Why can money be described as "government non-interest bearing debt" Trying to get some intuition on this statement I came across while reading Miguel Didrauski's dissertation "Rational Choice and Patters of Growth in a Monetary Economy". My sense is that it has something to do with the fact that money comes about from the Federal Reserve's purchasing of government bonds from the banks, thereby "injecting" money into the financial system. Would love a better idea of why this classification as "non-interest bearing debt" makes sense.

Let’s unpack “government non-interest bearing debt,” assuming that we are talking about government-issued notes and coins (dollar bills). (This does not include other instruments in monetary aggregates, like bank deposits.)

Money is an instrument issued by the government.
It pays no interest.
This only leaves “debt.”

Are notes and coins debt of the Federal Government? If we look at national accounts, they are considered liabilities of the consolidated Federal government. Most people use “debt” and “liability” to be synonyms, but there are technical differences (that I will not attempt to cover here).

One could argue that money being a “liability” does not qualify it as being a “debt.” This just means that the quoted statement is sloppy.

Note that there is another component of the monetary base - deposits held at the Federal Reserve by banks (bank reserves). The Federal Reserve is a bank, and those deposits are a liability, which is exactly the same as deposits held at private banks.

Why can these instruments be considered liabilities? When someone pays a tax to the Federal Government, the money is transmitted to the Treasury. The money holding is cancelled out against the tax liability of the tax payer.

I have seen arguments online that government money does not qualify as being a liability (or debt) since there is allegedly no promise to pay anything. (The argument also implies that accounting standards are incorrect.) I disagree with that view, and would note that to be formally correct, one would need to change national accounting definitions.


How to derive the demand function of $U(x_1,x_2)=x_1-x_2$ I'm trying to find the uncompensated demand function. How would you do that, when I have the following utility function $u(x_1,x_2)=x_1-x_2$, and the budget constraint $p_1\cdot x_1+p_2\cdot x_2=p_1\cdot e_1+p_2\cdot e_2$.

I've found the following.

$\max\ u(x_1,x_2)=x_1-x_2 \ s.t. \ p_1(x_1-e_1)+p_2(x_2-e_2)=0$

With use of substitutions I must maximize the following expression

$\max\ u(x_1,x_2)=x_1-\frac{p_1(e_1-x_1)+p_2e_2}{p_2}$

I find the f.o.c.

$\frac{\partial u}{\partial x_1}=1+\frac{p_1}{p_2}=0$

Some economics problems are deisgned to help us practice the basic tools (e.g., optimisation) of the trade. Others are designed to force us to think about the mechanics of a problem to help us understand the underlying economics better.

This problem falls into the latter category, so I recommend you give up on trying to usual calculus (which is premised on finding some sort of indifference curve tangent) and play around with the problem to figure out why this approach isn't working.

A consumer with $u=x_1-x_2$ is indifferent between the bundles $(4,3)$ and $(3,2)$. We can plot these and other indifference budles to draw an indifference curve:

Likewise, the consumer is indifferent between $(4,4)$ and $(5,5)$ and we can, in this fashion, get an indifference map:

From inspection of the utility function we know that the consumer is better off with more $x_1$ and less $x_2$, so utility increases in the direction indicated.

Now we can pick an endowment vector (e.g,. $(2,4)$) and a relative price (e.g. $-p_1/p_2=-1$) and plot the price line:

The consumer can trade from their endowment to any point along this line. By inspection, you should be able to figure out what the demand vector $\mathbf{x}=(x_1,x_2)$ will be.

Addendum: once you figure out what is going on here, your condition $$\frac{\partial u}{\partial x_1}=1+p_1/p_2$$
should make a bit more sense to you.


The Fed may increase the rates. But will that make the government debt unsustainable? The US Fed is increasing its interest rate targets. These rates will eventually affect most other interest rates in the US economy. In particular, interest rates on US government bonds will also increase, which should increase the US government debt servicing costs. Moreover, the government has over 10 trillion dollars in debt, so, the effect on its costs could even force it to increase tax rates. So, is the interest rate increase by the Fed eventually going to lead to an increase in federal tax rates? Thanks!

You have to differenciate the debt that is already existing from the one that is going to be issued: whenever the US Treasury issue a bond lets say a 10% coupon 10yrs... for a 100USD. It's still going to pay 10USD to the holders during the 10yrs. When you see the yield going up or down it's usually on the secondary market. I say usually because sometimes the government issues bond with a floating rate which can be impacted by a rate increase.

As for the new debt that is going to be issued you are right to say that this going to be more costly !


How to calculate inter-annual variation of inflation for a 3 months period? I have the monthly indexes taken from the National Institute of Statistics of my country (below), then I can calculate its inter-annual variation easily:

((index month year - index same month year - 1) / index same month year - 1) * 100

But my problem is that I want to compare this inter-annual variation against Financial Statements that show 3, 6, 9 and 12 months values. Then this inter-annual variation is useless because it shows the price variation only for a month and not for 3, 6, 9, 12 months period.

To solve this problem, should I calculate the cumulative inflation of 3, 6, 9 and 12 months of each year, then calculate de inter-annual variation of that cumulative inflation and finally be able to compare them to the Financial Statement inter-annual variation?

Is there any other way to do this more accurately ?

Without further details, what I'd do is what you said. Take an 3/6/9/12-month average of the price index and calculate growth based on that.


Why is a 'linear' regression model, with AR(1) error terms, a non-linear model? Our model: $y_t=X_t\beta+u_t$

Our error terms: $u_t=\rho u_{t-1}+\epsilon_t$ with $\epsilon_t\sim IID(0,\sigma^2)$, and $|\rho|<1$.

This results in $y_t=\rho y_{t-1}+X_t\beta-\rho X_{t-1}\beta+\epsilon_t$.
Why is this last model not linear in $\beta$ and $\rho$?

Is it because the parameters are multiplied with each other in the 3rd term? or is there something else?

Any help would be appreciated.

To be precise, a model is said to be a linear regression model when it is linear in its parameters. For extension, a model is said to be non-linear when it is non-linear in its parameter (Wooldridge, 2010, p.397).

As such, a linear model can have non-linear variables. A standard example is the Mincer equation, where wage is a linear function of education, experience and experience squared.

In your example, as your intuition tells you, parameters $\rho$ and $\beta$ are multiplied themselves, making it a non-linear model. However, your model is a rather special kind of non-linear model because its parameters can still be recovered using linear methods. In fact, you do not need non-linear methods at all. Your model is over-identified as you can test whether the estimated combined term is consistent with the individual estimation of each parameter or not.


Why does trade depress relative wages? I've read that increased trade tends to decrease relative wages of labor. What is the intuition behind this? Lower wages in labor imply lower demand for workers, but doesn't trade just encourage specialization, meaning that workers can just be hired by whatever industry they decide to specialize in?

The theory is that if you have three types of production sectors in the economy:

Sectors which could export more with liberalised trade
Sectors which could import more with liberalised trade
Sectors which could see little change with liberalised trade

then increased trade could tend to increase wages in the first type of sector, reduce wages in the second type, while leaving the third type less affected.  In addition, greater efficiency associated with liberalised trade could tend to reduce overall consumer prices, boosting the real value of all wages.

So for an economy which has a comparative advantage in low-wage sectors, this theory might suggest that the relative wage gap could narrow with liberalised trade.  By contrast, the same theory might suggest that the relative wage gap could widen with liberalised trade for an economy which has a comparative advantage in high-wage sectors.

This is only a theory and would require empirical confirmation.  Other things may be happening at the same time, such as changes in the local skill-sets or liberalised labour and consumer markets, which mean that the theoretical effects of liberalised trade are overwhelmed by other effects and the predicted relationship may not be seen.

An example of this sort of discussion can be read at https://wol.iza.org/uploads/articles/378/pdfs/how-does-international-trade-affect-household-welfare.pdf


CIA and Exclusion restriction I have recently got myself confused about CIA and wondered if somebody could perhaps help me disentangle my thoughts. Consider the regression

$Y_i = \alpha_0 + \Delta D_i + \beta X_i + \eta_i$

Where $X_i$ are controls/covariates and $D_i$ is the treatment dummy. The CIA says that $\eta_i \perp D_i |X_i$. If this holds the causal effect of the treatment can be estimated with $E[Y_{1i} - Y_{0i}|X_i] = \Delta$.

Is the CIA the same thing as saying $E[\eta_iD_i] = 0$? (considering $\eta_i$ should have mean zero because a constant is included in the regression?) Which then is the same thing as $Cov(\eta_i, D_i) = 0$? How is this related to $E[\eta_i|X_i] = 0$ Gauss-Markov assumption? Does this have anything to do with the exclusion restriction for IV which looks very similar?

The CIA assumption is equivalent to $E\{ \nu_i D_i \vert X_i \} = 0$. However, it is not the case that the unconditional expectation is equal to zero. The whole reason we need the CIA is that we don't have random assignment, but potentially we have random assignment conditional on the covariates we can observe.

I think it may help to think of $\nu_i$ as an error term that is composed of other variables $Z_i$ with effect $\gamma Z_i$. In this case, $\nu_i \perp D_i \vert X_i$ means that $Z_i$ does not predict treatment after conditioning on the observed covariates $X_i$.

To answer your IV question, this is indeed similar to the exclusion restriction in that you are making assumptions about the unobserved variables $Z_i$ in your data generating process and your treatment/instrumental variable. But I wouldn't try to connect the ideas too much or else you may come to wrong conclusions.


In this 3-way currency exchange, who loses, and by how much? Let's say, hypothetically, we have the following imbalanced exchange rates:

1USD = 1.2EUR

1.2EUR = 1000 JPY

1000 JPY = 1.5 USD

Let's say person A starts off with 1 USD, buys 1.2 EUR from B, then buys 1000 JPY from C with the 1.2 EUR, then finally buys 1.5 USD from D with the 1000 JPY.

Person A now has .5 more USD than they started with. Where did the .5 USD come from? Who lost that equivalent amount? Does it depend on the exchange rates before and after this imbalance happens?

If the starting balances were

A = 1USD
B = 1.2EUR
C = 1000JPY
D = 1.5USD

then the ending balances are

A = 1.5USD
B = 1USD
C = 1.2EUR
D = 1000JPY

so the simple answer to where the 0.5USD came from is D.

A more complicated answer would be some combination of B, C and D depending on how the exchange rates rebalanced to iron out this arbitrage opportunity.

For example if 1000JPY dropped back to 1USD, then D could do some exchanges with B and C leaving them where they started and D with 1USD, i.e. D lost the 0.5USD

But if the EUR/JPY changed so that 1.8EUR = 1000JPY, then C ends up with -0.5USD, if you do exchanges to restore the JPY and EUR to where they started.

If USD/EUR changed so that 1.5USD = 1.2EUR, B ends up with -0.5USD.


Federal Reserve Interest Banks have higher interest rate for debts than deposits to make money but does the U.S. treasury have the same interest rate for loans and deposits?

Not my field but I think this is a basic overview. If there are mistakes, please let me know and I can edit.

The monetary authority in the U.S. uses open-market purchases to manipulate a chosen policy instrument in an effort to effect macroeconomic aggregates. There is a general consensus now that the Fed's instrument is the effective federal funds rate, which is the weighted average of the rates at which banking institutions loan money to one another. So, monetary authorities use open market purchases in an effort to make this weighted average (the 'effective' rate) match their target rate.

There is another rate that matters here - the discount rate. The discount rate is the cost that banking institutions face to borrow funds from the Fed's discount window (which is a separate instrument of monetary policy). And note that the discount rate is distinctly different from the FFR. This rate, historically, trends slightly higher than the FFR.

The two rates above effectively allow the Fed to control the cost at which banks can borrow money. The first rate governs the cost of borrowing from other banking institutions. The second rate governs the cost of borrowing (for banks) from the Fed.

If I understand you correctly, you are also curious about the interest paid on deposits held by the Fed. That is, the interest that banking institutions earn on deposits with the Fed.

The Fed pays interest both on required reserves and on excess reserves.

Interest on Required Reserves (IORR) - this rate is set by the board and is intended to offset the implicit tax that required reserves imposed on banks.

Excess Reserves - The Fed began paying interest on excess reserves in 2008. According to Bernanke, this rate is another tool of policy that allows the Fed to set a floor on the overnight rate (synonymous with FFR).

Sources that will allow you to gain more depth:

excess reserves

discount window/discount rate

federal funds rate

open market operations


Unitary demand curve: p = 1 - q In my text book, many theories are explained using ad unitary demand curve: a consumer can buy 1 quantity of the product, or none.
The example of the demand function is $ p(q) = 1- q $

but that means if I want to sell one quantity the price should be 0?
I did simply p(q=1) = 1- 1 = 0

What does it mean?

This demand function is just normalized to unit. If you are not interested in the concrete quantity of your demand function, but you are interested how the demand of the specific market is distributed between firms, you can use this simple demand function.

For example, you can consider a normalized demand function in a Bertrand's game. Let's assume the firms are symmetric, there's no capacity constraints. The demand ($D(p_i,p_{-i})$) of firm $i$ is the following:

$$ D(p_i,p_{-i}) =
\begin{cases}
    0       & \quad \text{if } p_i > p_{-i} \\
    1/2  & \quad \text{if } p_i = p_{-i} \\
    1  & \quad \text{if } p_i < p_{-i} \\
  \end{cases} $$


Is investment in real estate a real investment? In the book The Financial Crisis and the Free Market Cure in chapter 3 author said that investment in real estate is not really investment.

It is jobs that create houses not houses that create jobs

Author motivated it as: when we investing in factories we create new jobs which are producing some goods and after a year we have factory + goods and permanent skilled job place, but investing in real estate (homes) will create only temporary work place (real estate agents, builders etc.) which exists as long as new home is building as far as I understood.

Purchasing new homes would count as an investment. According to Blanchard et al. Macroeconomics: a European Perspective pp 568 in glossary investment is defined:

Investment (I): Purchases of new houses and apartments by people, and purchases of new capital good (machines and plants) by firms.

The source above is the leading undergraduate macroeconomics textbook, so although the definition is not rigorous as it is an undergraduate text the houses are not included just haphazardly without thought. Also note the definition does not include land as correctly stressed in Brian's comment.
However, what the author in that book you cite probably has in mind is capital investment, which is specially investment in assets that will be used as factor of production (e.g. machines, trucks, factory). However, capital investments are not defined in terms of jobs that they create. That is, even investing in fully autonomous robot that would replace worker would be capital investment. This being said when capital and labor are complementary, which is still often the case, capital investment will also create more jobs.
Additionally, in economics when we talk about real variables, e.g. real output, real consumer spending, real investment etc. we mean inflation adjusted as opposed to nominal output, nominal consumer spending and nominal investment etc. that would not be inflation adjusted. So the book you are reading also does not seem to be following economic terminology much.


How does "buy low, sell high" relate to supply and demand? I'm taking introductory microeconomics, and I'm trying to consolidate my understanding by looking at some real world examples.
In a perfectly competitive market, there are many consumers and suppliers who are price takers. They are constrained to buy or sell at the accepted equilibrium price due to many competitors.
Therefore, we should expect $P^* = P_D = P_S$ for a certain good or service in a perfectly competitive market. However, having been to a foreign currency exchange at an airport, this does not seem to be the case! They are willing to buy an item (eg: USD) at a lower rate, but they sell it at a higher rate. So it seems that $P_D < P_S$ for the traders (looks similar to a tax wedge), assuming they are both buyers and sellers of the US dollar in the same market.
This example confuses me, as there seems to be two prices instead of one. In the textbook, if I were to buy $Q^*$ items at $P^*$, I should be able to also sell $Q^* $ items at $P^*$, not $Q^*$ items at $P < P^*$. Other examples of this can be seen whenever sellers and buyers are allowed to post their own listings; there always appears to be a price gap.
How do I explain these real world examples using the concept of supply and demand in a perfectly competitive market (and on the graph)?

In the comments @henry already provided you with the correct conceptual answer, I will try to offer some extra intuition and way how this could be modeled. Currency exchange is a combination of a retail market with service market so here if you would want to visualize it with supply and demand you would have to use two diagrams for both parts of the market.
If that still sounds too exotic just imagine classical retail. A supermarkets will first purchase its produce (let us say carrots) from carrot farmers. This will be separate market where supermarkets are the buyers and where they jointly together form demand and where farmers are suppliers. On this 'market for carrots from farms' there will be supply and demand and price given by the equilibrium.
However, once supermarkets acquire carrots then they will sell them on second retail market to regular consumers. On this second market, let us call it 'market for retail carrots' supermarkets are the suppliers and regular consumers are part of the demand. This market will have its separate price that might be different from the 'market for carrots from farms'. This however does not mean that market is not competitive because supermarket has additional marginal costs for warehousing those carrots, if they sell them just for price that covers these additional cost the market would be perfect (of course, in real life the market might not be perfect, but the point is  you can't just say it from the fact that there is a price differential).
In the same way the exchange window at an airport can be thought of operating at two distinct markets. At a market where it buys currency from individuals where the exchange windows are the customers and part of demand and people are the suppliers, and then second market where the exchange window operates as a retail and act as a supplier and people who buy currency are the buyers.
Again this is all consistent with perfect competition. Consider the following simple model:
Exchange window sells USD at price $P_H$, but buys currency at $P_L$ and exchange window additionally has to pay the person sitting at the window wage $w$ for facilitating intermediation (let us assume that wage is paid per unit of currency exchanged to simplify calculation).  Let the quantity here be the number of USD exchanged ($Q_{USD}$). Now this can be fully consistent with perfect competition. Let us suppose market is perfectly competitive so $P_H$ is treated by firms as being exogenously set (e.g. see any introductory economics text such as Mankiw Principles of Economics). This means that the profit function of this exchange window will be given by:
$$\Pi = P_H Q_{USD} - P_L Q_{USD} - w Q_{USD}$$
Now take the FOCs and we get:
$$ P_H - P_L - w =  0 \implies \underbrace{P_H}_{\text{price}} = \underbrace{P_L + w}_{\text{Marginal Cost}} $$
Hence, here we have literally a textbook example of  perfectly competitive market, where $P_H>P_L$ (e.g. a situation where firm buys low sells high). Yet there is no additional markup as price that the firm provides is exactly equal to marginal cost so the markup $\mu=1$ and we have perfectly competitive outcome.
The intuition here is that for the exchange window buying currency from people is part of their cost, but then they have other costs (e.g. wage in example above and in real life also capital costs etc) since the exchange window is in business of providing intermediation service. In perfectly competitive market price at which firms supplies product will be equal to marginal cost, but here the marginal cost equal not just the cost of accruing the currency from people in the first place but also marginal cost of intermediation.
Lastly note, that this is of course not enough to prove that exchanges are competitive, rather this is proving the opposite. Namely, a difference between price at which firm buys product and price at which it sells product in itself does not tell you anything about whether market is competitive or not. $P_H>P_L$ on both competitive and non-competitive markets. Here you would have to add more reasoning to argue it is competitive, like in a question you mention that when it comes to exchanges there are usually many firms offering the same service and so on. Or you could actually try to empirically estimate marginal costs of the firm and see if indeed firm just sells its product at marginal costs or if the prices are higher indicating both presence of markup and market power.


Which of Anscombe-Aumann's axioms imply the Sure-Thing principle? Consider an Anscombe-Aumann setting, and assume that a preference relation satisfies all original Anscombe-Aumann's axioms (rationality, continuity, independence, and monotonicity).

If we restrict attention to pure horse races (that is, acts without any objective uncertainty), the Anscombe-Aumann model boils down to a Subjective Expected Utility representation a la Savage. Therefore, over pure horse races, the decision-maker satisfies all of Savage's axioms, notably the Sure-Thing Principle (P2 in Savage's terminology).

I fail to see the direct connection between Anscombe-Aumann's axioms and the Sure-Thing Principle. Does anyone see how the Sure-Thing Principle is implied by Anscombe-Aumann's axioms? In particular, does it result from Independence only, or are Independence AND Monotonicity required?

As a first remark: the Anscombe-Aumann axioms, in particular Independence, are defined over acts taking the state space to a linear space (generally simple lotteries over consumption objects). Even when we consider the restriction of the model to purely subjectively uncertain acts, we still need to employ the full model or we will lose information.

That being said: Lets let $S$ be a finite state space, and $X$ a finite set of alternatives. Let $\Delta(X)$ denote all the lotteries over $X$ and $f: S \to \Delta(X)$ is an act. For an event $E \subseteq S$, let $f_{-E}g$ be the act defined by
$$f_{-E}g \begin{cases} f(s) \text{ if } x \in E \\ g(s) \text{ if } x \notin E. \end{cases}$$

Now, we can say that our model satisfies the sure thing principle if $f_{-E}h \succsim g_{-E}h$ and $f_{-E^c}h \succsim g_{-E^c}h$ then $f \succsim g.$ This definition is valid for all acts, not just ones without objective risk, but clearly you can consider only the relevant projection.

Assume the antecedent of the STP. From $f_{-E}h \succsim g_{-E}h$ and independence we have that
$$\frac12 f_{-E}h + \frac12 f_{-E^c}h \succsim \frac12 g_{-E}h + \frac12 f_{-E^c}h.$$
Notice we can rewrite this as
$$\frac12 f + \frac12 h \succsim \frac12 g_{-E}f + \frac12h$$
and, applying independence again, we get
\begin{equation}
\tag{1}
f \succsim g_{-E}f.
\end{equation}

In an analogous fashion, from $f_{-E^c}h \succsim g_{-E^c}h$ and independence we have that
$$\frac12 f_{-E^c}h + \frac12 g_{-E}h \succsim \frac12 g_{-E^c}h + \frac12 g_{-E}h.$$
Again, we can rewrite as
$$\frac12 g_{-E}f + \frac12 h \succsim \frac12 g + \frac12h$$
and, applying independence again, we get
\begin{equation}
\tag{2}
g_{-E}f \succsim g.
\end{equation}

Combining (1) and (2) via transitivity yields the desired relations. Going back to the prefatory remark, notice that to apply independence, we need to mix acts, appealing to objective risk. Thus, even when $f$, $g$, and $h$ have no objective risk, we still need risky acts to serve as an intermediary in the proof. In a sense, this is the grand insight to the whole AA framework---using objective risk to get around the necessity of an infinite state space by using the linearity of expectations to force the STP.

Notice only independence and transitivity were used. This should indicated that even state-dependent EU (where monotonicity / state-independence fails) or Bewley EU (where completeness is relaxed)  will still satisfy the STP.

Edit in response to a comment: Lets call the above notion of the Sure Thing Principle STP1 and say the preference satisfies STP2 if $f_{-E}h \succsim g_{-E}h \iff f_{-E}h' \succsim g_{-E}h'$ for all $f,g,h,h'$. Then if  $\succsim$ is a preorder, it satisfies STP1 if and only if it satisfies STP2.

First assume STP2 holds and that $f_{-E}h \succsim g_{-E}h$ and $f_{-E^c}h \succsim g_{-E^c}h$. Then by STP2 we have
$$f = f_{-E}f \succsim g_{-E}f \qquad \text{ and } \qquad g_{-E}f = f_{-E^c}g \succsim g.$$
Transitivity implies $f \succsim g$; STP1 holds.

Next, assume STP1 holds and $f_{-E}h \succsim g_{-E}h$. Define $\hat f = f_{-E}h'$ and $\hat g$ analogously. By definition
$$\hat f_{-E}h = f_{-E}h \qquad \text{ and } \qquad \hat g_{-E}h = g_{-E}h,$$
so our assumption is identically that
\begin{equation}
\tag{3}
\hat f_{-E}h \succsim \hat g_{-E}h.
\end{equation}
Further $\hat f_{-E^c}h = \hat g_{-E^c}h = h'_{-E}h$ so we have, by the reflexivity of preference, that
\begin{equation}
\tag{4}
\hat f_{-E^c}h \succsim \hat g_{-E^c}h.
\end{equation}
Now we can apply STP1 to (3) and (4) to obtain that $\hat f \succsim \hat g$, which, given their definition, exactly what we need to show for STP2 to hold.


An overview of 4 books for an undergrad course in Mathematical Economics I plan to self-study, at an undergraduate level, Mathematical Economics. It covers 3 main topics

Introduction to economy science

Microeconomy

Macroeconomy

Each of these have lots of sub-topics. And the recommended books are

Microeconomic Theory: Basic Principles and Extensions by  Walter Nicholson, Christopher Snyder

Fundamental Methods of Mathematical Economics by Chiang & Wainwright

Macroeconomics in the Global Economy by Jeffrey D. Sachs, Felipe Larrain

Intermediate Microeconomics: A Modern Approach by Hal R. Varian

My questions

What's the overview of these books for an undergraduate course?

Are they good for self-study? If not, could you recommend books to cover the mentioned topics for self-study?

What's a Mathematical Economics course like? One of my statistics professor once said that is not a difficult course but there are like tons of concepts that one needs to memorize  and there remains its complexity.

All four of those books are widely used at the undergraduate level. They are written with the intention to be text-books of a class, so they should be good for self-study. I  recommend you to read 1 and 2 before reading 3 and 4.

Will give you a basic overview of the way we think in economics, clarify some basic concepts and explain work-horse models in the discipline like supply and demand, which can be used in a lot more domains than expected. Several similar books are also very good, a common one is Mankiw's book Principles of Economics.

In economics, we use a lot of math, but  disproportionally certain areas of math more than others. A course in Mathematical Economics will focus on these tools we use. For example, it will focus a lot on optimization, linear algebra, calculus, analysis, differential equations, etc. Optimization and "comparative statistics" is probably the most important thing in economics, so a possible approach would be for you to learn up to there from Chiang, and then go to the other books and come back to Chiang if and whenever you need it. There are a lot of good similar books,  for example, "Mathematics for Economists" by Simon and Blume.

I am not familiar with this book, but Macro has tons of good textbooks. It will not be  math-intensive actually, so you will not need all of the tools learned in Chiang to read this one. A good substitute for this one would be Barro's Macroeconomics.

This is a classic textbook for intermediate Micro. Almost everyone I know learned from it, and it is definitely advanced for an undergrad, but as friendly as possible. It is hard to find a good substitute for this one.

If you have access to a library and find a topic hard to understand, I would look at how other authors approach it. This community will also be a useful resource if you use it properly.


Do actively managed ETFs help the economy in any way, and if so, how? Listening to the ARK Invest podcast, I've heard several times ETF managers saying that they have a positive impact on the economy because by choosing the most promising companies to invest in, they allow capital to be located to companies that deserve it. While I do get the argument for direct investment such as VC or PE, I don't see well how an ETF manager buying stocks in a company helps the company or some other element of the economy.
Do actively managed ETFs help the economy in any way, and if so, how?

Yes they do in in a several ways. The main ones are:

Trading (not just of the people who actively manage the EFT but generally) helps price discovery. Price discovery is an important role of stock market. It is socially beneficial for companies to be appropriately priced given their fundamentals and all other avaiable information as that helps divert capital to the right companies. Even if traders do not buy shares from company directly the market price of a share affects how much capital company get by issuing new shares. Furthermore, ETF are also not just for stocks but also commodities or exchange rates, where they help to correctly price those commodities or exchanges - which is again socially very valuable activity. Quick price discovery is one an important characteristics of well functioning capital markets. In turn empirically well-functioning capital markets have first order impact on economic growth  (have a look at Levine, 1997 or Levine 2005).

Trading improves market liquidity. It makes sure that whenever you want to liquidate stocks etc. you hold there is some buyer. For example, it would be much harder for people to save  by investing in stock market if it would be difficult to sell stocks you own when you need to. Having low liquidity can thus deter investment. In fact liquidity is so important that it is commonly listed in textbooks as one of the major determinants of asset demand (see Mishkin & Eakins: Financial Markets and Institutions ch 4). Consequently, even ignoring anything else just the fact that there is someone trading and creating liquidity in itself creates value and is beneficial for the economy.


how can I find the original work on the bases of which 2016 nobel in economics was given? I have been google and googling and asking around and I can not find the work(s) on the basis of which the nobel in economics was given yesterday. I really wanted to read them. does anyone know how to find it?

It is based on multiple pieces of work, most of which can be found in the prize committee's thoroughly referenced announcement.


First-price symmetric auction with discrete value I've been trying to work the following problem out but I can't quite seem to understand it, or the whole concept of first-place auctions. I don't understand how we get to the equilibrium.

The problem is the following: "Consider a first-price, sealed-bid auction in which a bidder’s valuation can take one of three values: 5, 7, and 10, occurring with probabilities 0.2, 0.5, and 0.3, respectively. There are two bidders, whose valuations are independently drawn by Nature. After each bidder learns her valuation, they simultaneously choose a bid that is required to be a positive integer. A bidder’s payoff is zero if she loses the auction and is her valuation minus her bid if she wins it. Determine whether it is a symmetric Bayes–Nash equilibrium for a bidder to bid 4 when her valuation is 5, 6 when her valuation is 7, and 9 when her valuation is 10."

In this case, we have discrete bids and discrete valuation, as well as different probabilities for each. Could someone help me out understand the problem?

Suppose you are one of the bidders and fix the strategy of the other one to be the one supposed.
Your payoff will be $\mbox{Pr(winning the auction, i.e., b>b')}(v-b)$, with b being your bid and b' being the other's bid and v being your valuation (or type).

Now, imagine you are the type-5 player.

If you bid an integer less than 4, you lose for sure because the other player bids more regardless of their type. Hence, your expected payoff is 0.

If you bid 4, (we assumed that) you win with probabilty 0.5 if the other one is of type 5 (and hence bids 4) and lose in every other case.
Hence, your expected payoff is $0.2*0.5*(5-4) = 0.1$.

If you bid 5, your payoff from winning is zero such that your expected payoff will be zero in any case.

If you bid more than 5, you make a loss when winning, making the expected payoff negative.

Hence, bidding 4 when being type 5 is a best response (with this restricted bid space!).

Similarly, imagine being a type-7 bidder.
Bidding less than 3 makes you lose the auction, and bidding 7 or more does not seem to be a good idea (see above). Now calculate the winning probabilites for bidding 4 (same as above, but higher winning payoff), bidding 5 (winning against type 5 for sure, but losing against other types), bidding 6 (winning against type 5 for sure, but against type 7 only with probability 0.5). Next, you repeat the exercise for type 10.
If you don't find a profitable deviation, you have got an equilibrium.


Relationship between Nash and Coasian bargaining solutions What is the relationship or difference between Nash and Coasian bargaining solutions? It is well-known that the Nash bargaining solution satisfies certain basic axioms. Which of these does the Coasian solution satisfy? Is the Nash solution applicable when there are externalities, and are the two solutions same/comparable in any sense?

There is no such thing as the "Coasian bargaining solution". This is a simple principle according to which parties find an agreement somewhere on the Pareto frontier when they bargain, which means that the outcome of the bargaining process is socially efficient (abstracting from equity issues).

The Nash bargaining solution refines our predictions by specifying where the solution is likely to be located on the Pareto frontier. In some sense, it is a subset of the Coasian bargaining outcome, which can be anywhere on the Pareto frontier. In contrast to the Coase principle, it is a theorem that rests on an axiomatic characterization.


What is a good way to generate realistic utility curves? I am aiming to program a basic simulation of a simplified economy to look at the impact of various interventions.

The economy will have N groups of homogeneous consumers and M producer / employer sectors. Each producer sector makes one type of good that the consumers can purchase, so there are M goods. To try to keep it (relatively) simple, the goods will all be independent with no close substitutes or compliments. E.g. goods will be steak and diapers, not steak and chicken, nor steak and potatoes.

Each group of consumers will need to have a demand curve for each of the M goods, as well as a "demand" for leisure.

Given the marginal utilities for each good, you can calculate a demand curve for that good. So, the approach I'm thinking is to generate utility curves for each good, then use those utility curves to derive demand curves which then drive consumer purchasing behavior and other downstream effects.

This brings me to the question, what's a good way to randomly generate a lot of plausible utility curves?

For example, if I wanted a linear utility curve I could randomly generate a slope and an intercept. That is simple and easy to do, but it misses diminishing marginal utility which is one of the most important features.

What's a form that's easy to work with, has relatively few parameters to specify, and still captures most of the key features of utility curves?

It's somewhat simple, actually. You can just use a Cobb-Douglas with $m+1$ goods available, the last one being leisure. So, you should have something like:

$$U(x_1,x_2,...,x_m,x_{m+1}) = \prod_{i=1}^{m+1} x_i^{\alpha_i}$$

Subject to $\sum_{i=1}^{m+1} \alpha_i = k$, where $k$ is the degree of homogeneity of the utility function. Usually, $k=1$ is considered reasonable.


What happens when a reserve bank runs out of foreign currency reserve? What happens to a country when a reserve bank runs out of foreign currency reserve?

This is an excellent question and it deserves a good answer and I will try my best here.

So what is a reserve currency? A reserve currency is a currency that other nations use for making global payments, loans and foreign exchange reserves.

The four currencies that are considered global are the US dollar (USD), the Euro, the Japanese Yen and China's RMB (yuan).

Now, what happens to a bank when it runs out of reserve currency, well, it depends who the bank is, where its located and what the reserve currency is that they have run out of.

If you are one of the four currency nations then you are exporting your currency, but you have to export enough into the global system to support the demand for payments, loans and reserves.

Central banks in general could also issue lines of credit which require payment in one of the four reserve currencies mentioned above.

This becomes part of someone's job at these banks to ensure that there is a harmonious balance on the balance sheet at all times between exporting currency, issuing credit and demanding payments.

Lets take a case study such as the EU banks where they had issued loans in Euros, and the fatal consequence of that started to become clear in 2016. Emerging market borrowers were forced to default as their currencies weaken against the Euro and the USD, driving the costs of servicing their debt denominated in Euros and USD higher.

Someone mentioned Venezuela above and yes this is what happened to them. Not that they ran out of foreign currency, but that the cost of servicing their debt denominated in USD and Euros soared to the extent that it weakened their own currency, in addition to their policy of expropriating businesses that did not belong to the government and other policies which finally lead to foreign investment high tailing it out of there and a vote of no-confidence for the now dead Bolivar.

Even nations have credit reports and credit ratings and you can imagine when they run into that kind of trouble, their ratings drop.

In my opinion, the system of reserve currencies is dysfunctional for everyone, creating and incentivizing fatal imbalances in trade, yields and debt. Some look to a basket of currencies from the World Bank known as Special Drawing Rights or SDRs as the solution, but all this does is tighten the coherence of a system that's already dangerously hyper-coherent, that is, highly susceptible to contagion.

But the concept of reserve currency and the balancing act that banks have to go through with it is not perfect and even gold had its limitations. Anyway, I hope this is some semblance of an answer or gets you closer to your answer.


Deflate level and flow variables using PPI and CPI What do statements like

Flow variables (such as dividend growth and returns) are deflated using the CPI index.

or

Level variables are deflated using the Producer Price Index (PPI).

mean?

What are level varibales?
I guess both indices correct for inflation but why would dividend growth/returns need to be adjusted?
How does one actually implement this deflation of variables? Is there a time series of the CPI and PPI available only and one simply has to multiply a particular variable with the index?

Level (also called stock) variable, is a variable that measures something at a given point of time. For example, measuring GDP in 2017 would be a level (stock) variable.
Flow  variable is a variable that measures the rate of change in the stock over time. For example, if GDP growth (which measures flow of GDP) was $10\%$ in 2017 that means that the level/stock of GDP increased by $10\%$.
Wikipedia actually has surprisingly excellent explanation on differences between level/stock and flow/growth variables that you can read here (see the general use part).
There is no reason why you would always want to apply CPI to flow variables and PPI to level variables. This must be something that is specific to the research you are reading and there must be some other reason behind it.
If you want to deflate a level variable using some particular deflator you can use the following formula:
$$Real X = \frac{Nominal X}{deflator/100}$$
If you want to adjust flow variable then you can first calculate the change in deflator and subtract that change from the flow variable that is:
$$ g_r  = g_n - \pi$$
where $g$ is the real ($r$)/nominal ($n$) flow/growth rate respectively and $\pi$ inflation rate which is the change in deflator. Also the above is a first order approximation. The exact formula is given by $1-g_r = \frac{1+ g_n}{1+\pi}$ but this exact formula is not often used.


What does "agent" mean in Pearce's formulation of extensive form rationalizability? While reading Pearce(1984), I can't understand what "agent" $j$ and agent $ij$ mean on page 1041:

  Consequently I associate a conjecture $$ c^{ij} = (c^{ij}(1), ... ,
> c^{ij}(N)) $$ with each information set $I^{ij}$ in $\Gamma$;
  $c^{ij}(k)$ represents what an "agent" $j$ for player $i$ believes,
  once $I^{ij}$ is reached, about what player $k$'s mixed strategy is. A
  conjecture $c^{ij}(k)$ over a set $A^k \subseteq M^k$ can be regarded
  as an element of $\bar{A}^k$ (see Appendix A).  I have noted that
  an agent $ij$, upon being reached, should not entertain a conjecture
  that does not reach $I^{ij}$. A further restriction, not invoked in
  other solution concepts, is appropriate: if the information set can be
  reached without violating the rationality of any player, then the
  agent's conjecture must not attribute an irrational strategy to any
  player.

Some notations:  $I_{ij}$ is player $i$'s $j$th information set, $M_k$ is player $k$'s mixed strategy set and $\bar{A}^k$ is the convex cone of $A^k$.

So an agent is definitely different from a player, but what else can it be to form a belief?

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

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

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

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


Why do externalities lead to a Pareto-inefficient outcome? So we know that under a Pareto-inefficient outcome, there is room for Pareto improvement, i.e. making someone better off without hurting anyone.

Assume that there is a drug company which is in competitive equilibrium: and $$N^S=N^L\\
|MRS|=|MP_n|=|MRT_{(c,l)}|$$
$\pi$ is maximised etc. So everyone should be happy right? Since we are in a competitive market,

But if this drug company makes some pollution which is a threat to the health of citizens, we call this case a negative externality.

By definition if such negative externalities exist, even though we are in a competitive equilibrium, we would be Pareto inefficient.

But how come we are Pareto inefficient? If we reduce the pollution somehow and reduce the externality, or create a market for pollution and let the pollution trade the firm would definitely be losing money since it would pay for the pollution. So isn't it impossible to make citizens better without making the firm worse off?

If you allow side payments then the issue you identify goes away in a Coase sense.

The citizens being polluted could pay for production to be reduced by one unit.  This amount would have to be between the benefit of the reduced pollution and the loss to the pharmaceutical firm from the reduced production. But this last figure is small: at the competitive equilibrium the firm is matching its marginal revenue with its marginal cost so its profit from the final unit of production is very small, while presumably the pollution effect is larger (if not then the competitive equilibrium is already efficient).

So the position with the side payment dominates the position without it in a Pareto sense, as both the citizens and the pharmaceutical firm are better off.  Possibly further side payments and production reductions would be even more efficient, at least until the marginal profit loss exceeds the value of reduced pollution; that point is then Pareto optimal and the starting point was not.

You may have to extend this slightly as the reduction in production also affects the customers of the pharmaceutical firm, who see a reduction in consumer surplus from the lower production. But again, side payments from the citizens to the customers can move to a Pareto optimal position, until the marginal value of the reduced pollution equals the combined marginal losses of the pharmaceutical firm and its customers.

Advocates of the "polluter pays principle" would describe this as unfair, but Pareto optimality does not judge fairness.  Another practical issue would be creating a mechanism which avoids free-riding and leads to an efficient agreement, a frequent issue with Coasian bargaining.


Ex-post vs Ex-ante Budget Balance in Auctions Have I understood this correctly?

When I say my auction mechanism is ex-post budget balanced it means that in practice (I have done market simulations) and according to the results my mechanism is budget balanced. whereas, if the mechanism is ex-ante it means we only anticipate that it is budget balanced?

A reviewer of my paper has asked me to explain in the paper what ex-post and ex-ante means. How would you suggest to explain it?

These are widely used technical terms with a precise mathematical meaning:

Ex-ante budget balance means that the expected sum of all transfers is zero.

Ex-post budget balance means that the sum of all transfers is zero with probability one. Some authors require that the sum of transfers is always zero.


Due to rising costs of college tuition, is it likely that the future will have less universities and the remaining only for those of much wealth? I am very sorry if this is worded wrong.  I've looked at the numbers myself and it astounding how much college has gone up in price even for commuters in a few decades.  People didn't need these massive loans in the 60's or 70's.  I am graduating in a year with a degree in Online Journalism and Media and spend over a grand a semester out of pocket AFTER loans and aid.

Many people think people like me are lazy because we need help to afford college.  I have seen articles of people who work 70 hours in the summer and full time during school during full time classes; but that a lot.  Some may not be able to handle that kind of stress especially if the major was like software engineering or IT Business.

Given this, are they right in what they AND by the numbers and how America has handled things, is college likely to be non-existent or for upper class people and rich in the future likely?

OK!!  I am very sorry it got opinionated and personal in paragraph 2.  I'm a worry wart who is here to learn about economics in what concerns me.  Please just answer the big top question.

Hemelt and Marcotte wrote a paper studying the effect of rising costs on enrollment, and as it turns out, students who choose to pursue degrees have very inelastic demand; people are still going to university and they will keep doing so, despite these tuition hikes.

I think most students (myself included) have pretty imperfect information about the market, and they also forego a lot of searching because of the value of leisure. Most of their decision to go to school will be liquidity constraints and support from social/kinship ties. Liquidity isn't so much a concern nowadays, if parents really want their kids to go to school.

That said, there seems to be a shortage of manual/trade labor, such as in line work, which pays around 40$ an hour for starters (I think), but the population of laborers there are aging and due to retire. The job market could just be very sticky, and the demand shock for school caused by technology will slowly fall, causing tuition to fall with it. That's a bit more speculative though, and I'm not sure there's a lot of literature on rising tuition, on a very cursory glance.


How to derive this Hicksian Demand? So I have this utility function where I need to find t expenditure minimizing value of x. Normally, I would get the marginal utility of goods x and y, but doing that in this case doesn't leave any variables, so setting that equal to the prices would give me 2/5 = 3/3, which doesn't make sense. How do I solve this? I feel like I know how to do it but I'm just missing a major step or two.

Since in this case, both utility function and the budget line are perfect substitutes and thus you can't equate the Marginal Rate of Substitution to the price ratio.

This problem can be solved this way,

$$\min_{x,y} \quad  3x+3y\\
    \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \textrm{s.t.} \quad  2x+5y=10\\$$

or

$$\min_{x,y} \quad  x+y\\
    \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  \ \textrm{s.t.} \quad  2x+5y=10\\$$

Here,
     $$MRS=\frac{MU_{x}}{MU_{y}}=\frac{2}{5}<1=\frac{P_{x}}{P_{y}}$$
or,  $$\frac{MU_{x}}{P_{x}}=2 < 5 = \frac{MU_{y}}{P_{y}}$$

Therefore the expenditure is minimum when the consumer spends his entire income on good y, that is $(x,y)=(0,2)$ is the bundle that minimizes the expenditure given the utility $u(x,y)=2x+5y=10$. This is depicted in the figure below:


Rationalizable strategies and Weak Dominance Can I find the rationalizable strategies for a game where none of the players has strict dominance but only weak dominance?

In 2-player games, the strategies that survive iterated elimination of strictly dominated strategies are called rationalizable. Note that even if no strategy is strictly dominant, there can be strictly dominated strategies. If you cannot eliminate any strategy, then all strategies are rationalizable.
Only if correlation of players' randomization is allowed, all strategies that are rationalizable (not never-a-best response) are also equivalent to those that survive iterated elimination of strictly dominated strategies in games with more players.
In any case, you can always find rationalizable strategies if a best response exists -- independent of whether a (strictly or weakly) dominant strategy exists.


Is it appropriate to change the base year of the real GDP to a more recent one? I have a dataset containing Venezuela's nominal GDP, real GDP, GDP deflator and population from 1997 to 2013. I am interested in calculating real GDP per capita, but the base year of the GDP deflator is 1997=100, which is the current base year used by Venezuela's Central Bank in all the national accounts.

Would it be correct to change the deflator's base year to 2010=100 in order to recalculate real GDP?

Or should I just use real GDP reported by the Central Bank even though the base year is outdated?

Changing the base year of a time series is fine if you know what you're doing, check, for example the question: How do I change the base year of real GDP using the GDP deflator and nominal GDP?

I'd, personally, use the real GDP series - you won't gain anything substantial with the mathematical conversion. It might be an useful exercise if you, for example, were to compare GDP growth in two different countries and would like the base year to be the same.


Do large- and mid-caps try to shun low share prices? As NASDAQ and NYSE stocks must be priced at least $1 per share, it feels intuitive and doubtless that large- and mid-caps fancy their share prices to outstrip and remain well over \$1. But what minimum (range of) share price do they desire? To wit, at what share prices would they  think about reverse stock splitting to boost their share price?

Why Some Companies Don't Split Their Stock explains why companies eschew low share prices.

  Why Not Split?

  There is not a whole lot of evidence to suggest that stock splits matter. Finance professors have examined stock splits and see no actual impact on a company’s value or performance.

  Many companies prefer to avoid splitting because they believe a high stock price gives the company a level of prestige. A company trading at $1,000 per share, for example, will be perceived as more valuable even though the firm's market capitalization may be the same as a company whose shares trade at \$50.

  Smaller companies may also wish to avoid stock splits because of a danger of share values falling too low. There have been cases where companies have split shares only to see the stock market dive, pushing shares below \$10. Psychologically, this may turn off some shareholders, and in extreme cases, share prices may be too low for a company to be listed on an exchange. Companies will avoid splitting to protect themselves from this possibility.

I have no expertise in this area whatsoever, but I've taken a quick look and see a significant body of research on reverse stock splits. Although there are many reasons that reverse stock splits occur, overall findings on the hypothesis of an optimal share price are inconclusive.

Here is a review of 26 articles published about reverse stock splits in international journals from 1970 to 2010. I'll quote from the abstract:

  Reasons attributed by firms for initiating a reverse split are ‘image
  improvement’, ‘artificial increase of price’, ‘reduction of
  stockholder servicing expenses’, ‘improving marketability’ ‘increase
  the stock's investor base’ ‘trading range hypothesis’ ‘signaling
  hypothesis’’ liquidity hypothesis’, ‘regulatory norms’ ‘facilitates
  going private’ and ‘compulsions from creditors, in case of a
  bankruptcy’. In the case of hypothesis testing, it is noticed that,
  researchers are not able to reach in a consensus on the outcome.

Section 3.5 of this review focuses on "a widely accepted belief that forward stock splits and reverse splits are intended to keep the stock price within some 'optimal range'." Radcliffe and Gillespie (1979) "commented that reverse split cannot achieve an optimum range." Studies that focus on the Hong Kong market in particular do no support an optimum trading range hypothesis, at least not in the case of reverse stock splits. However Jain et al. (2004) "documented a significant increase in institutional ownership for stocks with prices of $5 after the reverse split." Jog and Zhu (2004) "found that institutional share holding increases after reverse split which helped them to conclude that an optimum price can reached (at least to institutional investors) through reverse split."

So while there are numerous reasons that companies may benefit from reverse splits, there is not strong evidence for the existence of an ideal share price range. If there were such a price range though, the study by Jain et al. suggests that the minimum might be around $5.


Implications of abolishing Fractional Reserve Banking on mortgages and interest rates Suppose for a moment that someone with legislative power decides to abolish Fractional Reserve Banking and passes a law that forces banks to only lend the money they own, that is M0.
What would be the economy-wise implications of such a change in the long run and what in the short run? In particular with such a criteria in mind as mortgages, interest rates and dispossessions.

There is a long standing problem in most discussions of Fractional Reserve Banking (FRB), around the precise definition of money. Cash money (that is M0) is an asset on the banking system balance sheet, while deposit money (the liability) is the money that is created by lending.

Ever since the introduction of cheques specifically, and in general the ability to make direct transfers between two deposit accounts, deposit money has been the de facto form of money that is used in the economy. Cash money is maintained at a fractional reserve of deposits (it used to be a regulator of total deposits and lending, but in practice this isn´t the case anymore), and used primarily for inter-bank liquidity settlements, as transfers occur between bank accounts at different banks. Reserve requirements are now down to 2% or less in most countries.

So taken literally, the question is what happens to an economy when its money supply is reduced by 98%, and at the same time total lending shrinks by whatever proportion bank lending is of total lending in the economy (typically 1/3 or more).

In the short run, congratulations, you no longer have an economy. Nobody can pay their non-bank debts any more, because there isn´t enough money to pay them with. Bear in mind debt payments do not automatically adjust to changes in the money supply. That triggers a debt cascade causing wide-spread company failure. The accompanying impact on all prices causes massive disruption in the supply chain, because everything in the economy is now completely mis-priced relative to everything else. A 20% reduction in the liability money supply in the US in 1930-33 for example caused the price of food bought from farmers in some parts of the USA to be less than the cost of the fuel required to get the food to the market for sale. This event would clearly be far worse than that. Market based systems can and will adjust prices over time to compensate for money supply changes, but that´s the long term. It has been said that 'every civilisation is only 2 meals away from barbarism', and I´m afraid you just pushed yours over the edge.

In the long term, after a period of market exchanges being performed with cigarettes, and other money-substitutes, and those responsible for this mess being hunted down and dealt with appropriately, people will probably feel that fractional reserve banking wasn´t such a bad idea after all.  Some form of Germany Year 0 event will take place and the banking system will be restarted. Since all debt was effectively discharged during the "unfortunate event" the next few decades will probably be referred to as a golden age. By the survivors.

If instead we assume that rather than reducing the money supply (which we know is a bad idea), the banking system is instead converted so that there is no fractional reserve lending, asset cash is injected to replace debt, and maintain the current quantity of deposits. All deposits in the system are simply held constant from this point on, and you now have a constant money supply economy.

As a side note, everybody now has to pay for their bank accounts, because since banks are no longer lending institutions, they need a revenue source to fund their operations. Quite a large revenue source - ATM networks aren´t cheap.

The problems caused by a sudden drop in total lending are still present. In practice this will disrupt the economy in the short term, but hopefully not quite as badly as in the previous scenario.

The short answer though, is we simply don´t know how a constant money economy behaves in practice. There hasn´t been a constant money economy since fractional reserve banking was invented, and that´s at least 3-400 years now (depending where you put goldsmith banking in the banking continuum, and what country you´re in).

A lot of financial statistics would probably start looking very strange, since even correcting for CPI doesn´t adequately control for the impact monetary growth has on price measurements. It´s possible that the economy would settle down after a few years as everything adjusts around the constant money supply - that´s essentially the general equilibrium theory argument. It´s also entirely possible that the growth in the money supply that FRB provides over time makes it easier for adjustments to occur - a lot of arguments in favour of small positive inflation amounts essentially revolve around this - and that a bunch of issues we didn´t previously know about emerge and cause new problems.

While this is very much an open research question, it´s interesting to note that a side effect of some of the recent Basel 3 regulatory changes is that at least for the last couple of years, several countries including the UK have experienced stable money supplies. If this continues (it´s perfectly possible to regulate fractional reserve banking so that it doesn´t expand the money supply if you know what you´re doing - whether the central banks really know what they´re doing is also an open research question), then we may start to have some empirical data that can help shed light on this very interesting question.


Relation between demands of $x, y$ and $z$ Question: Consider a consumer with utility function $U(x,y,z)=y\min\{x,z\}$. The prices of all three goods are the same. The consumer has $100 to spend on these three goods.The demands will be such that:
(a) $y<x=z$
(b) $y>x=z$
(c) $x=y=z$
(d) None of the above
My attempt: The consumer will consume equal amounts of $x$ and $z$ because otherwise the allocation would be inefficient, that is, he can obtain the same level of utility by spending less. So $x=z$. I cannot figure out how is $y$ related to $x$ and $z$. I think the answer would be (d) None of the above because it does not matter if $y$ is less than or greater than or equal to $x$ and $z$.

Let $\min\{x,z\}=\Omega$, where $P_\Omega=P_x+P_z$. Now the problem becomes $U(y,\Omega)=y\Omega$, which is a standard Cobb-Douglas with degree 2 of homogeneity. Now in this case the choice for each good is:
$y^*=\frac{\alpha_y100}{P_y(\alpha_y+\alpha_\Omega)}\implies y^*=\frac{100}{2P_y}\;\;\;\;\;\;\;$in this case $\alpha_y=\alpha_\Omega=1$
For $\Omega$: $\;\;\;\;\;\Omega^*=\frac{\alpha_\Omega100}{P_\Omega(\alpha_y+\alpha_\Omega)}\implies \Omega^*=\frac{100}{2P_\Omega} \implies \Omega^*=\frac{100}{2(P_x+P_z)}$
Now, since $P_x=P_y=P_z$, let $P_x=P_y=P_z=P$ a general price, therefore substituting in our optimums:
$y^*=\frac{100}{2P}\;\;\;\;\;\Omega^*=\frac{100}{4P}$
Now it's straightforward (since we already know $x^*=z^*$ and as this is the optimum for $\min\{x,z\}$ which is $x$ OR $z$) that $y^*=\frac{100}{2P}>\Omega^*=\frac{100}{4P}$, so this implies that:
$y^*>x^*=z^*\;\;$****
Also I found this document, where this question is number 13.
Hope this helps.
Disclaimer: It would be helpful if other people could assess this approximation, since I hadn't never seen this problem before.


What is the average economic value of a human life? What is the economic value of a human life?

If there are multiple methods to use in calculating, what are they, which method is preferred, and why?

Considerations/sub-questions on methods

A. Is the calculation purely based on output value (i.e. wages, goods produced, etc.), or are there intangibles that must be included (value of innovations that cause progress for society, NPV of progeny, etc.)?

B. As a result of #1, are there things which reduce economic value in one's life?  For example, when one has gone on unemployment, is one's net economic value negative for that period of time?

C.  Is the economic value of life dependent on one's country/state/locale or the sector one performs in?  For example, is it correct to say the economic value of a life is different in the US than in South Africa (due to average output in real terms?

It depends on the context, of course, but most often in policy analysis "the value of a life" has nothing (directly) to do with output, etc, but instead means the maximum amount that people would want the government to spend in order to save a randomly chosen life.

So in a country of 300,000,000, the question is:  What, to you, is the monetary equivalent of a 1/300,000,000 chance of death?  Because 1/300,000,000 is a very small number, we don't have to worry terribly much about willingness-to-pay versus willingness-to-accept.  (Theory tells us that for small changes, the two willingnesses are effectively equal.)

Returning to the question:  How much would you be willing to pay to avoid a 1/300,000,000 chance of death?  Now multiply that value by 300,000,000.  That's the value of one life, and arguably the amount we'd want our government to spend to preserve a randomly chosen life.

Obviously there are problems with heterogeneity (you and I might not answer the question identically).  But as a general rough rule, the estimates tend to come in somewhere under $10 million.


Why does strictly Walrasian demand with quasi-concave utility function mean that the walrasian demand having only one single consumption bundle? In the context of Walrasian demand:

Suppose u is continuous, satisfies local nonsatiation, and is strictly quasi-concave, each $w(p, x)$ contains a single consumption bundle.

The proof I got from a textbook is:

Let $x $~$ y$ with $p^T x=p^T y =w$, $z=\alpha x + (1- \alpha) y$ with $0 < \alpha < 1$.
$p^T z =w$ because of the convexity of budget set.

Note: I understand why this makes sense graphically.

Case 1:

If $x \neq y$, strict quasi-concavity implies $u(z) > u(x) = u(y)$, thus $z$ is preferred to $x$ and $y$, hence $x, y$ are not elements of Walrasian demand.

Case 2:

Otherwise $x = y = z$.

For case 1, how can one be sure that the $z$ is unique?

For case 1, you can argue $z$ will be unique by contradiction:

Suppose ad absurdum there is another $z'$ that is feasible (i.e. $p^Tz' =w$) optimal and $z'\neq z$. Then you can consider a convex combination of $z$ and $z'$: $\bar z = \beta z + (1-\beta) z'$, for $\beta\in(0,1)$. Notice that $\bar z$ is still feasible (because it is a combination of two feasible bundles) and, because of strict quasi-concavity, $u(\bar z) > u(z')$ so that $z'$ cannot be optimal, a contradiction.


Are there any states that don't have debt? I've not been able to find any states that don't have debt to other states.  This, to me at least, seems really strange.  Are there any nation states that are not in debt to other states, if so which ones, and if not why can't everyone just settle the debts?

(Wasn't sure if I should ask this on the Politics Stack Exchange or here, please let me know if this is out of scope and I'll ask there.)

The classic answer here would be Libya and Brunei, but I think Libya now has debt.

Brunei is a strange case in that it uses a joint currency with Singapore dollar, controlled by the monetary authority of Singapore, so in effect you can use Singapore debt as a substitute for Brunei dollar investment.

Not having any debt, and having a free currency is generally a bad idea, since you cannot control interest rates. Furthermore, if you can afford not to have debt, then people will be begging to lend to you at such favorable rates it would be foolish not to borrow a bit.

On the other hand there are many counties with no net debt. Singapore and Norway don't need to borrow but do so to provide bonds for the financial markets. They then invest the money they borrow. Norway can borrow so cheaply they can buy US treasuries and make a profit.


The USA debt and the individual investor There is a lot of hype about the national debt of the USA being incredibly large, and I wonder if this has any implications about an individual investor? I understand that the risk of having a large national debt is that the government may be unable to pay for its bonds. But if an investor holds only stocks of private companies, does he have any reason to worry about this? If so, what can an investor do to protect against this?

Sure, government borrowing affects the small investor in many ways.

For starters, there is only so much money available for borrowing. The more the government borrows, the less there is available for everyone else. This pushes up interest rates and in some cases will make it impossible for the least desirable borrowers to get a loan at all.

If the government defaults on its loans, this would cause many problems. Details are debated by economists, but I don't know anyone who says it would be good for the economy.

As to what you can do personally to protect yourself ...

Of course there are political things you can do, like voting for and otherwise supporting candidates who campaign on economic policies that you believe are more desirable.

If you are worried about the government defaulting on its bonds, then don't buy government bonds.

If you are worried about the macro-economic effects of a government default, you could invest money in foreign countries that you believe have wiser debt policies.

Invest in companies that are more likely to survive or prosper in an economic downturn. Like, if there's a depression, people will still need food, so food-processing companies are probably relatively safe investments. If people are suddenly made poor, they're probably not going to buy frilly luxuries like video games, so those might be poor investments. But the rich tend to manage to get along no matter how bad things get, so services for the rich, like luxury yachts, might do well regardless. There are plenty of people out there who do research on this sort of thing that you could consult.

People who are deeply worried about government default often advise people to invest in commodities, especially gold. If the government goes bankrupt and takes large sections of the economy down with it, precious metals, especially gold, tend to hold their value.

If you're really worried you can build a compound in the wilderness, stock it with food and other supplies, and have an arsenal of guns to protect you from the marauding hordes after the economic collapse. :-) (Okay, I say that flippantly, but if you're convinced that things are going to get very bad, that would be a logical thing to do.)


Nested/Recursive Dynastic Utility Functions I want to find a way of representing a dynastic utility function in which not only the head of the dynasty's utility is dependent on its descendants' utility, but all members of the family tree gain utility from the utility of some of their offspring. In particular, I would like for the total utility of a person $U_{x_{i}}=u(x_i)+u(x_{i+1}) + u(x_{i+2})$ for all $i$ in the dynasty, where '$u(x_{i})$' denotes the utility of $x_i$ which is not dependant on the utility of children and grand-children ('non-parental utility'). So I want a model which allows us to say that the utility of the dynastic head is partly a function of the utility of his children and grandchildren's utility, but where his children's utility is again partly a function of his grandchildren's and great-grandchildren's utility, and so on.
In Becker and Barro's model, we have that \begin{equation}
    U_{x_0}=\sum_{i=0}^{n}N_i   \beta_i(u(x_i)).
\end{equation},
where $N$ is the number of descendants in a generation $i$ and $\beta$ is an intergenerational altruistic discount rate. The problem with this model is it lacks the 'nested' or 'recursive' feature explained above--it simply states that the dynastic head derives utility from his descendants' utility without taking into the consideration that his descendants utility might in turn depend on their descendants' utility.
Adding in the discounting element, let me give a concrete example: suppose I, as the dynastic head ($x_0$), directly receive 50% of the utility of all of my children (i=1) and 25% of the utility of my grandchildren (i=2). Let us say I do not directly receive any utility form the utility of my great-grandchildren. I will still indirectly receive utility from my great-grandchildren since my children receive 25% of their utility and my grandchildren receive 50% of their utility. If we assume for simplicity that my child had one child, which in turn had one child, which in turn had one child $u(x_3)=1$, then I indirectly gain $50\%*25\%*1 + 25\%*50\%*1$= 0.25 utils from my great-grandchild. How do I get a general expression for this phenomenon which holds for $n$ generations?
Any suggestions or pointers are hugely appreciated!

Here are two nice papers on recursive utility functions, a generalization of additive utility functions and compatible with "utility of the dynastic head to be partly a function of the utility of his children and grandchildren's utility, but where his children's utility is again partly a function of his grandchildren's and great-grandchildren's utility, and so on":
Blackorby, C., Nissen, D., Primont, D., & Russell, R. (1973). Consistent Intertemporal Decision Making. The Review of Economic Studies, 40(2), 239-248.
Blackorby, C., Nissen, D., Primont, D., & Russell, R. (1974). Recursively Decentralized Decision Making. Econometrica, 42(3), 487-496.


UK: Is there a list published by the government for the amount of tax paid by companies? I know of the website for data.gov which provides data but is a publicly available list of taxes paid by publicly own corporations like Apple? If not how do we know how much is paid by them?

For publicly own corporations, you can access their financial statements, where they record the amount of taxes paid (e.g. for Apple here). Notice that where the tax is paid depend on the location of the firm, and whether it is a multinational business. The latter type of firm is particularly problematic, because multinational companies use transfer pricing methods to optimise (i.e. lower) their tax burden. Therefore, it is difficult to determine where those taxes should be paid. Apple and other multinationals seem to be particularly keen to do this (e.g. here).

The reason that sometimes you see headlines stating that big companies do not pay enough taxes locally is because many of these analysis is done by those with access to detailed information like HRMC or Inland Revenue (e.g. here; NB: excuse the doggy source; could not find a better one).

Outsiders to these institutions can have access to this data only in a anonymous fashion (see data available for UK here), so you won't be able to trace Apple's taxation in the UK with such data (or at least you should not be able to do so).


the difference between $\hat{e}^2_i$ and $\sigma^2_i$ What is the difference between $\hat{e}^2_i$ and $\sigma^2_i$?

In regression, we assume that $var(e_i)=E(e_i^2)=var(y_i)=\sigma_i^2$.

Does this imply that $\sigma_i^2$(the sample variance) is equal to $\hat{e}_i^2$?

When we calculate FGLS (feasible generalized least squres), we consider $\ln(\hat{e}_i^2)=\ln(\sigma_i^2)+v_i$, where $v_i$ is just the error term. This seems that we distinguish $\sigma_i^2$ from $\hat{e}_i^2$.

But, when we calculate the robust robust standard error, we simply repalce $\sigma_i^2$ with $\hat{e}_i^2$. Thus, theses two are considered to be equal.

I am confused with these two terms. Can anybody clarify this?

Thank you in advance.

Certainly the true variance is not equal to the squared residual.

In the case or robust standard errors, it has been proven that if we use $\hat{e}^2_i$ we obtain a consistent estimator of the variance-covariance matrix as a whole, even though $\hat{e}^2_i$ is not equal to $\sigma^2_i$ and even though  each single $\hat{e}^2_i$ does not converge in probability to $\sigma^2_i$ (it converges to the true squared error, which is a random variable).

The fundamental reason for this result is that

$$E(\hat{e}^2_i) \to_{n \to \infty} E(e^2_i) =\sigma^2_i$$

So the OP's phrase

  When we calculate the robust robust standard error, we simply repalce
  $\sigma^2_i$ with $\hat{e}^2_i$. Thus, theses two are considered to be equal.

is simply wrong.


Core elements of Marxist Economics I am interested in understanding the differences between mainstream economics and marxist economics. For that, a guide about what is central to the marxist economic theory (not political or cultural theory) would be highly useful.

What are the core elements of Marxist economics?

PS: my emphasis on core aims to avoid this question being flagged as "too-broad". I also hope there is sufficient consensus within theorists in order to avoid being "primarily opinion-based".

From reading a selection of writings by Marx, I have come to understand the following three as the core elements of Marxian economics.

The labour theory of value. It asserts that the exchange value of a commodity $x$ (what quantities of $x$ that can be exchanged for another commodity) is determined by that labour time which is socially necessary to produce $x$.

Surplus value theory of profit. I.e., capitalists derives profit from their exploitation of workers. Suppose a capitalist purchases labour power from a worker for one day. To Marx, then, the value of one day's usage of this labour power is the value of the commodities which is necessary for the worker to live through one day. Say that it takes one fourth of a day to produce this amount of commodities, the value of which will be equivalent to the wage paid to the worker by the capitalist. This one fourth of a day is called necessary labour. Any work above this level is surplus labour from which the capitalist derives profit.

The theory of alienation. In the following I quote a passage from Marx's Economic and Philosophical Manuscripts of 1844. Relating this passage to the above core elements, I note that Marx somehow seems to think that the institution of capitalism structures parts of the social world.

The worker becomes poorer the more wealth he produces, the more his
production increases in power and extent. The worker becomes an ever
cheaper commodity the more commodities he produces. The devaluation of
the human world grows in direct proportion to the increase in value of
the world of things. Labour not only produces commodities; it also
produces itself and the workers as a commodity and it does so in the
same proportion in which it produces commodities in general.
This fact simply means that the object that labour produces, its
product, stands opposed to it as something alien, as a power
independent of the producer. The product of labour is labour embodied
and made material in an object, it is the objectification of labour.
The realization of labour is its objectification. In the sphere of
political economy, this realization of labour appears as a loss of
reality for the worker, objectification as loss of and bondage to the
object, and appropriation as estrangement, as alienation.
So much does the realization of labour appear as loss of reality that
the worker loses his reality to the point of dying of starvation. So
much does objectification appear as loss of the object that the worker
is robbed of the objects he needs most not only for life but also for
work. Work itself becomes an object which he can only obtain through
an enormous effort and with spasmodic interruptions. So much does the
appropriation of the object appear as estrangement that the more
objects the worker produces the fewer can he possess and the more he
falls under the domination of his product, of capital.


Can monopolistic dead weight loss persist without government intervention? If so how? Can monopolistic dead weight loss persist without government intervention? If so how? I am researching monopolies and find dead weight loss proposed as an evil of monopolies but i can not find any examples or understand the reasoning behind it. I have seen the graphs and understand them but why would new businesses not enter the market if there are profits to be earned.

If I understand you correctly, monopolistic deadweight loss persists without gov intervention because of the following:

Economies of Scale: if monoplist is able to produce at below the market prices due to the presence of economies of scale, then the monoplist is effectively able to retain its dominance in the market as new firms entering the market cannot undercut the monopolist. Thus, deadweight loss persists.

Patenting: Monoplist could patent its products and process innovation. A new entrant would have to come up with a new idea of a similar product to enter the market tha the incumbet dominates. This however is not usually possible due to very high initial R&D investment requirement.

Rent-seeking: It is also possible that a monoplist could lobby governments in order to influence policy related decisions. Tobacco and weapons manufacturng companies are known to spend large sums on lobbying efforts.

These effectively serve as barriers to entry.

In the presence of barriers to entry, monopoly profits effectively transfer income from households to the monopoly. The monopolist could also under-produce in order to maintain monopoly profits. Examples could be the production of "limited edition" goods which are usually priced above average market prices. Because the monopolist earns above normal profits, it may not invest in cost-saving technologies.

In order to minimise or elliminate the deadweight loss, governments tend to invoke antri-trust laws and regulate the markets and industries. Deadweight loss persists in the absence of action by governments.


When demand increases why does the price decrease but equilibrium price increase? On a demand curve when the demand increases the price will decrease. However on a demand and supply graph, when the demand shifts to the right, the price will increase. I understand why, but then what is the point of analyzing a demand curve, if it contradicts the market equilibrium graph?

I am sorry if this is a stupid question. It has only been a month since I have started economics in high school.

On a demand curve when the demand increases the price will decrease.

You actually mean "along the demand curve, a decrease in price will increase quantity demanded, all else equal". This is the law of demand, and it holds for ordinary ("non-Giffen/Veblen") goods that have downward-sloping demand curves. There is no shift of the demand schedule in this scenario:

  However on a demand and supply graph, when the demand shifts to the right, the price will increase.

Yes, when the demand curve shifts to the right (all else equal), the equilibrium market price rises to account for the fact that consumers are now willing to pay more. The increase in price is the mechanism by which excess demand at the initial price is cleared:

There is no contradiction here in the supply-and-demand model. Note that movements along the demand curve can only occur when we are away from a market equilibrium. These price movements are traced out by shifts of the supply curve and they continue until the new market equilibrium is reached.

Based on your vocabulary, you are likely misunderstanding the demand curve with actual quantity demanded.


How to verify Value Function in nonzero sum two player Differential Game? There are two agents $i=1,2$. The state $k$ is governed by $\tau_i\in[0,1]$ where
\begin{align}
\dot{k} = f(k,\tau_1,\tau_2).
\end{align}

Define the value function of player $i$ by
\begin{align}
v_i(k) := \sup_{\tau_i}\int^\infty_0{e^{-\rho t}F(k,\tau_i,\sigma_{-i})dt}.
\end{align}
where $\sigma_{-i}(k)$ is the policy function or a markovian stratgey profile of player $-i$. And $\rho>0$ is the time preference rate.

The Hamilton-Jacobi-Bellman equation reads
\begin{align}
\rho v_i(k) = \sup_{\tau_i}\{F(k,\tau_i,\sigma_{-i}) + v'(k)f(k,\tau_i,\sigma_{-i})\}.
\end{align}

Now assume I approximated a function $\hat{v}_i$ by value function iteration. How do I know that it's the true value function?

The first panel shows the final value function after iterating 80k (!). Should probably try an implicit method. The second panel shows the evolution from frist guess to final result $v^0\to v^j$, $j=80k$. Third panel is the distance between the value functions and fourth shows the error.

Note that the value function is convex-concave. This is due to the fact that for the limit case the law of motion tends to infinty $\lim_{k\to 0} \dot{k} = \infty$.

By the maximum principle optimality requires that the Hamiltonian
\begin{align}
H_1(k,\tau_1,\tau_2^*,\lambda_1) := F(k,\tau_1,\tau_2^*) + \lambda_1 f(k,\tau_1,\tau_2^*)
\end{align}
is concave in $(k,\tau_1,\tau_2)$ (sufficient condition). Now we have
\begin{align}
\rho v(k) = \max_{\tau_1} H_1(k,\tau_1,\tau_2^*,\lambda_1).
\end{align}

I was wondering if the value function must be (strictly) concave to ensure optimality?

Any reference is appreciated.


Do we really need accurate utility functions? Knowing that a utility function's primary purpose it to be used as a tool to rank consumption bundles, I was wondering:

  "do we really need to be concerned with accurate identification utility functions or would simple structural assumptions do?"

The main argument against this would be that by using misspecified  utility functions we would end up with inaccuracy in estimation of demand.

But in terms of using it as an tool to index consumer welfare, does it really matter?

To the extent you are constructing marginal decisions from preferences, the general answer is no.  Any utility function that preserves preference orderings maps to the same partial or total order ranking.  As a consequence, $U(w)=\log(w),w>0$ and $U(w)=\sqrt{w},w>0$ preserve preference orderings with respect to $w$. Issues can exist in the multivariate case as all orderings and partial orderings must be preserved.

In the other direction, though, it does matter.  If you are beginning with utility and mapping to preferences, then any transformation results in a different preference structure unless it results in the same indifference curve.  As an example, $U(w)=\log(w)$ and $U(w)=\log(w)+5$ have the same indifference curve and so could be treated as the same preference structure.

So the answer is, unfortunately, dependent on the exact question you are asking.  If only the ordering matters, then no, it does not matter.  If the structure matters, then it can matter.


What does non degeneracy mean for a preference? I saw a non-degeneracy assumption in Gilboa and Schmeidler's paper (maxmin expected utility with non-unique prior).

The statement is "Not for all $f$ and $g$ in $L$, $f \geq g$".

So can you explain the intuition for this assumption and give some example so that I can understand the "non-degeneracy" property better?

It means what Herr K. has guessed: there are acts $f$ and $g$ that the decision maker does not deem equivalent from the preference standpoint. In other words, the DM expresses a strong preference in at least one comparison he makes. a preference that does not satisfy it is a AA subjective expected utility with a constant index $u$ (i.e. such that the representation is $\int u dp$ for an arbitrary belief $p$). On the other hand if at least for one comparison the DM says $f$ is strictly better than $g$ then you satisfy it.


Revenues and cost functions Let's assume that there is a firm that produces a single good, $q=f(x)$, where $x$ is a single input. The firm can sell it on the market at a  price $p$. It's production cost is given by a cost function $c(x)$.

In the most microeconomics textbooks the profit maximization problem is expressed as

$maxΠ=max\{pq-c(x)\}$, where $q$ is assumed to be linear function of $x$.

I am wondering if there is a textbook (or a resource in general) in which profit function is expressed as

$Π=pf(x)-c(x)$, where $f$ is concave in $x$ and $c$ is convex in $x$.

Profits of a price taking firm take the form
$$ p q - c,$$
where $p$ is the price, $q$ is the output and $c$ is the cost. Of course there is a relation between the output $q$ and the cost $c$ in the sense that higher $q$ will correspond to higher $c$. As such, these two quantities cannot be chosen independently.

There are two possibilities to make this relation explicit: (i) you express everything in terms of output or (ii) you express everything in terms of inputs.

In case (i), one usually defines a cost function $c = c(q)$ which gives the cost necessary to produce an amount $q$. In this case, the profit maximization problem takes the form:
$$\max_q  p q - c(q).$$
In case (ii) everything is expressed in terms of inputs.  If we call $x$ the amount of inputs then we can write $q = f(x)$ as the total output that can be produced using inputs $x$ and $c = w x$ as the total cost of using an amount $x$ of inputs. Here, $w$ is the unit cost per input (e.g. the wage rate if $x$ is labour). In this case the profit maximization problem is given by:
$$\max_x p f(x) - w x.$$

The various functions are related by the identity:
$$w x \equiv c(f(x)).$$


The appeal of low-dividend stocks when trading with government debt Background: In the 1710s, the British government borrowed heavily to finance wars. To reduce the interest on this debt, the government converted this debt into stock from a private company. The private company would only be paid a fee by the government equal to half the interest the government was paying on its debt. The company uses these fees to pay dividend on the stock it issues, which it uses to buy outstanding government debt.

Question: Why would an investor sell 1000 British pounds of debt that might pay 4% interest in return for 1000 pounds of stock in the company that paid only 2% dividends?

In the paper cited at the end of this answer, the incentives for all three parties involved are discussed. Not only did the creditors suffer from a lower return after the conversion, they also faced longer maturities and, given the strong heterogeneity in lending terms across bonds, also a destruction of bond specific information.

Nevertheless, conversions in line with your description were beneficial for the owners of the converted bonds since the conversion increased liquidity (the liquidity of the shares highly contrasted the illiquidity of government bonds) and reduced the probability of government default. In addition, the shares represented claims on rents of the company. Though, for the specific case of the South Sea Company, there have never been any rents involved.

  Stephen Quinn, 2008. "Securitization of Sovereign Debt: Corporations as a Sovereign Debt Restructuring Mechanism in Britain, 1694-1750,"
  Working Papers 200701, Texas Christian University, Department of Economics. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=991941


General Equilibrium with Linear Production I don't think I understand how optimization problems with a linear function work as of now. If you have a production economy with two agents, two goods and Cobb-Douglas utility representation, and you introduce a firm with a linear production function and fixed costs that basically acts as a transfer from one good (say x), to the other good (say y), as far as I can see, the solution to the firm's maximization is to shut down.

This is what I am talking about specifically:

$$
u_1(x,y)=\alpha\ ln(x)+(1-\alpha)ln(y)
$$
$$
u_2(x,y)=\beta\ ln(x)+(1-\beta)ln(y)
$$
$e_1=(0,1), e_2=(1,0)$
with a linear production function for firm $f(x)=x$ where they use x as an input and produce y, and there is a fixed cost FC>0 only if they produce. My problem lies in how do I solve the firm's maximization problem? It's linear, so I don't think I can use the FOC like you can with the utility maximization problem. Intuitively, I "feel" like it's going to be a corner solution, but I don't know how to systematically solve optimization problems with a linear function.

If the firm takes output price and wage as given, then its supply is infinity if the price is larger than the wage, and it is zero if the price is equal, or lower, than the wage. If the price is larger than the wage, the firm by increasing output can make arbitrarily large profits, and thereby, in particular, cover its fixed cost. If the price is equal or below the wage, then there is no way of making profits, and therefore, the unique best option is to set output equal to zero.


About gross domestic product at factor cost GDP at factor cost= Net value added + Depreciation. Here my question is why depreciation added to Net value added? I am confused here: Net value added = Gross value added - depreciation; so the above formula becomes GDP at factor cost= Gross value added - depreciation + Depreciation. Here depreciation get cancelled and finally becomes GDP at factor cost= Gross value added.
Source: http://www.economicsdiscussion.net/national-income/components-national-income/top-17-components-of-national-income/18793

The best practice would be to use definitions from recognized international institutions such as the World Bank or the Organisation for Economic Co-operation and Development (OECD). In this document The OECD classifies three types of gross value added (1) at  basic  prices, (2) at producers' prices and (3) at factor cost.

Let first define gross value added at  basic  prices  as  output  valued  at  basic  prices  less  intermediate consumption valued at purchasers' prices. Then, gross  value  added at  factor  cost  can  be  derived  from  gross  value  added  at  basic  prices  by subtracting other taxes less subsidies on production.

As an example, GDP  at  market  prices  for  the  United  States  in  1992  was US\$ 6,234 billion.  As GDP at factor cost removes all net taxes on production, it would equal \$6,234 billion less \$506 billion or \$5,728 billion.

GDP at factor cost is thus a way of measuring gross value added at some prices. So, as far as I understand, it makes sense that depreciation get cancelled and finally becomes GDP (at factor cost) = Gross value added (at factor cost).

Why is depreciation added to Net value added? According to your source, if we deduct depreciation from Gross Net Product (at factor cost), we get Net National Product (at factor cost). So, if we add depreciation to NNP we get GNP.


Proof of Choice Coherence in Kreps (2013) In the first chapter of Kreps (2013), there is a proof that the choice function satisfies choice coherence. Kreps writes:

I do not understand how the third sentence of (b) logically follows from the previous two sentences. How do we necessarily know that there is a third commodity, z, in A? There might just be two commodities. Furthermore, how do we necessarily know that u(z) > u(y)? Why can't the consumer possibly be indifferent between z and y?

If there is no $z \in A$ such that
$u(z) > u(y)$ (perhaps because no other $z$ exists, perhaps for other reasons)
then by definition of $c_u$ we know that $y \in c_u(A)$. This would contradict the assumption of the third sentence, that $y \notin c_u(A)$.

  If, moreover, $y \notin c_u(A)$...


Why do central banks print money? If a country's central bank prints money, it causes inflation. However, apparently, small amounts of inflation is a good thing.

Why is the case? What would happen if central banks stopped printing money altogether (except to replace destroyed bills)?

If a central bank stopped printing money then deflation would eventually occur meaning the value of $1 would increase over time.

There is a simple intuition as to why this would happen. Imagine there is an economy where the only product either produced or sold is widgets. Lets assume that the central bank fixes the total amount of currency in the economy at $1,000. Lets also assume to keep the math simple that every widget produced every year is bought and consumed and that people in this economy don't ever save money and spend 100% of their income every year on widgets (this is a dubious assumption in real life but makes the math easy, it is a fair assumption in real life that citizens will spend a certain % of their income on goods and services every year that are consumable).

If the economy produced 100 widgets per year based on its level of production and those widgets were bought using the available currency then each widget could sell for $100.

Lets now say that due to population growth and increases in technology the economy can now produce 200 widgets. There is only $1,000 to buy the 200 widgets so each widget now sells for $50.

The price level has halved. In order to buy the same product (1 widget) you have to spend half as much money. If the central bank wished to keep price levels the same they would have to increase the money supply to $2,000 to keep up with he increase in productivity. This is why you expect a central bank to increase the money supply over time.