in the market. Market forces will lower the price of the bonds in response to the increase in expected future coupon streams from these alternatives.


How to distinguish between nominal and real GSP growth?

Real GDP (RGDP) is a measure of the value of goods and services produced in an economy over a period of time for a fixed set of prices. Nominal GDP (NGDP) is a measure of the value of goods and services produced in an economy over a period of time for  the prices over that period in time. The way they calculate changes in RGDP is to first measure changes in NGDP, separately measure prices, and then subtract the difference. For NGDP in year $t$ and reference price year for RGDP of $k$ it works like this:

$$NGDP_t = RGDP_{t,k} \cdot \frac{P_t}{P_k}$$
Rearrange:
$$\Rightarrow RGDP_{t,k} = NGDP_t \cdot \frac{P_k}{P_t}$$
Take logs:
$$\Rightarrow \ln(RGDP_{t,k}) = \ln(NGDP_t) +\ln(P_k) - \ln(P_t)$$
Now we can calculate a change ($\Delta X_t = X_t - X_{t-1}$):
$$ \Delta \ln(RGDP_{t,k}) = \Delta \ln(NGDP_t) + \Delta \ln(P_k) - \Delta \ln(P_t)$$
But by definition $\Delta \ln(P_k)=0$ because the reference year prices don't change so:
$$ \Delta \ln(RGDP_{t,k}) = \Delta \ln(NGDP_t) - \Delta \ln(P_t)$$
So as claimed above, the percent change in real GDP ($\ln(RGDP_{t,k})$) equals the percent change in nominal GDP ($\Delta \ln(NGDP_t)$) less the percent change in prices ($\Delta \ln(P_t)$).


Are billboards beneficial for the economy? Why?

While advertising can be zero sum, here are two additional dimensions you might want to consider.

Billboards, like other forms of advertising, can inform. In this way Ford can talk about their new 8 seat minivan while GM talks about the more fuel efficient engine of their latest model. This can result in happier customers who value their product better and are willing to pay higher prices for this more ideal product.

Billboards, in ways not paralleled by other most other forms of advertising, have a negative externality akin to pollution. When the NY Times decides to increase their number of advertisements slightly they bear the costs in customer unhappiness, giving them an incentive to adjust until the private costs and benefits of a marginal ad are equated. But not so with the billboard. The billboard is typically adjacent to public space, so if a nasty billboard ruins the scenery or obscures another billboard the billboard owner doesn't internalize those costs. Since the private benefits of ad revenue continue to accrue to the owner, this leads to too many billboards even if some level of billboard production would be socially desirable.


Financial Economics and International Economics

The difference between them is as follows:

International Economics: Following the definition from the famous textbook by Krugman et al. (2017) the international economics is defined as a branch of economics that focuses on the special problems of economic interaction between sovereign states.

Financial Economics: According to W. Sharpe financial economics is a sub-field of economics that "concentrates on exchanges in which money of one type or another is likely to appear on both sides of a trade."

Why? The purpose of science is not just to come up with new ideas but to also organize them and categorize them. Thats the reason why we dont have just Physics but also astrophysics, geophysics, theoretical physics etc, why we dont have just biology but zoology, botany etc, why we dont have just psychology but clinical psychology, forensic psychology etc.

How? At some point the knowledge in any branch of science will become so wast that some scientists decide to focus only on special subset of the science and hence create sub-branch. For example, all physical sciences started as natural philosophy and all social sciences as moral philosophy but as  science grew in complexity they started to diverge into different fields like physics, biology, economics or psychology, and as science grew ever more complex these fields further subdivided into their respective subfields.

  Will a model of international economics suddenly become a model of financial economics if I simply change the names?

Its not about changing names. A model becomes an international economics model if it is applied to economic situation involving two or more sovereign states. A financial economics model will be a model thats applied to a situation where transactions involve money on both sides of a trade.

However, note the same models might be useful in different sub-fields. For example, laws of thermodynamics are widely used directly or indirectly in many branch of physics. A model that includes laws of thermodynamics but is a model pertaining to stellar phenomena will become an astrophysical model. A model based on laws of thermodynamics applied to some geothermal spot on earth will become geophysics model.

  I saw myself repeating the same exact basic math and coming to the same conclusions, different names notwithstanding.

Yes, if a two subfields look at similar interactions its highly likely that they will use similar models and will result in similar conclusions. If anything I would be very worried if a scientific model/theory would work only in one narrow application and was unusable anywhere else. A hallmark of successful scientific theory is if it can explain a large number of phenomena with the least amount of effort. For example, marginal utility can explain a large number of phenomena whether you apply it labor economics, industrial organization, financial economics etc. Its a good sign when a scientific theory can be applied to multiple situations and yields similar conclusions (of course conditional on also testing those conclusions and making sure they are accurate).

References:

Krugman, P. R., Melitz, M. J., & Obstfeld, M. (2017). International trade: theory and policy.


Income Elasticity of Demand for Higher Education

Real GDP is a variable for aggregate income. You might think of your model very loosely as an "aggregate demand function". Then, as the elasticity of a function $\varepsilon=\frac{\partial f}{\partial x}\frac{f(x)}{x}$ can be expressed in terms of logarithms $\varepsilon=\frac{\partial \ln f}{\partial \ln x}$, in your estimation it would amount to say that, ceteris paribus, the elasticity of (assuming average) higher education to real income per capita is $0.47$. This implies that the "demand" for higher education is inelastic ($\varepsilon \in (0,1)$), which kind of makes some sense.  Within that framework (aggregate average, not consistent with demand theory), I think a better model would come from adding ${(\ln RGD)}^2$ to your model, to let the "income elasticity" describe some nonlinearities as it would sound really strange that if RGDP would go up 1000x average education would go up 470x, as this would mean people would be living some centuries before completing their education...


Question about violating the zero conditional mean assumption

If you introduce any sort of correlation between the explanatory variables $X$ and the error $\epsilon$ then the zero conditional mean may be violated. In your example, if you were to assign women their training time according to their age, then the exogeneity assumption breaks.

More formally, this last condition means

$$
\mathbb{E}[\epsilon|X] = 0
$$

If, wlog we assume $\mathbb{E}[\epsilon] = 0$, and there's a non-vanishing correlation between $X$ and $\epsilon$ then

$$
 0\not= \mathbb{C}{\rm ov}[X,\epsilon] = \mathbb{E}[X^t\epsilon] + \mathbb{E}[X] \mathbb{E}[\epsilon] = \mathbb{E}[X^t\epsilon]
$$

therefore $\mathbb{E}[\epsilon|X]\not = 0$


Why is Price Vector Orthogonal to Vector connecting two bundles on Budget Hyperplane

Note that $p$ is not orthogonal to consumption vectors on the budget line, but it is orthogonal to a any vector $v$ that satisfies $x+v=x'$ with $x,x'$ in the budget line. MWG are drawing vectors starting from some $x$.

About the slope: In the budget line you can see that the slope for any $x$ is $D_x (p.x)=p$ (that is the line that is drawn from $x$). That line or vector can be represented with the function $x_2=(p_2/p_1)*x_1$ (note that if $x_1=p_1$, $x_2=p_2$). The slope is $p_2/p_1$.

On the other hand, all vectors on the budget line satisfy $x_2=(-p_1/p_2)*x_1+w/p_2$. The slope here is $(-p_1/p_2)$. This slope is the rate of exchange. Both slopes imply that the two functions (the vector $p$ and the budget line) are orthogonal. Or maybe it's better to say that the orthogonality between the budget line and the vector $p$ imply that $dx_2/dx_1=-p_1/p_2$, that is, the last term captures the rate of exchange.


Prediction market based on LMSR: Sell, or buy other side?

For the market it does not matter, the prices/chances change exactly the same:
ea-10/(ea-10+eb) = ea/(ea+eb+10).

For you as the trader, selling 10 yes shares is preferable. It means you get your money out and can invest it elsewhere.


As I explained in the edited question, the comment-question made by @caverac made me write the models out in their respective long form versions. Doing this made it obvious that an MA(1) structure can be imposed and the model is shown below.  As far as I can tell, the long form of this model cannot be transformed to a lagged dependent variable model (what I refer to as the short form ) nicely like can be in the  AR(1) and pure noise cases.

Long Form of Koyck Distributed Lag Model With MA(1) error term:

$y_{t} = \beta \times \sum_{i=0}^{\infty} \rho^{i} x_{t-i} + \epsilon_t + \rho \times \epsilon_{t-1}$


What does "agent" mean in Pearce's formulation of extensive form rationalizability?

I have not read this paper in full, I am merely guessing based on some parts.

It seems to me that agent $ij$ is short for "agent $j$ for player $i$".

A player's strategy assigns a move/choice of action to each information set $I^{ij}$. Depending on the story of the game you can think about this move as being executed by the player herself or maybe just agents of the player. Kind of like with subgame perfection you can assume that the strategy must fullfil some conditions in each information set $I^{ij}$. When explaining these conditions it is easier to assume that the player does not have independent but somehow 'logically restricted beliefs' in every information set, but that all her agents have 'logically restricted beliefs'. So an agent $ij$ is basically just a player's strategy in $I^{ij}$.

By 'logically restricted beliefs' I mean the restrictions posed on conjectures.


Elasticity of subsitution: a redundant calculation?

Why would one need to graph the function? Isn't any information in the graph already given in the function?

In  a certain sense all calculations are redundant as they are mathematical tautologies. Yet these indices make some things more clear, which is obviously useful.


Greece default and why are US States not seen defaulting?

Two reasons:

The United States has a capable federal government that takes care of social insurance transfers and countercyclical economic policies. The American states spend less.
The American states have stronger anti-tax sentiments, and increasing public spendings face opposition from business and rich people.

Take the 2008 crisis for example.

As for 2008, all developed countries, including Greece, had a lot of bad debt in the private sector and a subsequent recession due to the credit crunch. The United States immediately approved two things in response: a $700 bn stimulus and the Fed's QE programs. They cleared bad debt and supported business in 2009.

These measures was done at the federal level. It's the federal government that took additional debt. And the debt looked like this:

(McKinsey - 2012 - Debt and deleveraging)

The EU was slower. And its recovery fund lent money to European countries (as if the US fed government lent money to the states), so increasing their debt-to-GDP levels. This is how the EU, IMF, ECB happened to be the holders of all Greek bonds and a demanding creditor, as for now.

In short, US states got their federal stimulus for free, while Greece had to buy the stimulus on its own.


Update of Fed mandate(2020) - "shortfalls of employment"

First, this is not change in mandate, Fed cannot just change its mandate unilaterally, as the mandate is given to Fed by US congress (see this Fed Richmond essay on that)  this is just change in its goals in pursuit of their current mandate.

Does "maximum employment" mean potential rate of employment?

According to Fed 'maximum employment' means:

Maximum employment is the highest level of employment or lowest level of unemployment that the economy can sustain while maintaining a stable inflation rate.

So taken at face value this would mean that by 'maximum employment' they mean  non-accelerating inflation rate of unemployment (NAIRU).

In what way does the substitution of "deviations" for "shortfalls" change the mandate?

It does not change the mandate at all, it changes the Fed's goals in pursuit of their current mandate. A deviation by definition means either positive or negative change from the target (eg unemployment being either above or below their target). If they only look at a shortfall from the target level that would mean they are only concerned if unemployment is above the target but not if it is below.


Causes of interlocking directorship connections between firms

I've heard of this phenomenon but not for the reasons you suggest:

  The largest corporations tend to have the most interlocks (Table 4).
  This may occur because the directors of the largest corporations are
  the most knowledgeable, the most capable, and the most accomplished
  men available. Other corporations would naturally seek their advice
  and would rather have them on their board than men of less ability.
  This may also occur, however, because of factors unrelated to
  managerial ability. The director of a giant corporation undoubtedly
  has more personal influence with other companies,  with potential
  investors, and with the government than the common man. Having the
  director from a large corporation on your board may also lead to
  profitable business with that corporation.

Dooley, P. C. (1969). The interlocking directorate. American Economic Review 59(3), 314–323