Reason for marginal revenue is less than price in monopoly I understand the fact that marginal revenue is less than price because in the monopoly firm faces a downward sloping demand curve.

As well as, by expanding output firm is going to lower the all the cost of its previous outputs as well.

However, I don't fully get the picture how this is appropriate.

Is there any good example in real life?

Most internet providers rarely consider to decrease their price to win market shares. One possible reason could be because the additional revenue P(Y) from a new costumer joining the provider, would not compensate for the total loss of revenue P'(Y)Y from the group of regular subscribers (Y = several millions?). Instead, most providers invest a lot of effort to discriminate between these two groups and try to propose interesting prices only for new subscribers.
In "real life", you may not observe such a foolish thing, and will find only few concrete examples of monopolies having reduced their price in the hope of winning market shares. It is not because you do not observe such a behavior, that monopoly theory is useless. Quite the contrary, the chapter explains why you rarely observe such a foolish behavior.


Where does the current debate stand on passive vs active monetary policy? The debate between active and passive monetary policy is mentioned in most macroeconomics textbooks. Where does the current debate stand? Has a consensus been reached among economists? Do economists today broadly agree that one is better than the other, or, at least that one is better than the other in certain situations etc.?

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


Why doesn't AD curve self-correct to higher price level in LR? In textbooks it is usually taught that once actual price level is higher than expected, short-run aggregate supply will eventually shift up so that new expected price level is closer to the actual price level, until AD and AS intersect at the long-run AS curve. But why doesn't the AD do the same thing? When people start to expect a high price level, they will bargain for higher income and interest rates, so they can now buy more things at any price level, that means AD will shift up also. Why such an asymmetry exists between AD and AS?

It does, in the long-run.  It's partly a question of response time, and as you outline, AD has intervening steps that AS does not (wages in most markets are sticky and take time to adjust, while sticker prices in many markets can change in a day or less).  In general, thinking carefully about response times will help alleviate some of the ambiguity in the models you're looking at.


What is the best way to estimate a demand curve? I did a linear regression on quantity sold and price for a good and simply the coefficients don't make any sense. number of observations = 16
Demand=1868 -14*P
Suply=0 +45*P
So p*= 1421.778  and Q*= 31.59507
Is there an error in the calculations? the P* =\$1421,778  does not make any sense since the product price is \$79. would it be due to the low number of observations? Or is a linear model not the most suitable for estimating a demand curve? if so which one would be best?

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).


Name for a tax that captures all goods and services produced? Is there a name for a consumption tax that basically captures the GDP (all goods and services produced in the nation)?

Value-Added Taxes (VAT) are supposed to capture most goods and services produced in the private sector, but there can be exceptions within a country’s laws.

Even if the exceptions were eliminated, there are some non-market components to GDP that would be missed (e.g. imputed values, like the “rental value of owner-occupied housing”). (You need to go into each country’s GDP definition to find the list of imputations.)


Is GARP trivially satisfied with only 1 good? As with all revealed preference work, when the number of goods is greater than 1, then GARP (Generalised Axiom of Revealed Preference) is not always trivially satisfied. However, is it always the case that GARP is trivially satisfied when bundles only contain one good?

My take on it is that it is possible to violate GARP when the consideration set is only 1 good. However, empirically speaking, it should never be observed, as it really does not make sense from any rational point of view (ceteris paribus).  So theoretically, it is possible to violate GARP in a 1 good economy, but this is something we would never imagine observing.

(I've been having this discussion with a supervisor, and he seems to believe that GARP should never be violated with one good as it makes absolutely no sense for it to occur, despite my argument that it is theoretically possible)

I assume by "GARP" you mean "Generalized Axiom of Revealed Preference". One can take GARP to be satisfied with one good, but it's a rather vacuous type of "satisfied"; with one good the concept "preference" don't really have any meaning. You can't have any preferences if there's only one option.


Strongly and strictly increasing utility functions What's the difference between Strongly and strictly increasing utility functions?

What I know is that if $x'>>x $ where $x'$ has all elements strictly greater than $x$ then $U(x')>U(x)$, I think this is the definition of Strictly increasing utility function. And if $x'>>x$ , then $U(x')\geq U(x)$, this is the definition of Increasing function(monotone) function. I've no idea about Strongly Increasing function. Can anyone show a graphical example if this strongly increasing assumption is violated, how will the graph look like? (Utility function's graph)

Reference is from GEOFFREY A. JEHLE PHILIP J. RENY, Advanced Microeconomic Theory.

The term strongly increasing function is non-standard in economics (and I believe also in math) and should have been clearly defined in the main text.

The following definitions are given only in their Appendix 1, p. 529 (2011, 3rd edition):

As the following text states:

  a strictly increasing function need not be strongly increasing, but every strongly increasing function is strictly increasing


OPEC's market share strategy: What is the benefit of market share in a fungible market? Coverage of the recent fall in oil prices frequently mentions OPEC's decision to defend their market share, sacrificing price in the process. I understand how market share is important from a marketing perspective: strong brand loyalty gives a firm power to charge a premium over similar products. However, since oil is fungible, what is the benefit of maintaining market share? When I buy oil today, I don't care who I bought it from yesterday, right? What is the benefit OPEC receives by maintaining market share?

The benefits of market share in the somewhat-fungible oil market:

pricing power (because OPEC is big enough to retain pricing power in the long term because they're a big % of the market. They're just choosing to not use that pricing power right now, perhaps because they're choosing to bankrupt competitors)
geopolitical strength

Note that there are additional explanations:

Saudi is one of the lowest short-run-marginal-cost producers, so you'd expect them to be one of the last to cut production, just through normal business, regardless of the other stuff
we know that most known fossil-fuel reserves are going to stay in the ground, so reserve-owners are now under pressure to try to ensure that theirs aren't, and someone else's are.
You could view the last few years as a sucker-trap: high oil prices lured in lots of investment into new production outside OPEC. An oil price below $30 bankrupts many of those new entrants, who have high debt-servicing costs and high production costs. And because of that, future investors will be much more wary, and require much higher returns
Saudi knew that the international sanctions on Iran were on the way to being lifted. If Saudi had cut oil production, it would have weakened its market strength (and thus also its political strength) relative to Iran upon its return to the international oil market.


What books to read to learn about geography and how it affects economic development? I saw youtube videos like how geography doomed Africa and heard how Japan's prosperity is an anomaly due to its isolation and they got me interested.

A good starting point which should be accessible to people at all levels is the book "Guns, Germs, and Steel" by Jared Diamond.

I believe this is one of the first and main seminal works in this area.

That being said, it is not settled science that geography (alone) can doom a country's economy.


Effect of exogenous parameter on three player SPNE profits Consider three agents $A_i$.

$A_1$ moves first and selects $0\leq q_1\in \mathbb{R}$. $A_2$ moves second and selects $0\leq q_2\in \mathbb{R}$. $A_3$ moves third and selects $0\leq p_1\in \mathbb{R}$ and $0\leq p_2\in \mathbb{R}$.  $0\leq x\in \mathbb{R}$ is a parameter.
$A_1$ tries to maximize $u_1(q_1,p_1, q_2,p_2, x)$, with $\frac{\partial u_1(q_1,p_1, q_2,p_2, x)}{\partial q_1}\geq 0$ and $\frac{\partial u_1(q_1,p_1, q_2,p_2, x)}{\partial p_1}\geq 0$, and independent of $q_2,p_2,x$. $u_1(q_1,p_1, q_2,p_2, x)$ is continuous in all its inputs.
$A_2$ tries to maximize $u_2(q_1,p_1, q_2,p_2, x)$, with $\frac{\partial u_2(q_1,p_1, q_2,p_2, x)}{\partial q_2}\geq 0$ and $\frac{\partial u_2(q_1,p_1, q_2,p_2, x)}{\partial p_2}\geq 0$, and independent of $q_1,p_1,x$. $u_2(q_1,p_1, q_2,p_2, x)$ is continuous in all its inputs.
$A_3$ tries to maximize $u_3(q_1,p_1, q_2,p_2, x)$, with $u_3(q_1,p_1, q_2,p_2, x)$ increasing for all $p_1<\bar{p}$ and decreasing for all $p_1\geq \bar{p}$; $u_3(q_1,p_1, q_2,p_2, x)$ decreases in $x$ and $q_1$; and $u_3(q_1,p_1, q_2,p_2\rightarrow \infty, x)=-\infty$; $u_3(q_1,p_1, q_2\rightarrow \infty,p_2, x)=-\infty$. $u_3(q_1,p_1, q_2,p_2, x)$ is continuous in all its inputs, but we do not know more about its properties for $p_2,q_2$.
We assume that in case that an agent is indifferent between two or more strategies that there exists a decision rule that selects exactly one of these strategies. These rules are known by all agents.

The existence of a unique SPNE is quite clear. However, there could be multiple other equilibria that would lead to the same profit profile (specifically equilibria in which each agent gains the same profits.)
Question: Does $A_3$'s profit decrease in $x$? If yes, why? If not, is there an easy assumption that we need for $u_3(q_1,p_1, q_2,p_2, x)$ behavior with regard to $q_2,p_2$? (I think I miss the forest for the trees) Does the sum of all agents' profit decrease in $x$?
My immediate intuition is yes, because otherwise $A_3$ would be able to pass on all its "losses" to the other agents.

Let's solve by backward induction.

In stage 3, player $A_3$ solves:
$$
\max_{p_1, p_2} u_3(p_1, p_2, q_1, q_2, x).
$$
Given the assumptions, $A_3$ will set: $p_1 = \overline{p}$ and in general $p_2$ will be a function of the $q_1, q_2$ and $x$, denoted by $p_2(q_1, q_2, x)$. For a solution to exist, you have to assume that $u_3$ is not unbounded in $p_2$.

As $u_2$ is independent of $p_1, q_1, x$, In stage 2, Player $A_2$ solves:
$$
\max_{q_2} u_2(q_2, p_2(q_1, q_2, x)).
$$
$u_2$ is increasing in $q_2$ and $p_2$. If $p_2(q_1, q_2, x)$ is increasing in $q_2$ then $A_2$ will set $q_2$ as big as possible, so there is no optimal solution. Else, there might be some optimal level of $q_2$, say $q_2(q_1, x)$.

In stage 1, player $A_1$ solves:
$$
\max_{q_1} u_1(q_1, \overline{p}).
$$
As $u_1$ is increasing in $q_1$ there will probably be no solution to this. So likely this problem is unbounded. If we assume that $q_1 \le \overline{q}_1$ for some fixed value $\overline{q}_1$, then $A_1$ will set $q_1 = \overline{q}_1$.

Going back to the utility of player 3, we therefore see, after substituting:
$$
u_3 = u_3(\overline{p}, p_2(\overline{q}_1, q_2(\overline{q}_1, x),x), \overline{q}_1, q_2(\overline{q_1}, x), x).
$$
It seems like the change in $u_3$ due to a change in $x$ is ambiguous. As it also influences the optimal choice of $q_2$ (of player $A_2$), and $p_2$ of player $A_3$.


How do Marxists account for fiat money? LTV predicts that fiat currency, which requires zero labor to produce, should have zero value. Empirically, fiat currency does not have zero value. How do Marxists account for this. The to responses I have gotten so far are that labor does go into printing(though very little in comparison to the price) and that fiat currency is merely a token of money. In which case what is the money in this regard and how can any of this be empirically tested?

Marx's theory of product-value is often called a "labour theory of value" though he never used it himself to describe his "law of value". He also had a theory of exchange-value to try to explain market phenomena.

Marx did have a theory of the materialisation of labour in gold. But fiat or credit money has no intrinsic value (if it did then it would not be fiat), though it does have an exchange value, broadly speaking the value that can be acquired by spending it.  Marx argued that the use of money obscured the real value ("congealed labour-time") involved in transactions and exchanges.

That is not really testable, but what may be testable is the extent that relative prices of different commodities reflect the labour involved in their production, and if so whether these reflections are of average or marginal labour, and what causes changes in relative prices over time.  Whether you would want to is another question: it is all a bit 19th century.


Interrelationship between inflation and foreign capital flow For the below let's assume domestic currency is ₹ and foreign capital is in \$

Foreign Capital Inflow => ₹ Appreciates (Because of more \$)

But consider this,

Foreign Capital Inflow => More ₹ in circulation (Since \$ have to be exchanged into ₹ before actually using in India) => More Inflation => ₹  Depreciation

What is wrong in this second reasoning?

I think the flaw in your reasoning is expecting that foreign capital inflow would lead to more ₹ in circulation.  When investors bring in capital, they are buying ₹ that were previously in circulation.  This additional demand without additional supply is exactly what drives the price of the ₹ up.  There is no increase in the quantity of ₹ circulating unless the government/central bank responds in some way.


How to show average cost is falling if we have IRTS Using maths how could I show this, I am able to show that AC>MC By differentiating AC with respect to q and assuming AC is falling , but how do show its falling in the first place if we have increasing returns to scale. Thanks

aso I know that IRTS means f(tz)>tf(z) where f is productions function gives us maximum amount of output for a given set of inputs Zi.

A production function $f: \mathbb{R}^k \rightarrow \mathbb{R}$ exhibits increasing returns to scale if for $\alpha > 1$:

$$ f(\alpha \mathbf{x}) > \alpha f(\mathbf{x})$$
This implies the directional derivative of $f$ at $\mathbf{x}$ in the direction of $\mathbf{x}$ is greater than $f(\mathbf{x})$. (Let $\alpha = (1+ \epsilon)$ then $\frac{f(\mathbf{x} + \epsilon \mathbf{x}) - f(\mathbf{x})}{\epsilon} > f(\mathbf{x})$ then take limit as $\epsilon \rightarrow 0$ to obtain $\nabla_\mathbf{x} f(\mathbf{x}) > f(\mathbf{x})$.)

Given a price vector $\mathbf{p}$ the cost function gives the minimum cost to produce a quantity $q$.

$$ c(q) = \min_\mathbf{x} \left\{\mathbf{p} \cdot \mathbf{x}  \mid f(\mathbf{x}) \geq q \right\} $$

The Lagrangian for this problem is $\mathcal{L} = \mathbf{p} \cdot \mathbf{x} + \lambda (q - f(\mathbf{x}))$. The first order condition is $\mathbf{p} = \lambda \nabla f(\mathbf{x}^*))$. Take the dot product of both sides with $\mathbf{x}^*$ to obtain $ c(q) =  \mathbf{p} \cdot \mathbf{x}^* = \lambda \nabla f(\mathbf{x}^*) \cdot \mathbf{x}^*=\lambda \nabla_{\mathbf{x}^*}f(\mathbf{x}^*)$.

Our previous result on increasing returns to scale then implies $c(q) > \lambda f(\mathbf{x}^*) = \lambda q$.  By the envelope theorem, marginal cost is $\frac{dc}{dq} = \frac{\partial \mathcal{L}}{\partial q} = \lambda$. Combining, this gives us marginal cost is less than average cost for an increasing return to scale production function:
$$ \frac{dc}{dq} < \frac{c(q)}{q}$$

That immediately implies average cost is decreasing in $q$.

Intuition

A more intuitive way to think about this is that increasing returns to scale in the production function implies that for $\alpha > 1$:

$$ c(\alpha q) \leq \alpha c(q)$$

If the production $f$ scales more than linearly in inputs, the cost of producing a quantity scales less than linearly. You can show this without any calculus at all.

Once you have that, divide by $\alpha q$ and you immediately obtain:

$$ \frac{c(\alpha q)}{\alpha q} \leq \frac{c(q)}{q} \text{ for } \alpha > 1 \text{ and IRTS}$$
That shows for an increasing returns to scale production function, a higher level of production has a lower average cost.


How to estimate Italian parking data starting from German parking data? I am currently investigating the economic impact of the parking pain in Italy. I have just found out this INRIX Research which is absolutely stunning, but it only focuses on US, UK and Germany market.
I was wondering if there is any indicator/KPI to derive the Italian Parking Pain Cost starting from Germany's data.
You can find below a summary snapshot from the report:

Here you can find a direct link to the public report.
Do you know any indexes or KPIs to take in consideration? How would you solve this problem?

I'm not entirely sure this would be possible to do using German data, though very happy to be corrected.
It seems that the data you have is largely driven by parking search costs, therefore could you not try and find internationally comparable data on travel to work time, control for a few bits and then try and see whether you can find parking search costs as having a significant effect? Then you could just apply that effect to the data on italian travel to work time and make the assumption that's reasonable.
For data:
The Italian statistical authority (https://db.nomics.world/ISTAT) provide some brilliant survey data on citizens views on quality of life - perhaps there's something you could infer from there, or view whether data is offered on expenditure on parking enforecemnt. Similarly, the WEF's Travel and Tourism/Global competitiveness index may have indicators on travel to work time.
A very all out approach would be to collect data on council meeting minutes to see how often parking comes up as an issue.


How does foreign trade work in a planned economy? I know that in a planned economy all economic processes are ruled by the state and that there are disadvantages such as too much bureaucracy and that sometimes deals are not always met with demand... But how is foreign trade ran in a planned economy and are there any advantages or disadvantages in such? And how do exporters deal and go ahead in a planned economy?

The trade in itself was not that much different per se but it was restricted and overseen by the government.
For example,  USSR was net oil exporter and most of its oil was sold for US dollars at international market prices and then USSR used dollars to buy imports that government officials decided to import. For example, you can see overview of trade in USSR in Zoeter (1983). This is really not that much different from Russia's state companies selling oil and gas at international markets now.
One peculiarity of trade in many centrally planned economies was that it was not rare to trade in kind, as due to general economic mismanagement most centrally planed economies had very weak currencies so they either had to trade paying with hard currency (e.g. dollars), or trade was conducted in kind as the famous Pepsi -  Stolichnaya vodka/warship in kind trade (yes as bizarre as it might sound that is not typo they exchanged some warships for Pepsi as well).
From economic point of view there is no advantage to government completely overseeing/controlling trade to this extent (I don't think there are many serious economists who would even entertain that as a serious option). A disadvantage of such arrangement is that government faces an informational asymmetry when it comes to the preferences and demand of its population, so when government tries to guess how much goods should it import it will likely get it often wrong resulting in shortages. In fact foreign consumer goods were as a result not even widely avaiable to ordinary citizens (see this Investopedia explainer). As a result foreign imports were often avaiable primarily through special shops (in Russia 'Beryozka') where people had to pay in hard currency effectively excluding ordinary non-privileged people, or through black market.   However, it is hard to disentangle how much this was due to mismanaging trade and how much due to general economic mismanagement under central planning.


What are some critiques to the principle of comparative advantage? The principle of comparative advantage says that, in a free market, any agent should produce more of the goods for which they have a comparative advantage. The model is usually applied to advocate for the benefits of international trade. This answer to another question has a great explanation of the theory. In the same answer, some commenters criticized the application of the principle to international trade as misleading.

I got curious about that critiques, so decided to ask a new question: what are some critiques of that model?

One of the most common critiques is that the standard model is a static analysis.  While a country might be better off today by focusing on its comparative advantage, its longer term prospects depend on the future of that industry, particularly on how quickly productivity can be improved.

For instance, in David Ricardo's original example, comparative advantage recommended that Portugal should produce wine while England produced cloth.  Maybe that's okay as a static analysis, but over time the productivity of wine production improved slowly whereas for England,

  exports of cotton cloth led to accumulation, mechanisation and the whole spiralling growth of the industrial revolution.

The idea that a country should temporarily distort free trade in order to establish industries in which it wants to develop a comparative advantage is often known as "dynamic comparative advantage".  The East Asian economies are frequently referred to as a good example of countries using these ideas successfully.  South Korea didn't start out with a comparative advantage in steel, for instance -- it created one through extensive state intervention.


Constant Returns to Scale and Positive Marginal Products In a simplified model in the search theory of unemployment, let $M=\mu{m(u,v)}$ be the matching function where $u$ and $v$ is unemployment and vacancies respectively. Given $m(u,v)$ has constant returns to scale and positive marginal products, how do we show that the job finding rate $f = M/u$ increases with labour market tightness $\theta=\frac{v}{u}$?

Given CRTS, I can rewrite $f$ as follows: $f=\mu{m(1,\theta)}=\mu{}m(\theta)$. How can you then show that given positive marginal products, we have $\frac{df}{d\theta}>0?$

Given $m(u,v)$ is CRTS we have the property that $m(u,v)=\frac{\delta{m}}{\delta{v}}v+\frac{\delta{m}}{\delta{u}}u$. Divide by $v$ to get in terms of $\theta$: $m(\theta)=\frac{\delta{m}}{\delta{v}}+\frac{\delta{m}}{\delta{u}}\theta$.

Thus, it clearly follows that:

$\frac{df}{d\theta}=\mu\frac{dm(\theta)}{d\theta}=\mu\frac{\delta{m}}{\delta{u}}>0$ given that we have positive marginal products


Do Hong Kong highschool teachers earn more than Hong Kong quants? According to Teach in Hong Kong, Hong Kong highschool teachers earn around

  HK\$23,530 to HK\$54,665 (approximately \$3,000-\$7,000 USD) per month

while CUHK's Quantitative Finance Graduates Face Encouraging Employment Status (2004) says Hong Kong quants, at least those who are fresh graduates, have an initial

  average monthly salary of HK$13,291.

Is there anything suspicious about this? I would expect quants to earn more than highschool teachers. Then again, the figure for quants is for fresh grads while the figure for highschool teachers is for those who have at least 2 years teaching experience and with education degrees (eg PGDE).

As you said it doesn’t make sense to compare entry level finance jobs with non-entry level normal jobs. Salary increase in finance is usually quite large - also many have bonus schemes, which many statistics leave out of the “average salary”. Over time definitely the Quant will make more than the school teacher.


How saving and investment influence growth in the long run? Here are 4 points from my class.

  • Because resources are scarce, devoting more resources to
  producing capital requires devoting fewer resources to producing
  goods and services for current consumption.

  • Consequently, the accumulation of capital involves a tradeoff.

  • When governments encourage saving and investment, they also
  encourage growth and in the long run this raises the standard of
  living.

  • A well-functioning and carefully regulated financial market, one
  that quickly and efficiently brings savings and investment together
  with minimal risk and in a transparent way, is a critical ingredient
  in the recipe for economic growth.

I can conclude that saving and investment are good for growth, but I cannot tell exactly why. Can someone make it clearer, maybe with a concrete example?

The result you are asking about follows more formally from the Solow model. It's definitely worth looking into. I won't go into the model specifics, since I believe you are after a simple example.

First, note that what economists refer to as capital is not really what most people mean when talking about capital. For us, capital is typically a production factor that is not labor. A good example is a machine. For agriculture it could also be something like fertilizer. These are all things that help you produce more and that is how you get growth from capital.

Suppose you are a farmer who can produce 10 potatoes a year currently. You sell those potatoes and then can decide to spend that money consuming (e.g. buying steaks) or you can invest it in "capital". If you spend the money on a tractor and some fertilizer, you can produce 20 potatoes next year. That is how investment leads to growth. That is also why you need to give up some consumption today in order to grow your production and have more consumption tomorrow.


How to calculate Debt to GDP ratio quarterly? I know the formula Debt to GDP ratio = Debt : GDP
I have debt quarterly data and GDP (yearly and quarterly).
The one that make me confuse is, when i use Debt Q1 2014, for example it wont match with GDP (since GDP is only for 3 months January-March).
What type or Which GDP date should i use as denominator, GDP Q4 2013, or GDP Q4 2014?

Debt is a stock variable, measured in dollars. (I will use “dollars” for the local currency for simplicity.)
GDP is a flow, with units of dollars per accounting period.
These two concepts are different, and so any ratio is a convention, without any “correct” answer.
Let’s assume that we want to follow the usual convention, and divide the stock of debt by the GDP generated during time it takes for the Earth to go around the sun. There are a number of standard ways of doing this.

Take the debt level at the end of the year, divide by the total of GDP for the same year (sum of four quarters). This gives us an annual series.
For any quarter, take the debt at the end of the quarter, and divide by the rolling 4-quarter sum of GDP.
For any quarter, take the debt at the end of the quarter, and divide by the annualized quarterly GDP.

One could imagine even more alternatives, such as comparing the average level of debt in the year to annual GDP.
You just choose one, and explain your choice.


What is low unemployment and low gdp growth symptomatic of? Obviously there are caveats with GDP, if you build a bridge to nowhere it counts as GDP, but if you mow your own lawn or volunteer to pick up garbage it doesn't count, and so forth and so on. However, assuming unemployment is low, then one could argue people would have less time to preoccupy themselves with volunteer work and contribute to the "economy" as measured by GDP.

I had Germany in mind at the time of writing, so use Germany as a default for the economy in question for this post. Nonetheless, at the risk of going too broad, I think this question can just as easily be posed for the general case. So feel free to broaden the scope beyond Europe.

Question

What is the prevailing theory behind a country exhibiting low unemployment but also low or even negative growth in gdp?

For brevity, you can specify which GDP you assume (inflation-adjusted, income approach or expenditure approach) or for robustness you can try to address low unemployment coupled with low gdp growth implications under all 3 measures of GDP

One simple explanation can just be that unemployment is artificially low. Perhaps many people went out of the labor force (i.e. stopped looking for a job) after a long period of not being able to find one, and now they don't count as unemployed in the data. Similarly, maybe the economy is not growing enough to create good jobs, but many people are partially employed so that the unemployment rate looks artificially low again because even though people have jobs, they might want to work more hours, but can't.

There might be other more interesting causes, but I think that exploring them will require to zoom in a particular country and take into account the institutional details, etc.


What is the logic of Bagehot's policy of high interest rate? I have a doubt about monetary policy, as suggested by Walter Bagehot. He wrote a book "Lombard Street" in 1873, to comment on a recent banking crisis. There he recommends these measures to stop a banking panic:

That the central bank lend freely.
At a high rate of interest.
On good banking securities.

The second point is particularly puzzling. In his own words:

  First. That these loans should only be made at a very high rate of interest. This will operate as a heavy fine on unreasonable timidity, and will prevent the greatest number of applications by persons who do not require it. The rate should be raised early in the panic, so that the fine may be paid early; that no one may borrow out of idle precaution without paying well for it; that the Banking reserve may be protected as far as possible.

(From Wikipedia: https://en.wikipedia.org/wiki/Lombard_Street:_A_Description_of_the_Money_Market)

This goes counter the main narrative in the press today, which is that central banks have to lower the interest rate in order to increase lending and economic activity, not to increase it. Bagehot's policies could actually exacerbate the crisis! A high interest rate might produce deflation, which exacerbates debts, like in the Great Depression. What is going on here?

We need to distinguish between a crisis and a normally functioning financial system. During a crisis, there is an unwillingness to lend  against collateral at any price (interest rate). Financial firms are liquidity constrained, and they assume that the entities that want to borrow are similarly constrained. Being able to fund positions in securities at any price is a huge relief, since that means you are not forced to sell (at a distressed price).

As an example, imagine that a financial firm needs to borrow at 12% interest to finance a position in corporate bonds. If that borrowing is done for a month at that rate, the total interest cost would be 1%. This is probably going to be much less costly than being forced to sell the position; a loss of 20% would not be unusual in such a situation.

Furthermore, the crisis lending is done by the central bank to financial firms facing financing issues; it is not aimed at the broad public. During the Financial Crisis, lending programs were aimed at banks and security markets, not non-financial entities.

The level of short-term rates does not really matter that much; once the markets return to normal, you will be able to fund your positions at a much better rate. Having to pay a high rate of overnight interest for a week on a long-term security is not a big deal.

The argument for lender-of-last-resort operations at a high level of interest is that you do not want this facility to be a regular source of financing for the financial system.


Are businesses included in economic institutions? 1st definition from businessdictionary.com:
Network of commercial organizations (such as manufacturers, producers, wholesalers, retailers, and buyers) who generate, distribute, and purchase goods and services. See also financial institutions.

2nd definition from econlib.org:
1. Specific agencies or foundations, both government and private, devoted to collecting or studying economic data, or commissioned with the job of supplying a good or service that is important to the economy of a country. The Internal Revenue Service (the IRS—the government tax-collection agency), the U.S. Federal Reserve (the government producer of money), the National Bureau of Economic Research (a private research agency) are all examples of economic institutions.
2. Well-established arrangements and structures that are part of the culture or society, e.g., competitive markets, the banking system, kids' allowances, customary tipping, and a system of property rights are examples of economic institutions.

Which one is correct? Also, on wikipedia it says businesses are a part of institutions. https://en.wikipedia.org/wiki/Institution

Unfortunately, economists don't have a standard, universally-accepted definition of what an 'institution' is.

Hence, depending on what you're trying to study and whom you ask, businesses may or may not be an institution. So, in a way, both definitions are correct.

If you're interested in different conceptual approaches to institutions, Avner Greif has written an interesting survey on it, with plenty of references that might be worth looking at.


How to estimate "necessary" economic output using Leontief input-output impact analysis? In particular: how to handle imports I'm trying to estimate what the "necessary" economic output of a society is using Leontief input-output impact analysis. The data I have available is OECD input-output tables (see link). I'm not a trained economist, so please correct any mistakes you see in my thinking.
My idea for how to make this estimation is the following: proceed with a standard impact analysis and get the Leontief matrix L. Then check how much economic output x_need that remains  if we let the consumers spend only a "living-wage budget" proportionally to the different sectors of the economy (so if 50% of spending in the original demand goes to say food, then 50% of the living-wage final demand should also go to food). So basically: calculate x_need by f_need, where f_need is the new final demand vector that has been altered by letting private consumers only spend their living-wage-budget. Then we can compare x_old and x_need to see the differences in economic output.
I hope that this so far is not controversial.
Now here's the question: how do I handle imports (and exports) in the construction of f_need?
I want f_need to represent the final demand of the domestic private consumers when spend precisely their living-wage-budget. Exports can probably simply be removed since they don't provide goods and services to the domestic population. But what about imports? How do I best deal with them in my estimation? I see two general strategies for how to do so:

Ignore imports. Alter private domestic consumer according to their living-wage-budget, remove exports, and ignore imports (i.e. don't make any changes in how imports affect final demand f_need). This gives us f_need, which we can use to create x_need for comparison with the original economic output x_old.
Assume that all imports are domestically produced. Create and compare x_need to the economic output x_own_produce the country would have if all imports were produced domestically. Get x_own_produce from a final demand vector f_own_produce that we get by assuming that all imports are domestically produced. Get f_need by removing exports and assuming that domestic consumers only spend according to their living-wage-budget. We can then get x_need from f_need, and finally compare x_need with x_own_produce.

I hope that the above is understandable. Let me know what I need to clarify otherwise.
Detailed questions:
Which of the two general strategies gives a better estimation? Are there better strategies that I can use to make my estimation?
Any (constructive) feedback is appreciated.

If you want to model exports and imports you need  interregional (or multiregional) Leontief input–output model instead of standard one.
The way how these models work is that you will have separate foreign sector in your input output model, along what you can see in the table below (taken from Hewings, G. J., & Jensen, R. C., 1987):

This is in spirit similar to assuming that foreign are just some other production sector - but the issue is that spending and productivity might not necessary be the same as at home. There is also more nuance to it. I would recommend going over the above mentioned Hewings, & Jensen (1987) which has all the details on how input-output analysis is different for open economy.


Imports not used in the country, still counting in the GDP calculation? When we calculating GDP we use the given formula

$GDP = C + I + P + X - M$

Here $M$ means the imports.
My question is: What if I am not currently using the imports. For example I might have by the goods and preserve in the warehouse. In that case, Do the imports really affects GDP.

GDP is the total amount of domestically produced output in the referred period. If $C^H$ is the consumption of domesticly produced goods, $C^F$ is the cosumption of goods produced abroad,
$G^H$ is the government expenditure on domesticly produced goods, $G^F$ is the government expenditure on goods produced abroad and so on we have:
$$GDP = C^H + G^H + I^H + X = \\
C-C^F + G-G^F + I-I^F + X =\\
C + G + I + X - (C^F +G^F +I^F) \\= C + G + I + X - M$$
That is imports do not affect GDP from accounting point of view. It is just easier to subtract them directly as in the last equation although we are after the first.
My textbook (Mankiw) used to say: If you purchase goods abroad and store them, this is an investment into inventory in the period in which they were imported i.e. $I^F$ goes up. This is the same as if you produce a car at home and fail to sell it. In this case the car is counted in $I^H$.


USD/CAD fx: What's the difference between Buying USD and Selling CAD? Beginner question here.
I'm Canadian, and my investement account is, by default, in CAD currency.
Recently I wanted by buy a US stock so I had to convert some of my CAD money in USD money.

There would have been other ways, but this led me to use an FX tool. The interface was similar to this:

Action: [ ] Buy [ ] Sell

Currency: [ ] CAD [ ] USD

So basically, in order to do what I wanted to do (convert CAD to USD), I had 2 options:

A) Buy USD

B) Sell CAD

What's the difference between both actions ?

Should be no difference.

You are either (1) buying USD by selling CAD or (2) selling CAD to buy USD.


How will the UK's economy be affected, if it will be a hard Brexit? Will the outcome of Brexit have any positive impact on the UK market? Are there any available studies on this topic?

The UK government published "Implications for Business and Trade of a No Deal Exit on 29 March 2019" on Tuesday.


Calculating Gini Coeffecient What's the fastest way (or formulae) of manually calculating Gini Coefficient of equal-sized bin income data?

Example:
No of individuals in group: 4 4 4 4 4
Income of each group:       1 2 3 4 5
respectively.

All of these answers are true but don't provide an easy solution which doesn't use excel/code. Gini can be fairly easily computed by hand too.

The Gini coefficient fundamentally shows the shaded region above the lorenz curve in order to get a relative gauge of the distance the lorenz curve is from the line of equality. Fundamentally what this shows is the average distance between incomes. with 1 being the highest possible income and 0 being the lowest.

One way to calculate this is to simply calculate the area between the line of equality and the Lorenz curve.

This is clearly pretty difficult to do. Luckily there is an easier method.

Gini is also equal to: (The average variance for all incomes) / (2 * the mean)

The average variance for all incomes can be calculated by constructing a matrix of all incomes and then calculating the distance between each income.

For your example:

  | 1   2   3   4   5
__|___________________
1 | 0   1   2   3   4
2 | 1   0   1   2   3
3 | 2   1   0   1   2
4 | 3   2   1   0   1
5 | 4   3   2   1   0

Then add up all of the distances within the matrix to get the total variance.

0 + 1 + 2 + 3 + 4 + 1 + 0 + 1 + 2 + 3 + 2 + 1 + 0 + 1 + 2 + 3 + 2 + 1 + 0 + 1 + 4 + 3 + 2 + 1 + 0 = 40.

Then divide it by the total number of elements within the matrix to get the average variance.

Average Variance = 40 / 25 = 1.6.

Now divide the average variance by the average income times two.

Mean = (1 + 2 + 3 + 4 + 5)/5 = 15/5 = 3

Mean*2 = 6.

Since the gini is equal to: (The average variance for all incomes) / (2 * the mean):

Gini = 1.6 / 6 =  .2666

Which is what the other users got through more complicated methods.


Roy's identities for Stone-Geary utility functions I'm having trouble showing Roy's identity for the following Stone-Geary utility function:

$$U(x)=\prod_{i=1}^n\left(x_i-\gamma_i\right)^{\beta_i}$$

where $\sum \beta_i=1$ and $\gamma_i$ is the minimal consumption of $x_i$.

I showed that the Marshallian demand (which I confirmed using multiple sources) is

$$x_i=\gamma_i+\frac{\beta_i\left(I-\sum_{j=1}^np_j\gamma_j\right)}{p_i}$$

Therefore, the indirect utility function is

$$V(x)=\prod_{i=1}^n\left(\frac{\beta_i \left(I-\sum_{j=1}^np_j\gamma_j \right)}{p_i} \right)^{\beta_i}$$

I applied a monotone transformation to simplify the indirect utility function:

$$W(x)=\sum_{i=1}^n\beta_i\left(\left(\ln(\beta_i)+\ln \left(I-\sum_{j=1}^np_j\gamma_j \right)\right)-\ln(p_i)\right)$$

Therefore,

$$\frac{\delta W}{\delta p_i}=\frac{-\beta_i\gamma_i}{I-\sum_{j=1}^np_j\gamma_j}-\frac{\beta_i}{p_i}$$

$$\frac{\delta W}{\delta I}=\frac{\beta_i}{I-\sum_{j=1}^np_j\gamma_j}$$

$$-\frac{\delta W / \delta p_i}{\delta W / \delta I}=\gamma_i+\frac{I-\sum_{j=1}^np_j\gamma_j}{p_i}$$

Basically, as you can see, something doesn't add up: the $\beta_i$ is missing from the numerator. Thus, Roy's inequality is not verified. Where did I mess up?

(Note: I've also tried without the transformation. This is a much more tedious process but it yielded the same answer; the $\beta_i$ was still missing)

Monir is correct to point out in the comments that $\ln$ is not a linear transformation. It is an increasing transformation, however, and so should not matter as long as

$$ \sum_{i=1}^n p_i \gamma_i < I$$

In any case, your mistake is in the derivatives you find. Here are the correct expressions:

$$\frac{\partial W}{\partial p_i} = -\gamma_i \sum_{j=1}^n \frac{\beta_j}{I - \sum_{k=1}^n p_k \gamma_k} - \frac{\beta_i}{p_i} = -\frac{\gamma_i}{I - \sum_{j=1}^n p_j \gamma_j} - \frac{\beta_i}{p_i} $$

$$ \frac{\partial W}{\partial I} = \sum_{j=1}^n \frac{\beta_j}{I - \sum_{k=1}^n p_k \gamma_k} = \frac{1}{I - \sum_{j=1}^n p_j \gamma_j} $$

Roy's identity then gives you the Marshallian demand you've initially, and correctly, derived.


Is the forex market a form of bartering? I had this showerthought that the forex market is pretty much currency bartering. The forex market seems to be different from commodity or stock markets in that you exchange one currency for another. How does the forex market resemble and differ from bartering?

No by definition forex is not bartering. By definition (see here) bartering is

Barter is an act of trading goods or services between two or more parties without the use of money (or a monetary medium such as a credit card). In essence, bartering involves the provision of one good or service by one party in return for another good or service from another party.).

In forex market you are exchanging money for money. Even if you would want to consider the foreign currency a good on an account that it is not legal tender in your country of residence (which would be debatable), you are still exchanging money for that good - not another good. So this cannot be barter exchange by definition.


Contest game: second order condition satisfied, but negative profits? The following is taken from Nti (1999)

Consider a 2 player game in which each exerts effort in attempt to win a prize. Let $V_1$ be player $1$'s valuation of the prize and let $V_2$ be player $2$'s valuation, where $0<V_1< V_2$. Player $1$ and $2$ expend efforts $x_1$ and $x_2$ respectively to win prize $p=1$. The cost of effort is $1$ per unit. Given a profile of effort levels ($x_1$, $x_2$),the probability that player i wins the prize takes the symmetric form

$$p_i(x_1,x_2)=\frac{x_i^r}{x_1^r+x_2^r}$$

$r$ is the returns to scale parameter associated with effort $r>0$. Profit is

$$\pi_i(x_1,x_2)=v_i\frac{x_i^r}{x_1^r+x_2^r}-x_1$$

In equilibrium (Nash-Cournot) player $i$ exerts effort $x_i^*$: $$x_i^*=\frac{rv_i^{r+1}v_{-i}^r}{(v_1^r+v_2^r)^2}$$

If both follow the equilibrium strategy, $i$'s probability of winning is
$P_i=\frac{v_i^r}{v_1+v_2^r}$. Inserting these two into the second equation for player 1 (with simplification) yields

$$\pi_1(x_1^*,x_2^*)=\frac{v_1^{r+1}}{(v_1^r+v_2^r)^2}\big[v_1^r+v_2^r-rv_2^r\big]$$

The second order (sufficiency) condition $\frac{\partial^2\pi_1}{\partial{x_1^2}}=\frac{rv_1^{1-r}x_2^rx_1^{2r-2}}{(x_1^r+x_2^r)^3}\big[rv_2^r-v_2^r-v_1^r-rv_1^r\big]$ is satisfied iff $$rv_2^r-v_2^r-v_1^r-rv_1^r<0$$

However, it is clear that for $x_1^*$ to be a Nash Equilibrium, $\pi_1(x_1^*,x_2^*)\geq0$ and hence that $$v_1^r+v_2^r>rv_2^r$$

which is a stronger requirement than the second order condition. Hence, it is possible that the second order condition is met but not that $v_1^r+v_2^r>rv_2^r$. My question is what happens when this occurs? Is there no Nash equilibrium here? Does the player who makes negative profit drop out, if so what does the remaining player do?

Well it says in the paper on p. 423:

"Thus the sufficiency assumption implies a unique pure strategy equilibrium. And if the sufficiency assumption is violated, at least one player will receive a negative payoff; that player can improve by reducing his or her effort to zero, which will destroy the equilibrium." [emphasis mine]

So that player will not make any effort because he/she cannot win. I leave it to you to figure out what the best reply from the other player is in that case.

I guess to be completely mathematically correct one would have to formulate these kind of games with non-negativity constraints, but because it complicates the analysis they're often left out and an interior equilibrium is either assumed or, as here, checked afterwards.


What happens to a production possibilities curve whenever there is too much labor? If too much labor is added to a country's production, what happens to the production possibilities curve?

What should happen? It grows. A production possibilty curve shows that the number of goods that can be produced is limited. If there is "more workforce than needed" (supply of work exceeds demand), prices for work descend, due to competition. That means that you can employ more people with the same capital. So if there are enough of the other limiting production factors (such as soil) available, you can produce more of both products.
Of course the product which is more labour-intensive (in the often used example of butter and guns that would probably be the guns) will profit much more from that.


The new Keynesian IS curve: What determines output? The New Keynesian IS curve can be described by the following (log-linearisation around the steady-state):$$y_t=E_t(y_{t+1})- \frac{1}{\theta}(i_t - E_t\pi_{t+1}-\rho)$$
where $\displaystyle\frac{1}{\theta}$ is the intertemporal elasticity of substitution in consumption, $\rho$ the discount rate,  and the remaining terms have their usual interpretation.
In the book Dynamic Macroeconomics, by Alogoskoufis, in chapter 16 (page 461), the author states:

Recall that this is nothing more than the Euler equation for
consumption, supplemented by the assumption that all output is
consumed, and the same relation was derived in the new classical model [it's eq. 14.10]
of chapter14. However, in contrast to the new classical model, where
output is determined by aggregate supply, in this model, because of
staggered pricing, output is determined by aggregate demand. Thus, it
is the IS curve that drives output ﬂuctuations.

I do not understand in what way is the output being determined by aggregate supply in the free price setting, nor by the aggregate demand in the sticky prices one.

The solution to your question is price stickiness, or as the author calls it staggered pricing. Let's assume a typical question in the Basic New Kenesian DSGE Model: What happens when a technological shock hits the economy?
More productive firms can produce cheaper but may not be able
to lower their prices due to price rigidities thus demand from the households stays at a lower level. The market clearing condition is supply equals demand and since demand won't increase output in the economy will be constraint (your paper uses determined but this might be the source of confusion) by the demand side. In this scenario one speaks from a negative output gap (Output is depressed in comparison to a world with flexible prices). In a flexible price scenario firms can lower their prices and thus household simultaneously increase demand, as firms want to increase production.
If you want to know more about price stickiness the basic DSGE models often implement the form suggested by: Calvo, Guillermo, “Staggered prices in a utility-maximizing framework,” Journal
of Monetary Economics, 1983, 12 (3), 383–398.


Data Set of Bourguignon and Morrison 2002 AER This question is about the following paper:

F. Bourguignon and C. Morrison "Inequality among World Citizens: 1820-1992", American Economic Review, Vol. 92, No. 4. (Sep., 2002), pp. 727-744.

On p.730, the authors say that

  The data, data sources, and assumptions behind them are available at:
  (http://www.delta.ens.fr/XIX).

But the link is dead.

Does anyone know where their data can be accessed /downloaded?

P.S. I am interested in data which were used in calculating Gini and other indices reported in the paper.

The wayback machine has snapshots: https://web.archive.org/web/20120217010359/http://www.delta.ens.fr/XIX/


Walras's Law V.S Say's Law- Is there a difference? I've been going over the concept of Walras's Law and often references to Say's Law. I've heard and have seen online that they are really the same thing however by looking at the definitions I notice a common difference.

  Walras’s law:
  “For any price vector $p$, we have $()≡0$; the value of the excess demand  is identically zero.”

  Where excess demand $z(p)$ is defined as:
  $$z(p)=\sum_{i=1}^n(x_i(p,m)-\omega_i)$$
  where $x_i(p,m)$ is our marshallian demand for good $i$  and $\omega_i$ is the initial endowment of good $i$.

Conversely,

  Say's Law:
  "aggregate production necessarily creates an equal quantity of aggregate demand" (from Wikipedia).

  or $$Q_s(p)=Q_d(p)$$

Would it be safe to say that Walras's Law makes reference to only consumer demand (which is transferred through a market and is not "consumed" by the firm themselves via inventory investment), While Say's Law is a statement regarding both demand by consumers and producers regardless of whether or not it goes from producers to consumers or producers back to themselves in form of inventory investment?

The rationale for this argument comes from the fact that we do conciser inventory investment to be included in demand even though it does not change hands in a market.

The way you have defined excess demand, it is only consumer excess demand. But Walras's law holds in any private ownership economy at all prices (at which demand and supply are well defined). Walras's law is basically equivalent to consumers spending their budget fully.

Let there be $l$ commodities, so every commodity bundle is an element of $\mathbb{R}^l$. There are $m$ consumers and $n$ firms. The set of production plans firm $j$ can produce in terms of net-output is $Y_j$. With this convention, if $p\in\mathbb{R}^l$ is the price system and $y\in Y_j$ a production plan, $p\cdot y=\sum_{k=1}^l p_k y_k$ is the resulting profit. Every consumer has an endowment $\omega_i\in\mathbb{R}^l$ and a (potentially zero) share $\theta_{ij}$ in firm $j$ and the resulting profit. Every firm is privately owned, so each firm's shares sums to one, $\sum_{i=1}^m\theta_{ij}=1$.

At the price system $p$, the budget of each consumer is $p\cdot \omega_i +\sum_{j=1}^n \theta_{ij} p\cdot y_j$. If the consumer $i$ demands $x_i$ and spends their whole budget, we have $p\cdot x_i=p\cdot \omega_i +\sum_{j=1}^n \theta_{ij} p\cdot y_j$. Summing up and using that prices are linear,
$$p\cdot\sum_{i=1}^m x_i=p\cdot\sum_{i=1}^m\omega_i+p\cdot \sum_{i=1}^m\sum_{j=1}^n \theta_{ij}y_j$$
$$=p\cdot\sum_{i=1}^m x_i=p\cdot\sum_{i=1}^m\omega_i+p\cdot \sum_{j=1}^n\sum_{i=1}^m \theta_{ij}y_j$$
$$=p\cdot\sum_{i=1}^m x_i=p\cdot\sum_{i=1}^m\omega_i+p\cdot \sum_{j=1}^ny_j$$
$$=p\cdot\bigg(\sum_{i=1}^m x_i-\sum_{i=1}^m\omega_i-\sum_{j=1}^ny_j\bigg)=0,$$
so the value of aggregate excess demand is zero and Walras's law holds. But nothing in the argument requires prices to clear markets so that supply equals demand,
$$\sum_{i=1}^m x_i-\sum_{i=1}^m\omega_i-\sum_{j=1}^ny_j=0.$$
The latter is clearly a sufficient condition for excess demand to have the value zero, but very far from necessary.

Walras's law is a provable result under some standard assumptions (that guarantee that consumers spend their whole budget), but Say's law is not a formal result in any way.


Confused about what is meant by adjusting for inflation In class, we have been using this calculator in order to see the effects of inflation.

https://www.rbnz.govt.nz/monetary-policy/inflation-calculator

I am slightly confused by what is meant by "adjusting for inflation". I read online that this means the effect of inflation is removed. I've also listened to a lot of speeches where people talk about adjusting for inflation.

In the case of this calculator, what does it mean to adjust for inflation? It doesn't mean we remove the effect of inflation, right? And is CPI used to measure the increase in inflation?

And with this calculator, are real or nominal values being used?

(I've been studying economics for a couple of weeks, so sorry for the basic question!)

Things change in price over time. For example, a movie ticket in 1955 might cost \$.50, and a movie ticket today costs about \$10, 2000% as expensive in 2019 as in 1955. (source)

These are nominal prices. That is, what is the number of dollars I need to pay for a movie ticket?

However, these nominal prices might go up for two reasons. It could be that the item is getting more valuable. Or it could be that the dollar is getting less valuable. In other words:

(1) One is that the relative price of movie tickets might be going up. That is, movie tickets are getting more expensive relative to other goods. For example, imagine a loaf of bread also cost \$.50 in 1955, but cost \$5 today (I'm making these numbers up). In 1955, you'd have to give up one loaf of bread to have enough money to buy a movie ticket. But today, you'd have to give up two loaves of bread to buy a movie ticket. So movie tickets have gotten more expensive relative to bread.

(2) Another reason that movie tickets might get more expensive is because everything gets more expensive together. In other words, the value of the dollar drops. In 1955, you could trade a single dollar for two movie tickets, or for two loaves of bread. Today, you can't trade a single dollar for even one of either. In other words, a dollar today is less valuable than a dollar in 1955.

This second reason, where the value of the dollar drops, is called inflation.

Adjusting for inflation is a process of getting rid of any price changes that happen for reason (2). This is done by calculating (usually using something called the Consumer Price Index) what the prices of things would be if the dollar still had the same value that it did in a different year - if inflation had not occurred (we've adjusted for inflation).

According to the US Inflation Calculator, a single dollar in 1955 is 855.8% as valuable as a single dollar in 2019.

So that 2000% comparison of movie ticket prices we had before? That actually represents that movie tickets are 2000/855.8 = 2.34 (234%) as expensive in 2019 as in 1955 - a 134% increase in relative price. The rest of the nominal price increase is because the dollar itself got weaker.


Intuition: Difference in price elasticities of demand due to different bases Source: pp 91-92, Principles of Microeconomics, 7 Ed, 2014, by N Gregory Mankiw

  If you try calculating the price elasticity of demand between two points on a
  demand
  curve, you will quickly notice an annoying problem: The elasticity from
  point A to point B seems different from the elasticity from point B to point A. For
  example, consider these numbers:
  Point A: Price = \$4, Quantity = 120
  Point B: Price = \$6, Quantity = 80

  Going from point A to point B, the price rises by 50 percent and the quantity falls by
  33 percent, indicating that the price elasticity of demand is 33/50, or 0.66.
  By contrast,
  going from point B to point A, the price falls by 33 percent and the quantity
  rises by 50 percent, indicating that the price elasticity of demand is 50/33, or 1.5.     $\color{darkred } { \text { This
difference}}$ arises because the $\color{darkgreen } { \text {percentage changes are calculated from a different base.}   }$

Though I calculated these 2 different price elasticities of demand and understood the last sentence, the big pictures or the deeper intuitions elude me? How can I naturalise this such difference?

What's the intuition behind  $\color{darkred } { \text { This
difference}}$, caused by $\color{darkgreen } { \text {percentage changes [that] are calculated from a different base}   }$ ?

The solution to this issue is called "Arc Elasticity", used for "large" absolute changes. On the surface, the formula for Arc Elasticity is the familiar one, for example for price elasticity of demand

$$\eta_{arc}= \dfrac{ \text{
Percentage change in quantity demanded }} {  \text{ Percentage change in price } }$$

But the thing is how these percentage changes are calculated: If we went from quantity $q_a$ to quantity $q_b$, then while we "usually" calculate the percentage change as $(q_b-q_a)/q_a$ for the Arc Elasticity we divide by the mid-point of the interval -not by the point we started with. Same for price. So

$$\eta_{arc}= \dfrac{ \text{
Percentage change in quantity demanded }} {  \text{ Percentage change in price } } = \frac {\frac {q_b-q_a}{(q_b+q_a)/2}}{\frac {p_b-p_a}{(p_b+p_a)/2}}$$

$$\implies \eta_{arc} = \frac {q_b-q_a}{p_b-p_a}\cdot \frac{p_b+p_a}{q_b+q_a}$$

Re-arrange the terms at will to suit your own mnemonic triggers.

The Arc Elasticity has the convenient properties

(1) it is symmetric with respect to the two prices and quantities,
(2) it is independent of the units of measurement,
(3) it yields a value of unity if the total revenues (price times quantity) at the two points are equal.

See Allen (1933).

P.S. to OP: Use this for your other question.


Hedonic regression and attribute-shares in house prices Given a house with price $P$ and attributes $h_1,\dots,h_n$, I want to estimate how much each attribute costs as a percentage of house price $P$. In other words, if we express house price as the sum of the costs of individual attributes
\begin{equation}
P=c_0+c_1h_1+\cdots+c_nh_n,
\end{equation}
where $c_0$ is the "baseline cost" of a house and $c_1,\dots,c_n$ are costs of housing attributes $1,\dots,n$, I'm interested in computing
\begin{equation}
p_i=\frac{c_ih_i}{P},\quad i=1,\dots,n,
\end{equation}
where $p_i$ can be interpreted as the cost share of attribute $i$ of a house with price $P$.

Suppose I have data on $P$ and $h_i$'s. The natural way is to run a hedonic regression to estimate the $c_i$'s. However, I face the following difficulty:

Some of the estimated $c_i$'s may be negative, which leads to the corresponding $p_i$'s also being negative. For example, an $h_i$ could be distance to work, which reduces house price as the property is located farther and farther away from work. This creates a problem for interpreting $p_i$ as a cost share since it's less than zero.

Is there a standard method in the literature to deal with the problem of negative coefficients in hedonic regression? Any reference or tips would be greatly appreciated.

What you are proposing is an unusual application of hedonic regression in respect of house prices. The method is most commonly used for one of two purposes:

a) To explain and perhaps predict relative house prices.

b) To estimate the value of characteristics of houses and their neighbourhoods, especially those which are hard to value in other ways such as non-market environmental goods.

When the method is used for either of these purposes, negative parameters are unlikely to be viewed as a problem.  Taking one recent study as an illustration, Mora-Garcia et al (2019) estimate hedonic regressions with negative parameters on various regressors (see Table 6, pp 15ff).  Their discussion (p 25) notes the negative parameters without concern (focusing rather on the consistency of the negative signs between different models).   When the aim of a hedonic study is to estimate the effect on house prices of an evironmental ‘bad’ such as air pollution, a negative parameter on the pollution regressor is to be expected.  Komarova (2009), for example, found negative parameters for several air pollutants in Moscow (see Table III p 323 and Interpretation p 324).

It’s only your particular aim of analysing house prices into positive cost shares that makes negative parameters a problem.  There isn’t a standard way of dealing with the problem because for most studies it isn’t a problem.

There are however some ideas in the literature that may be helpful.  In the case of distance to work (and generally of distance to any amenity), an alternative is to use some measure of accessibility with the property of associating greater ease of access with a larger regressor value.    Heyman et al (2019) review various measures of accessibility used in hedonic studies.  In particular their Equation (3) in section 3.3.2 contains a term of the form $e^{-c}$, where $c$ is cost of travel between zones, giving that measure the desired property.  Franklin et al  (2003) present a rather sophisticated index of accessibility to work, also with the desired property, that takes account of multiple work locations with different numbers of employees (see  Equation 2 p 5).

A general approach that could be used for any regressor that is found to have a negative parameter would be to derive from it a measure defined so as to vary in the opposite direction.  Suppose for example that age of property $A_i$ was found to be significant and to have a negative parameter, and the highest age in the sample was 100 years.  One could simply replace it by a regressor defined as $100-A_i$.  Or one could define a scale of discrete points, say 5 for 0-10 years, 4 for 10-25 years, and so on.  Trying out different measures of this kind might have the additional benefit of improving the fit of the regression.


The Fed pays 1.50% interest on reserves; so why are interest rates so low? Since 14th Dec 2017, the Federal Reserve Bank has paid 1.50% interest on excess reserves.

So why do depositors' interest rates still remain so low? According to BankRate, across the US, the national average savings account interest rate is 0.09% and only a handful of banks offer 1.50% or more.

The Econ 101 story would go something like this:

  If Bank A offers 1% and Bank B offers 1.3%, then consumers will move all their savings to Bank B. Bank A will then compete by raising its rate to 1.31%, which is still profitable since it can deposit its money at the Fed for 1.50%. Bank B will then raise to 1.32%, etc. Competition will ensure that the interest rate is driven up towards 1.50%.

I imagine there are some transaction and administrative costs, but I don't see how these could explain the huge gap between the national average savings interest rate (0.09%) and the interest rate paid by the Fed to banks (1.50%). I do believe also that there is no limit to the reserves that banks can place with the Fed (though please correct me if I'm mistaken on this point).

What am I missing here? Or: Why does this market deviate markedly from the perfectly competitive ideal?

Some possible general explanations off the top of my head (but I suspect there may be other more specific institutional factors that I'm not aware of):

Consumer ignorance. (Similar to this recent working paper which documents that people fail to pay off those credit card debts that charge the highest interest, and instead adopt some sub-optimal "balance-matching" heuristic.)
Consumers face transaction/psychic costs moving their money about, setting up new accounts.
Banks offer other services, so consumers may still prefer to save with a bank despite its lower interest rate.
Menu costs - it's somehow costly or maybe bad publicity to frequently change the bank's savings rate.

There are several issues here:

There are banks offering close to $1.5\%$, some well-known such as Goldman Sachs and American Express
Most banks currently have excess reserves deposited in the Federal Reserve System which they could use for lending if they wanted to, so they are not missing profitable commercial lending opportunities due to lack of deposits
Many customers are leaving their money in very low interest accounts, possibly through inertia or the attraction of other banking services, and so banks have less incentive to push up interest rates.  If customers want more, they can go for longer-term certificates of deposit yielding over $2\%$
In eras of "normal interest rates", banks took a margin.  For example the old anecdotal 3-6-3 rule for bankers (pay $3\%$ percent interest on deposits, lend money out at $6\%$, and tee off at the golf course at $3$ p.m.) might have been associated with a base prime rate of around $4-5\%$ percent and a default rate of around $1-2\%$.  So with a base rate of $1.5\%$, short-term savings rates should not be expected to be close to this.  Earlier in the cycle when Fed interest on excess reserves rates were $0.25\%$, this margin was not compatible with positive savings rates; only now are banks able to restore their margins


Why are the YTMs of TIPS of longer maturities more sensitive to current interest rates and inflation rates? According to this website, the yields of TIPS of longer maturities are greater than that of TIPS of shorter maturities. It seems counterintuitive since yields of longer-maturity bonds, which are based on expectations of the average of future inflation and interest rates over the holding period of the bond, should be less affected by current economic conditions. On the other hand, the site writes that the shorter-maturity TIPS are less sensitive to current interest and inflation rates. Why is this so?

{Comparison of TIPS yields}

In order to understand the TIPS yield curve, you need to look at the breakeven inflation curve. Breakeven trades literally pay off based on the gap between realised inflation rates versus the entry breakeven rate. This is the fundamental valuation metric for these bonds; the quoted yield is the residual.
(There is the issue of embedded risk premia. This is complicated by the breakeven being a spread; the premium in the breakeven is the difference between risk premia in the conventional and the inflation-linked. There are factors that could push the risk premium in the breakeven to be positive or negative.)
The implication is that investors project breakeven inflation, and the shape of the indexed yield curve (quoted inflation-linked yields) is forced to price that inflation trajectory. The resulting shape can be very unusual, particularly at short maturities.

On the other hand, the site writes that the shorter-maturity TIPS are less sensitive to current interest and inflation rates. Why is this so?

Short-dated bonds have lower durations. As for the statement about inflation, your phrasing implies an incorrect statement.

The sensitivity to breakeven inflation depends upon the duration, with longer duration bonds being more sensitive (by definition).
The sensitivity to realised price changes is equal for all TIPS: a shock to the CPI index moves the value of all bonds by the same percentage amount. (All cash flows are indexed, and if the start point of the index is shocked, all cash flows have the same percentage shift.)


Type of good that can be owned but not consumed when used I'm an econ noob so apologizes if this is a dumb question.

I'm trying to find if there is categorization of a good that can be owned but is not consumed when used. Tools are an example of this. A hammer is owned and can be used repeatedly without diminishing it (I'm ignoring that it can break over long use). This is compared to a something that is owned but is consumed, like food or lumber or something that is public and is not consumed when used, like a park.

The reason I'm interested in these goods is I want to determine what it means to fairly share goods of this type. I'm hoping knowing the what this type of good is called will help me search for work around it.

As I understand it, the best way to answer your question is to translate your description in to the language of economics and to understand the way that economists talk about these things.

To put this in to the language of economics, these would likely be "durable goods" with very low rates of depreciation. "Capital goods" (or just, capital) are a type of durable good. It is usually assumed that all durable good depreciate at least at some positive rate. This isn't a terrible assumption as, in your example, a hammer might rust over time---even if that time period is very, very long.


Does it make sense to apply complex mathematics in economics given that the result can be off by substantial percentage points? Complex mathematics make sense if the results can be calculated with precision. This applies for the physical sciences like physics and engineering. Economics is more of a social science subject. Does complex mathematics make sense in this context?

In the field of economics complex math is often used for

a) Economic modelling

There are usually tons of factors that influence even the simplest economic event. It is often necessary to resort to complex math to include all the variables that represent those factors in the right way.

b) Analysis of statistical data

It is often very difficult to support economic theories with good data, again because there are so many factors in play. On top of that, many simple mathematical instruments have drawbacks and should not be applied in certain situations. For example, to test relationship between two variables, you can use a simple correlation coefficient, but there are cases where outliers or certain patterns can make it unreasonably high or low. Then you can use simple linear regression, but if you spent months gathering data you may want to spend a few days trying to build a custom regression equation for a better fit. Finally, if you are preparing a paper for publication, you may want to use as many statistics as you can to try to convince reviewers and readers that your findings are actually true.

Drawbacks of using complex math in economics

1) There are not that many readers out there who are proficient in advanced mathematics. Unless you want to limit your target audience to a few math enthusiasts, keep it as simple as possible.

2) If you are preparing a paper for review at a journal, keep in mind that reviewers in economic journals are not necessarily mathematicians. It usually takes longer for math-heavy papers to get reviewed and the quality of those reviews may not be great, unless its a top journal.


What resources are available for learning Dynare? What resources are available for learning Dynare? I think it'd be nice to put together a list of resources that available to those new to Dynare. I've had a little experience with it but it'd be nice to know what resources I might be able to go to for questions on the beginner/intermediate level. Also, I would prioritize resources that have full-fledged examples. Does anybody have any suggestions?

Eric Sims at Notre Dame has an excellent set of self contained notes.

He uses a small neoclassical model as an example and goes over the model derivation, how to construct each block of Dynare code, different simulation options, interpreting output, and how to do higher order approximations. Full code is included for each step in the notes.


preference convexity and existence of equilbria Consider a production economy with $L$ goods, a single consumer and a single producer whose production set are given by $Y\subset R^L$. Question is to find the existence condition of equilibria of this economy.
I think the existence conditions are:

continuity and monotonicity for consumer preference

convexity for firm's technology.

Generally, convexity of consumer's preference seems to be required also for existence of equilibria. However, I cannot find the counter example that there is no equilibrium of this economy if consumer's preference is not convex and all other consumptions are satisfied.
Convexity of consumer's preference is really a condition of existence of equilibria in this one consumer-one producer economy?

Consider an economy with two commodities. Production is trivial, $Y=\{0\}$, there is a single consumer with endowment $(1,1)$ whose preferences are represented by the utility function given by $u(x_1,x_2)=\max\{x_1,x_2\}+1/2\cdot x_1 +1/2\cdot x_2$. These preferences are continuous, strictly monotone, but not convex. You can verify that there is no equilibrium in this economy by showing that for no price system, the demand of the consumer equals the supply of $(1,1)$.


In simple terms: what are the implications of homothetic and nonhomothetic consumer preferences? I am looking for a simple explanation of the implication of having homothetic/nonhomethetic preferences in relation to consumers' preferences when consuming goods.

From a mathematical point of view, if the function $f(x,y)$ is homogeneous (of any degree), and $g()$ is a function whose first derivative is everywhere non-zero, then the function

$$H(x, y) = g[f(x,y)]$$

is homothetic. In economics, we usually impose something more restrictive, namely that $g' >0$. But this makes a homothetic function a monotonic transformation of a homogeneous function. Now, homogeneous functions are a strict subset of homothetic functions: not all homothetic functions are homogeneous.

Therefore, not all monotonic transformations preserve the homogeneity property of a utility function. The simplest example is Cobb-Douglas utility. It is homogeneous of degree one. In an ordinal utility framework, we are ok with monotonic transformations, so we can consider the natural logarithm of it. Fine, but the natural logarithm will not preserve homogeneity. Nevertheless it will be homothetic.

The fundamental property of a homothetic function is that its expansion path is linear (this is a property also of homogeneous functions, and thankfully it proves to be a property of the more general class of homothetic functions).

In consumption theory, this means that, keeping the prices or the price ratio constant, if we vary the income of the consumer, in the $(x,y)$ plane the  tangency point of the income constraint with the highest feasible indifference curve will always reflect a fixed ratio $x/y$. This in turn implies that expenditures for each good grow all at the same rate as income, and so expenditure shares remain constant for the whole income range (always for a given price ratio).
While this may sound restrictive, in fact, it has been shown that homothetic preferences do not impose any special restrictions on aggregate demand (essentially due to the endowment vector being arbitrary and independent of preferences, which messes, or frees, things up).


Lessons From Successfully small island economies What economic and development lessons/strategies can developing Caribbean countries learn from successfully small island nations like Singapore?

I like this question, in the sense that although it is broad, I think it can be answered concisely and factually.

Singapore and China (from your previous question) are largely authoritarian countries. So they were both able to exert a lot of government influence over their development programs.  In this respect, they are not similar to Caribbean countries.

However, in other respects, Singapore is a good case analog because it is an island with very few natural resources and a relatively small population with correspondingly small domestic economic prospects.

Here are some pillars that underpinned Singapore's meteoric economic development.

Create stable and market-friendly government.  Economic development takes a long time, and it's hard to execute it if government changes frequently.  Also, governments need to be prepared -- over time -- to relinquish control over their economies as they transition to market-based.  Both Singapore and China accomplished this deliberately and in an ordered fashion (moving too quickly can cause chaos...see Russia for example).
Create stable currency and a good banking system.  Singapore, like many developing countries, decided to peg its currency to the US dollar, which gave it exchange rate stability and familarity.  Banking systems are crucial to ensuring liquidity and investment for economic growth, so installing a currency board, conservative fiscal policy, a decent bank, and a set of quasi-government commercial banks helped create financial infrastructure from scratch.
Invest in general economic infrastructure.  Singapore carefully built out physical infrastructure (roads, communications), legal infrastructure (courts and business law), and talent infrastructure (through schools and workforce training) to reduce economic friction, create economic resources, and maximize economic opportunity for development.
Seed strategic industries.  Singapore identified major industries that could help drive economic growth, and used a combination of government subsidies, pro-business laws, and economic protectionism to nurture these industries.  These investments included: making Singapore a low-cost manufacturing hub and a shipping hub (early economic development), and then subsequently a banking and communications hub (later development).
Assist trade.  The Singapore government worked closely with private and semi-public enterprises to help push through trade negotiations with countries (US, Japan, China, etc), reduce tariffs, and generally make Singapore an easy location for trade.  This was crucial to expanding the scope of the economy, because with fewer than 4 million people (at the time), the domestic economy could not be sufficient to drive growth.
Attract foreign direct investment.  As the economic infrastructure took root, Singapore became an attractive destination for foreign direct investment.  The government assisted with courting and promoting foreign direct investment into the country, which provided investment capital to build out the economy.  Tax and relocation subsidies helped a lot here.

Not all of these approaches will be applicable to Caribbean countries (e.g. Singapore's location was particularly strategic as a shipping hub), but not all of them need to be replicated in order to create fertile conditions for economic development in the Caribbean.


What is the fundamental problem with Pakistan's economy? Why is Pakistan repeatedly defaulting?

2008 - Pakistan seeks USD9 billion IMF bailout to avert crisis
2013 - Saudi Arabia come to Pakistan’s Rescue with USD15 Billion Energy Bailout Deal
2014 - Saudi Arabia loaned Pakistan USD1.5bn to shore up economy
2015 - IMF approves USD506 million for Pakistan under bailout programme
2017 - China bails out Pakistan with USD1.2bn loans

What is the fundamental problem with Pakistan's economy?

Let's split the problems into two categories, proximate and fundamental. It is easy to confuse the two categories or mix the problems of fundamental nature with those of proximate. Econoimc historians, in the pursuit of determining the causes of Britain's industrialisation have come up with several plausible explanations. I think we can use their framework to explain why Pakistan faces economic problems. I believe these factors are relevant in this case - Pakistan has not been able to take off from the low growth state for a while now. If I remember, it was a success story in the 1990s, but it could not sustain its high growth. In that sense, the country faces Malthusian straightjack.

Quality of Institutions. Every since North and Weingast (1989) claimed that Britain's take off in the eighteenth century was possile thanks to its Glorios Revolution when the Crown transferred much of its power to the Parliament. With this transformation, Britain was able to lift itsel from centuries of low growth state, first in the world. Does this give any explanation to why Pakistan faces the problems it has had for years. I would say it does. First. The quality of institutions is poor in Pakistan - rules of the game are not enforced properly. The political and social setting is not condcuive to growth - property rights are not secure, corruption is rampant, it is, possibly, institutionalised, and the presence of the rent seeking political elite obstructs the enforcement of rules. The necessary institutions have eveloved there, but they do not function in a way that permits growth. Daron Acemoglu (MIT) has successfully built on North's work, Acemoglu has a nice book on why nations fail. I would recommend you to read it.
Culture. Joel Mokyr has been putting the idea of 'cultural supremacy' in centrestage to explain the Industrial Revoltuion. I think his ideas could as well provide some explanation why Pakistan is facing problems. Historically, Mokyr believes, the beliefs, values, and preferences in society that are capable of changing behavior were a deciding factor in societal transformations. He goes on explaning what these transformations were and how they lead to the take off of Britain. Does Pakistan have the type of culture Mokyr is referring to, possible yes, but it is suppressed due to the presence of the issues outlined above in point 1. (will continue later)
Ideology/Religion. Pakistan is a hotspot of religious conflicts. The conflicts are not between religions but within religions. Tribes fighting tribes and depriving the young generation from education (girls and women especially). Such a culture suppresses innovation and discourages innovative behaviour. There is a growing literature on the role of religion in economic growth. Consensus has not been achieved as in other areas, but the papers look into catholicism vs. protestant vs. anglican vs. bhuddism vs. islam vs. judaism etc. vs. growth. It is probably not possible to quanitify religion's role in growth precisely. There is a misconception that religion suppresses innovation. Some papers point at the events of the past, there have been many including the locking up of Galileo for his claims about solar system which we today know were true. Pakistan is an Islamic country (in fact, it is Islamic Replublic of Pakistan). Does Islam hinder growth there? The facts point at No. Islam, like any other religions, promotes peace, grwoth and wellbeing but people adhering to Islam do not follow the teachings correctly. Economic historians agree that during the time of Abbasid Caliphate, Muslims had their golden age. It would not be an exaggeration if I claim that muslims were the only people making progress in all aspects of life at the time. Much of the World was in turmoil (Europeans had not seen a long lasting peace until nineteenth century, spurts of wars hindered growth for a long time). Exceptions could be given to the nations of the Far East (China). So, what is the issue here, it is surely the individuals and groups wages conflicts between various religios factions. These acts do not promote growth.

The other factors (i.e. low investment, human capital, terrorism, etc.) causing the problems are generally proximate.

(I will add more as soon as I have time)


Does $U(x,y) = x^2 + y^2 + 2xy$ represent transitive, monotonic preferences? I'm a monitor for a microeconomics course and a student came up with this question. That this utility function represents monotonic preferences I think it's clear. Both goods have positive and constant marginal utilities. What I think is less clear is if this preference relation is transitive. How can I assess it?

Any preference relation represented by an utility function is transtive.

Suppose $x \succsim y$ and  $y \succsim z$ and $\succsim$ is represented by $U$. Then $U(x) \geq U(y)  $ and $U(y) \geq U(z)$, so $U(x) \geq U(z)$  and then $x \succsim z$.


The equilibrium effects of a change in government purchases on consumption I can't get a homework problem started due to wording. I desire to understand it, so I will only put down enough to show my line of thought.

we have a utility function to maximize, say $u(c,\ell)$, and some production function $Y=zF(K,L)$. The government purchases $g$ units of the consumption good using a lump-sum tax $\tau$.

My question: the problem states "government purchase does not enter consumer's utility."

Does this mean that we do $\max_{c,\ell}u(c,\ell)$, relating $c=\ldots - \tau$, and do not do $\max_{c,\ell} u(c,\ell) + \phi(g)$, also with some relation?

Thanks for any clarification

Generally government purchase would have effect on the price of goods in the market (the "crowding out" effect). The question is just saying that $c$ and $\ell$ are not functions of $g$.


Strategic form: mixed strategy nash equilibria? The question I am dealing with is:

  Find all Nash equilibria in pure or mixed strategies.

This is what I have done so far..

Pure strategy nash equilibria

By observing best responses, the PSNE are $(u2,l2)$ and $(d2,r2)$

Mixed strategies

Solving for $\tau$:

$10\tau +2(1-\tau) = 5\tau +8(1-\tau)$

$\tau^{*}=\frac{6}{11}$

Solving for $\sigma$:

$10\sigma +2(1-\sigma)=5\sigma+8(1-\sigma)$

$\sigma^*=\frac{6}{11}$

Therefore: $(\tau^*,\sigma^*)=\left(\frac{6}{11},\frac{6}{11}\right)$

The correct answer is apparently:

  $(\tau^*,\sigma^*)=\color{red}{(1,1)},\color{red}{(0,0)}$ and
  $\left(\frac{6}{11},\frac{6}{11}\right)$

It seems that the correct answer has omitted my pure strategy nash equilibria. I also don't know how to get $(1,1)$ and $(0,0)$. Any chance you could help me out?

Thanks.

The probability vectors you gave in red describe pure strategy NE. (They assign probability one to an action.)

$\tau$ shows the probability that the column player plays action $l_2$.
If $\tau = 1$, then he will play $l_2$ with probability one. This is essentially another way of saying that he plays the pure strategy $l_2$.

One way to get these probability vectors is to find the PSNE as you have done. The PSNE $(u_2,l_2)$ means that the Row player plays $u_2$ with probability one, and the Column player plays $l_2$ with probability one.
According to your notation this means that $(\tau, \sigma) = (1,1)$.


Supply/Demand Curve for Excise tax that's being passed 100% on to consumers I'm doing a paper on the 'coca-cola tax' the tax on all sugary drinks. The premise is that it is an excise tax, which will then be passed 100% on to consumers. What I'm struggling with is how the supply demand curve appears.

In a normal excise tax, you would have something like the attached image, withe the area of Yellow AND Purple representing the tax (albeit more proportional), as both consumer and producer have their share of the tax burden. However if the producer passes the tax burden on to consumers, then the only the area in yellow would exist? Assuming the P1-P0 represents the amount of the tax.
So if i drew the same graph as below, but without the purple area, it makes sense to me, but it contrdicts all the models. UNLESS the supply is nearly perfectly elastic. Which you could argue it would be for the beverage industry?
I'm confused, help me out please

[][1

The reason you have trouble with that normal graph is beacause it contradicts your premise. Therefore, you can't use it.

I assume you mean the real burden (incidence) is passed on 100% to the consumers.

In that case you need a graph that allows for that. Your graph implies that both share the tax to some degree. To analyze a tax passed on completely to the consumers you need adequate supply and demand functions that allow for it.

As you mentioned, one possibility is a perfectly elastic supply function and a standard demand function.

Another possibility is a perfectly inelastic demand function and a normal supply function.

The reason both of these work is because the tax burden is carried by the less elastic side. For one side to carry the full burden we need something to be perfectly (in)elastic.

You have suppliers completely avoiding the tax burden. So you need suppliers to be very elastic compared to demanders. This can be done by making suppliers themselves perfectly elastic. Alternatively you can just making demanders perfectly inelastic and then by contrast the suppliers will be the much more elastic side and not carry any of the tax burden.

After you do that your tax burden area should be only one color.


Does Russia have higher inflation than US and Canada? If so, why in this particular case does money supply increase doesn't lead to higher prices? My understanding is that Russian inflation in recent years is considered to be running in the 5-6 % range, while US and Canada - in the 2-3% range (as measured by price increases/CPI). But I'd expect that the inflation of the money supply in Russia is much lower than in North America, as the Russian government spending deficit is in the low single digits % of GDP, while US and Canada annual budget deficits are both above 15% of GDP in 2020, necessitating much higher amounts of money printing by central banks.
Are my assumptions incorrect, or is there a logical explanation of this phenomena? Does money supply inflation not translate into price inflation, are there other forces at play, etc?
[EDIT] I understand that the relationship is not direct (as per Krugman),
but I want dig into what could be happening in this particular example.

Is CPI misrepresenting actual price inflation in 'some' of these countries (so
nothing to explain)?
Is money velocity different between them, affecting the value of money in each of these countries differently?
Are international trade and currency exchange rates a factor?
Have the recent Canadian and US increased deficits have not been prolonged
enough, and inflation is behind the corner?
Is USD status of a reserve currency - an important factor?

Or Something else...

The annual inflation was 5.8% in March 2021 in Russia. There are many reasons for this inflationary pressure such as the weakening of the ruble (Russian Currency) in comparison to the United States dollar. There is another reason for high inflation due to high government spending at the end of 2020 and at the beginning of the year 2021. In comparison to Russia, the inflation rate in the US is 4.16 % as of May 12, 2021. In Canada, the inflation rate is 2.2% in March 2021. Therefore, Russia has more inflation compared to the United States and Canada.
Moreover, your assumptions about deficit financing are reasonable and correct.


Screw foreign investment, lets just print money We often hear of countries securing foreign investment. Stores like this are trumped as major achievements. Foreign investment also has criticisms - profits generated in a country end up going abroad, and there can be national security issues.

Would it make sense to print money instead? The usual argument against printing money is inflation. However, in the linked story, 30bn of foreign money is coming in, so the economy has to cope with that additional spending. If that was printed money instead, it seems that effect would be the same - at least in the local economy.

The other side to this is currency markets and reserves - foreign investment creates demand for the local currency, which printing money doesn't do.

"Foreign Direct Investment" is to be understood as bringing in an economy productive capital, and not just purchasing power.
When an economy is seriously below full employment (of capital and labor), then a case can be made that "printing money" (i.e. creating purchasing power out of thin air) may not result in just inflation, but it may indeed bring into production input factors (labor and capital) that are currently unemployed. Compared to Foreign Direct Investment, we have the following differences:
Creating purchasing power through printing money relies on an indirect effect: you strengthen demand and expect that this will lead to increased supply, which in turn translates into higher employment/output. This may mitigated by
a) increased imports rather than increased local factor employment to satisfy the demand
b) institutional issues that may obstruct bringing into production the idle local factors
c) imbalance in available unemployed factors - e.g. you may have too many unemployed people but not much unemployed infrastructure.
Foreign Direct Investment in almost all cases is partly translated into imports (the foreign investors bring in their funds which are then partly paid back abroad to import capital infrastructure that is not available in the local economy), but apart from that similarity it
a) increases supply and local employment directly and
b) by design it takes a priori into account the possible imbalance in the availability of local factors, and corrects from them, since it wants to arrive at a factor mix that will be able to produce.
In a more general perspective, we could say that by printing money, if the policy fails you will just burden the economy with inflation (which has transactional costs). But with Foreign Direct Investment, even if it fails eventually as a commercial enterprise, the local economy has nevertheless gained, even as a one-off, the part of the FDI that has been consumed locally: it is an inflow of real output from the outside world.