Why is the Market-Clearing Price also an Equilibrium Price? When the price is such that supply equals demand for e.g. bicycles, everybody who wants to buy a bike at that price gets one, and every bike gets sold. Everybody goes home happy and the marketplace clears. Hence the price at which the supply and demand curves cross is the Market-Clearing Price.

This isn't enough to make it an equilibrium price. "Equilibrium" means that if the price is there, it'll stay there. If it's a stable equilibrium, then even if it starts above or below that price, it'll get pushed towards it.

I feel like I understand why prices starting below the market clearing price, will get pushed up. Of course a firm will raise prices: they can charge more per unit, and sell more units (assuming a rising supply curve).

If you start above market-clearing price, there is a trade-off, because sales are demand-limited (assuming the demand curve is decreasing). Raised prices would mean more revenue per sale, but fewer sales. Lowering the price would mean more sales, but less revenue per sale. Intro textbooks (e.g. Mankiw) seem to claim that the mere fact of there being a trade-off at all, is sufficient to push prices down, but it doesn't seem like that to me. Whether lowering prices would increase profits depends on the slope of the demand curve; if it's shallow enough, then the large increase in revenue-per-sale could make up for the small decrease in number of sales.

If I'm not wrong then a firm with a monopoly on bicycles would set prices to maximize revenue, i.e. the area of a rectangle whose length is quantity and whose height is price. The corner of this rectangle would lie somewhere on the demand curve, at or above the market-clearing price. The profit-maximizing price might be one where there's excess potential supply (bikes you would have been willing to make and sell - presumably you didn't actually bother making them).

I assume that competition is what makes the difference, and somehow forces prices down to (but not below) the market-clearing price, making that the equilibrium for competitive markets. But I don't get how this works, e.g. why underselling won't stop being worth it until there's excess demand.

(This is referring both to the initial question and to the comment. I would respond to each individually, but I don't think I have the reputation to address the comment directly.)

Paraphrasing a bit from your question, you're right- an equilibrium price is one where no firm has an incentive to deviate in their pricing or production decisions, and demand is perfectly satisfied (again, given the price). While the exact "mechanism" that would push price down might differ depending on what market type you're considering, the common feature will be that there is always a marginal incentive to deviate down to the lower price.

In terms of perfect competition- as you mentioned, it can be seen as a race for different firms to undercut their competitors, until they hit the no profit condition. That pushes the market clearing price down to marginal cost, which is the equilibrium price.

For monopolists, they're looking to maximize profit, not necessarily revenue. But, as every firm does, they choose a price p to satisfy:

$$
max\{q(p-c)\} = \pi
$$

They will choose a price higher than the one found under a perfectly competitive framework; hence why the market clearing price, and equilibrium price, is higher under monopoly than perfect competition.

But if the monopolist were to set a price different from the one that satisfies that maximization problem, they are pricing, as you described, too high. That tells them when to produce more units at a lower price; until their profit maximization price is hit. That becomes the clearing price, and the equilibrium price for a monopolist.

I'm sorry if that was too repetitive or elementary. You're question is an excellent one, and a somewhat subtle point has to be made. If it wasn't clear, or you'd like it re-framed, let me know!


How exactly does a central bank determine how much to cut/increase interest rates? We all know under what circumstances a central bank tries to cut interest rate and when it tries to increase interest rates, but how do those people know exactly by how much it should change?

I mean, there can be some trial and error, but what are the targets they chase and how exactly do they calculate the money demand, etc. There should be some basis to their conduct.

They don't know for certain. It's an inexact science. They do the best they can.

Alan Greenspan was known for pouring over all the economic data available for hours while mostly in the bathtub trying to make sense of what was happening in the economy. But ultimately, it came down to making an informed decision based on knowledge, reasoning, experience and intuition.

Policy objectives (which are quasi-political) can also come into play as sometimes desired results can compete. The classic example of this is economic growth vs. inflation.

Critics of government monopolized central banks argue that it is impossible for any single individual or group of policy makers to choose rates correctly and overnight interbank lending rates should be allowed to float freely and be determined by the market vis-a-vis supply-demand equilibrium. Hence the popularity of LIBOR and to a lessor extent EURIBOR as these are closer to market pricing than, say, the Fed Funds Rate. However, these are still only averages of central bank policy decision and, therefore, are not purely market-driven.


Why does a model that is used for policy analysis needs its shocks and parameters to be structural (= invariant) to the shock under consideration? In their paper, " New Keynesian Models: Not Yet Useful for Policy Analysis"

V. V. Chari, Patrick J. Kehoe, and Ellen R. McGrattan

argue that one needs a structural model in order to analyse the effect of economic policy. More specifically, they argue that it needs enough microfoundations consistent with the data such that both the models's shocks and parameters are structural. But in my opinion, they don't really explain why that is the case.

I understand that IF it is the case, you can do policy analysis, and the results of this analysis will always apply, because the model is unchanged nevermind any policy. This was the Lucas critique, on models that used adaptive expectations.

Why is this the case? Isn't it reasonable to assume that, in addition to many economic variables, also many parameters that govern micro behaviour will be influenced by a policy shock? Which contradicts their claim? Or do they only say that those parameters related to the shock under consideration cannot change? Why not? Isn't it wishful thinking one can ever settle down on a structural, fixed, microfounded model, as too many parameters governing micro behaviour depend on too many things like institutions, policy, technology, ... ?

Additional question: expectation formation is a microfoundation I guess. So, if we use the adaptive/heterogeneous expectations approach instead of the rational expectation assumption: I guess if an agent switches from a fundamentalist rule to an trend following rule (see the book and papers by Cars Hommes and De Grauwe and Zi), this is a structural change to the model? Or is this not structural, because the switching is a structural part of the model? However, it is exactly this endogenous switching that happens in response to (policy) shocks. How does this switching relates to the condition that models should be structural in their shocks and parameters to be used for policy analysis?

Some more context below:

"We begin by clarifying the distinction between reduced form and structural shocks.
This distinction is critical in policy analysis. The reason is that in order to do policy analysis,
we need to predict the consequences of changes in policy both for outcomes of the standard
economic variables and for welfare. Such a prediction is possible only with a structural model.
Speci…cally, a structural model must have two ingredients. First, the relevant elements of
the model— including the shocks— must be invariant with respect to the policy interventions
considered. Second, the shocks must be interpretable, so that we know whether they are what
could be thought of as “good shocks”that policy should accommodate or “bad shocks”that
policy should o¤set. Shocks which have both of these properties are referred to as structural
shocks and ones that do not are referred to as reduced-form shocks.

Proponents of the New Keynesian model argue that it is promising for two reasons. It
represents a detailed economy that can generate the type of wedges we see in the data from
interpretable primitive shocks; and second, it has enough microfoundations that both their
shocks and parameters are structural, in that they can reasonably be argued to be invariant
to monetary policy shocks. A model with both of these features would potentially be useful
for monetary policy analysis."

This is due to the famous Lucas critique.

To make long story short, in the past in the heyday of Keynesian macroeconomics it was quite normal for macroeconomists to just postulate some relationships based on relatively casual empirical observations like for example the Philips curve which says that there is positive relationship between inflation and employment.

However, this ignores some fundamental facts that such relationship only holds as long as people do not expect inflation. The (original) version of Philips curve did not really postulate any deep relationship between the two variables just assumed that it holds.

In short Lucas harshly criticized such approach as the (old) Keynesian approach gives you the correct predictions only as long as you assume that people are passive agents that do not adjust their behavior when government changes its policy. But that is not really reasonable assumption as we know from microeconomics people are not just passive actors, when government changes its policy people try to find ways how to take the maximum advantage of the new policy regime.

The Lucas critique is basically a generalisation of the Goodhart's law which states that "when a measure becomes a target, it ceases to be a good measure"

If you add structural microfoundations you create more rich model which actually has an ability to take account for peoples reaction to changes in policy.

For example, the New Keynesian version of Philips curve instead of assuming that there is positive relationship explicitly models peoples/firms expectations and shows that when  they do not expect inflation it is rational for them to increase employment but when they do it is rational for them to just adjust contracts in a way to account for inflation (for example linking pays to inflation). Hence in such model no matter what is the government policy (with respect to inflation) the answer will be always 'correct' in the sense that it does not just assumes there is a relationship but it explicitly models the reasons/mechanisms why there is sometimes positive and sometimes no relationship between inflation and employment.

  Isn't it reasonable to assume that, in addition to many economic variables, also many parameters that govern micro behaviour will be influenced by a policy shock?

Not really in the sense the microfoundations are set in the New Keynesian macro models. In such models when we talk about microfoundations we talk about proving the results of the model assuming that for example people are rational, have rational expectations and interact in the markets.

To affect such micro behavior the policy would have actually change fundamentally how people behave.

I suppose from sociological perspective you could argue that in a long term policy can change how people behave (I am not expert on that). But from economic perspective it is completely valid to say that model with solid microfoundations is policy invariant.

Moreover, note an extremely important caveat is what the authors from which you quote say here:

  Must be invariant with respect to the policy interventions considered.

Hence, it is not even necessary to make structural model that is invariant to any conceivable policy that you can imagine but rather the policies that are important for the model, like in Philips curve transitioning from market economy to centrally planned economy where property rights are abolished would certainly invalidate many micro foundations and probably changed conclusions, but different monetary policy doesn't and thats what is important.

Regarding your edit of a question, when it comes to microfoundations its not really about rational/adaptive expectations per se - it is about justifying people having such expectations based on some fundamental model of human behavior.

De Grauwe (and others) in his recent work takes a lot of inspiration from behavioral economics. In a sense his models are microfounded they just tweak the classical rational choice theory by adding some behavioral flavor to it. But I used the word in 'a sense' on purpose because to my best knowledge there is no general behavioral theory of human behavior. Rather he takes the rational choice theory and tweaks it by assuming that people are sometimes rational but in other situations not (or many of his models can be also interpreted as saying some portion of population is rational while other not).

Hence he uses some sort of microfoundations in a way that he has some model of fundamental human behavior based on which results are derived. But I would say there is some room for disagreement about that because since there is no general behavioral theory (at least not one accepted in macro for sure) you could argue that his assumptions on human behavior are ad hoc and not proper microfundations as he just assumes some behavioral regularities without really proving that they are not  policy dependent or giving some ‘deeper’ justification why some behavioral assumptions are made and not other other than showing that there is some support from them from behavioral economics or evidence (although I am just playing devils advocate - I actually really like the work of De Grauwe).


How did the authors of the (Credit Suisse) Global Wealth Databook calculate the Gini coefficient? how are you doing? I read the Global Wealth Reports from Credit Suisse and I wondered how the authors calculated the Gini coefficient. For example, on page 84 of this databook from 2010, how did they calculate it? Can somebody show me how they did it? I would like to recalculate it in excel. Thank you very much.
Example from the Databook 2010

The GINI has fairly standardized calculation so you can just follow the standard formulas. The GINI is the ratio of the grey area on the plot below (taken from wikipedia - which also mentions the formulas below) to the total area. Hence if you already have data where these areas are calculated you can simply compute GINI as:
$$GINI= \frac{A}{A+B}$$
If you have raw data then you can use formula:
$$GINI= \frac{\sum^n_{i=1}\sum^n_{j=1} |x_i-x_j| }{2n^2 \bar{x}}$$
where $x_i$ is the income of person $i$ (or if you are calculating wealth inequality wealth of person $i$). The formula above can be also rearranged in a different ways, so some textbooks/sources can express it in different way but the results will match.
Next the formula could be also expressed in terms of income distribution:
$$GINI= \frac{1}{2\mu} \int \int p(x_i) p(x_j) | x_i - x_j | dx_i dx_j $$
where $\mu$ is the mean of distribution of $x_i$.
You can find more on these in Sen, Amartya (1977), On Economic Inequality (2nd ed.). If you want something solely focused on GINI then Yitzhaki and Schechtman. The Gini methodology: A primer on a statistical methodology. Vol. 272. has an exhausting literature review on GINI.


Wouldn't abolition of cash give rise to a substitute currency? Some countries (e.g. Sweden and Denmark) plan to abolish physical cash in the future and restrict the use of cash to electronical deposits. One of the reasons for this is to prevent hoarding / boost spending of money, which could be achieved by introducing negative interest rates on deposits far below zero.

However, as far as I know, in times of hyperinflation, people resorted to substitute currencies (either foreign currencies or commodities like cigarettes). Wouldn't the same happen if cash was abolished?

For example, suppose the bank charges 20% or more on deposits and you can't withdraw your money in cash (since there is no cash), and you don't want to buy stocks or property for some reason (it's risky or hard to liquidate) and suppose other people have the same problems. Wouldn't it be reasonable then to create and use some alternative currency, like cigarettes or maybe a local currency, which you can store physically?

"Cash" is an emergent phenomenon of human economic organization. It exists for lots of reasons, as a provider of economic anonymity, a low transaction cost solution to the double-coincidence of wants, a portable medium of exchange, and a tool of economic accessibility for all including those in the informal economy, foreigners, the unbanked, and those with poor credit, among others.

A country can make it difficult to use cash in the interest of thwarting anonymity and convenience, usually to prevent money laundering and tax evasion. They can do so by taxing the use of cash, failing to enforce contracts calling for cash, refusing to make more, even criminalizing the possession of cash.

But cash is unlikely to die easily. We know from the experience with drug and alcohol prohibition as well as the international ivory and rhino horn trades that while the regulation can can certainly influence prices and thereby quantities demanded, it is awfully difficult to destroy a market for a valuable product. For a more specific example, possession of money is forbidden to US convicts. Nevertheless, they have developed internal monetary economies based around canned fish, shelf-stable pastries, as well as cigarettes and stamps. Cigarettes also emerged as money in WWII P.O.W. camps, showing that even the Nazis couldn't keep a monetary economy from forming.

Sweden in particular has a significant additional obstacle to keeping currency out of their economy. They share boarders with Norway and Finland, each with their own currency. Go to practically any boarder region or tourist spot around the world and you'll see tellers happy to take dollars, euros, or yen in addition to the local currency. It is especially difficult to ditch cash when other sources of cash are available.


Econometric model for TFP I want to model TFP series using an econometric model, be it AR(1) process, unit root with drift drift process etc. I was wondering if anyone knows of published papers discussing various methods of modelling technical progress. Alternatively, type in your model of TFP.

Thank you

Check the article:

Olley, G. Steven, and Ariel Pakes. The dynamics of productivity in the telecommunications equipment industry.

This is an Econometrica paper (1996). It is the standard method to estimate productivity nowadays.


World Bank lending categories I need to do data visualization of World Bank lending category for some countries using source from their page. When I was going through it I found some inconsistencies in categories they use to describe lending groups. According to the World Bank we have three lending group:

IBRD,
IDA,
BLEND

but to describe other data they used following markers:

IDA only  - IDX,
IDA total - IDA,
IDA Blend - IDB,
IBRD only - IBD,
IDA & IBR TOTAL - IBT

Which of the three lending group correspond to six following markers? I mean is IBRD same as IBD (IBRD only), etc?

Source [1] and [2].

As this page states:

  International Development Association (IDA) countries are those with low per capita incomes that lack the financial ability to borrow from the International Bank for Reconstruction and Development (IBRD). Blend countries are eligible for IDA loans but are also eligible for IBRD loans because they are financially creditworthy.

Therefore the classification of countries can be representd with the following Venn diagram:

The final category, IBT, compromises IDA + IDBR, equivalent to IDX + IDB + IBD.

Note: this is my interpretation, and not based on an official definition (which I couldn't find).


What are some books for pricing theory with heavy math? What are some books for pricing theory with heavy math?

I've finish reading pricing theory by Hirshleifer and another by Lansburg but both are not math intense.

Darrel Duffie is the graduate school standard for asset pricing:

Gary Becker and Milton Friedman also have titles that fall within your prompt and are very accessible given your background


Money in utility function - Value function I am reading Walsh's (2003) book on monetary economics. Specifically the chapter on money in utility function. I understand the basics of a value functions but I can't seem to get the same results as the author.

Where

I.e the per capita budget constraint. He then finds an expression for $w_{t+1}$:

This is the first source of my confusion. Previously he defines output per worker as a function of capital per worker, i.e $y_{t}=f(\frac{k_{t-1}}{1+n})$ where $n$ is the population growth rate. But all of a sudden he changes it to $\frac{f(k_{t-1})}{1+n}$. I am aware that there are many typos in this book, is this just one of them or am I missing something trivial?

Either way, he uses the budget constraint to express $k_{t}$ as $w_{t}-c_{t}-m_{t}-b_{t}$ and the definition of $w_{t+1}$ to express the value function as:

Now, I don't know if it is because I am sleep deprived or because there is a typo, but I just can't seem to get the same results as Walsh. E.g, differentiating w.r.t $c_{t}$ I get:

$u_{c}(c_{t},m_{t}) + \beta*V_{w}(w_{t+1})[\frac{-f'(w_{t}-c_{t}-m_{t}-b_{t})}{1+n}(-1)+\frac{1+\delta}{1+n}(-1)]$

While Walsh gets

Am I missing something obvious or is there a typo?

Thanks in advance!

Your calculation has two typos a) you type two times the minus sign related to $f'$ and b) you write $(1+\delta)$ instead of $(1-\delta)$. If we correct for these we have

$$u_{c}(c_{t},m_{t}) + \beta V_{\omega}(\omega_{t+1})\left[\frac{f'(\omega_{t}-c_{t}-m_{t}-b_{t})}{1+n}(-1)+\frac{1-\delta}{1+n}(-1)\right]$$

Taking out the minus sign and $1/(1+n)$, and compacting $f'(\omega_{t}-c_{t}-m_{t}-b_{t})=f_k(k_t)$  we have

$$u_{c}(c_{t},m_{t}) - \frac {\beta}{1+n}V_{\omega}(\omega_{t+1})\left[f_k(k_t)+1-\delta\right]$$

which is the expression in the book.

As regards the definition of output per worker:
Given the clarification in the comments, aggregate output during period $t$ is

$$Y_t = F(K_{t-1}, N_{t})$$

while $N_t = N_{t-1}(1+n)$.

I guess constant returns to scale are assumed so per capita magnitudes are

$$y_t = \frac{Y_t}{N_t}  = F\left (\frac{K_{t-1}}{N_t}, \frac{N_{t}}{N_t}\right ) = F\left (\frac{K_{t-1}}{N_{t-1}(1+n)}, 1\right )$$

Now, consider the notational/conceptual problem here: we will tend "automatically" to write $K_{t-1}/N_{t-1} \equiv k_{t-1}$ due of the same index, but $K_{t-1}/N_{t-1}$ is economically meaningless because $K_{t-1}$ is not combined in production with $N_{t-1}$. This ratio describes "capital used in period $t$ per worker in period $t-1$".

Anyway, if we clearly declare in building the model that we define $k_{t-1}$ in this way, then we end up with

$$y_t = f\left(\frac {k_{t-1}}{1+n}\right)$$

and the budget constraint for period $t$ is correct while the one for period $t+1$ is not. How this affects the first-order condition with respect to consumption?

(Notice that with these notational coventions, "capital per worker during period $t$" is $k_{t-1}/(1+n)$ -I have argued elsewhere why it is preferable for modellers to adopt the meaning that $k_{t-1}$ represents the value at the beginning of period $t-1$ and so is used in the production of period $t-1$).


What are some database like websites about lower levels of economics (micro/macro) for a research project? I'm looking for some websites; books or videos on the beginning levels of economics like micro and macro economics to do a research project projects on.  I found some course videos but they were a bit confusing.  I'm not sure what specific fields I'm supposed to begin with but I'm looking for but the lower levels of subject in both micro and macro economics.

What are some clear and trustworthy resources you recommend.  One's like database with the reference links (works cited) would be really good.

Fama-French library
has good data on which you can test your first Fama-French regression model.

I have found this video on Youtube that might help you with this first project.

Ps.: It would help a lot if you were more specific about what you want to learn. I can give other suggestions, but I really don't know what you are looking for.


Is the world economy highly-dependent on the United States of America? How dependent is the economy of the world on the United States?

Can US policies have disastrous impacts on other superpowers in the world such as Germany?

For example, take into account countries such as Iran and Turkey which were hit by US sanctions and their economy soon deteriorated.

I want to know if the same can happen to a country like Germany, UK, or Japan if at some point in time US decides to impose similar measures on such countries or even decide to stop doing business with them?

In brief, can German economy, as an example, survive without the United States? Are they heavily-dependent on the US?

During 2017 US GDP made up 24.03% of global GDP, so yes, the world economy is heavily dependent on the US.

Specific effects on individual countries depend on current levels of trade.  The one country that would be most negatively affected (especially given news about the NAFTA negotiations), would be Canada (582 billion traded with a GDP of 1.653 trillion).  Most other countries probably wouldn't experience that level of total economic collapse, but depending on what scenario you're suggesting things aren't going to go well regardless since the US is also instrumental in doing things like the dollar being the global reserve currency and being the basis of the petro trade, as well as subsidizing global security (mostly in regards to international shipping and piracy).


Why does the Fed not fiddle with the reserve ratio? We often hear in the news of the Fed changing the interest rate. Why do they not commonly alter the reserve ratio?

Won't either be capable of expanding or contracting the money supply?

The operating procedures the Fed has followed has changed over the years. I will first discuss the situation pre-2008, and then discuss the current situation.

Situation 1994-2008.

The Fed has an interest rate target, and the amount of excess reserves in the system was typically very small. Under normal circumstances, the Fed controls the amount of reserves in the system with open market operations. If nothing else happens, if the Fed buys \$1 billion in securities, it will create \$1 billion in reserves. (Exceptions include: banks may exchange reserves for notes and coins, and if there was a shortage of reserves, banks would be forced to go to the discount window to borrow to meet reserve requirements.)

In other words, the Fed has to supply whatever reserves are required by the banking system. Banks lend first, then search for reserves later. If there is a shortage in the system, the Fed has to create reserves to meet demand, or else the interbank rate will go above target.

This means that reserves follow lending decisions, and the only influence the Fed has on the level of the money supply is through the moderating effect of interest rates on expectations.

Note that this explanation is known as "endogenous money", as opposed to "exogenous money", and which version is correct is/was a major debate. The endogenous money stance seems to be closer to the modern consensus; Monetarists were the main propenents of exogenous money. I believe that the modern version of "exogenous money" is more complex than the old belief (the central bank directly sets the level of the money supply), and the short-term story ends up being similar to my description above. Unfortunately, undergraduate textbooks tend to push the old exogenous money story.

From this standpoint, changing the reserve ratio will do very little, it just changes the amounts of reserves that the Fed has to create/destroy in order to hit its interest rate target. The reserve ratio has an effect on the competitive position of banks versus non-bank financial firms, and so reserve ratio changes end up having a distorting effect on competition.

The general irrelevance of reserves in monetary policy explains why reserve requirements were abolished in many developed countries, such as Canada.

The current situation features large amounts of excess reserves; changing the reserve ratio would imply no change in policy, as all that happens is that some existing reserve positions are reclassified, with no other effect.


Government expenditure multiplier in the new-Keynesian model? Does a temporary increase in government expenditure increase output in the standard new-Keynesian DSGE model? Is it possible to draw any intuitive parallels between the impact of government expenditure in these model and in the IS-LM model?y

The "standard" New Keynesian model could be many things, but suppose that we're dealing with the basic log-linearized 3-equation model (intertemporal Euler equation, New Keynesian Phillips curve, and monetary policy rule) exhibited, for instance, in Gali's textbook.

In most variants of this simple model, a temporary increase in government expenditure will almost always increase output, but the intuition is different from the Old Keynesian IS/LM model. The extent of the increase depends on the monetary policy rule.

If the monetary policy rule targets inflation of exactly zero (assuming trend inflation is also zero), then it turns out that there is no difference between the effects of government expenditure in the NK model and the effects in a purely real model; by successfully targeting zero inflation, we effectively negate the effect of the NK model's nominal frictions. Since the underlying real model produces an increase in output when government spending increases (ignoring effects of possible distortionary taxation used to fund this spending), we get this in the NK model with inflation targeting as well, but it's not very exciting. It's a purely classical story: all else equal, consumers work harder when their consumption is lower, and thus consumption does not drop one-for-one with increases in government spending.

If the monetary policy rule happens to target a constant real interest rate, then in the basic NK model the "multiplier" is exactly 1: the constant path for the real interest rate leaves consumption unchanged, and the increase in output exactly equals the increase in spending. If the monetary policy rule targets a constant nominal interest rate during the stimulus, then there is an additional effect because future stimulus spending produces expected inflation that lowers the real interest rate and boosts consumption. This is the source of "multipliers" >1 in the basic NK framework. See Woodford's 2011 AEJ macro paper for more details on this.

None of this comports with the traditional Keynesian 1/(1-MPC) multiplier. This is for a couple reasons, but most important is the fact that the basic NK model features fully Ricardian consumers who intertemporally smooth consumption and anticipate future taxes levied to pay for current spending. Gali, Lopez-Salido and Valles's 2007 JEEA comes much closer to the traditional story by adding ad-hoc "non-Ricardian" households.


Why did the Swiss National Bank abandon its currency peg so suddenly? There are many theories about why the Swiss National Bank (SNB) abandoned its currency peg a few days ago.

My question is more specific:  why did they make the change so sudden?  Why not reduce the peg to 1.19 (Francs needed to buy one Euro) one month, 1.18 the next month, and so on, until a reasonable balance is found, taking into account all of the factors that the bank would want to consider in targeting an exchange rate?

Disambiguation update: Some of the commentary/responses below maybe should be directed at the following related questions:

Why did some call maintaining the peg "expensive"?
Why did the SNB decide to end the currency peg?

Just to synthesize the other two answers together a bit and "join-the-dots".

Setting the Scene

Since 2011 SNB had decided that it wanted to prevent the CHF from strengthening past 1.2 CHF per EUR.  In order to do this it had to do either or both of:

Discourage people from buying CHF.  One way to try do this is to keep rates low.
Sell CHF by the bucket load.

Keeping rates low at the short end is easy enough - that's the base rate.  But that was scuppered by the low EUR short rates.  Keeping rates low at the long end is trickier, but can be done by not issuing too many bonds.

Selling CHF is fine, but that means buying other currencies.  By the end of December the SNB had bought 85% of GDP worth of foreign currencies.

At this point the SNB decided that it did not want to keep expanding the balance sheet.  Why it decided this is a different question (as the question points out).  The question is how to end a cap once you hold a huge Euro position.

The Sudden Act

Once the SNB had decided it could not defend the cap, it had three ways it could act.

Stop supporting the cap, but not tell anyone
Tell people at the same time that it stops supporting the cap
Tell people before it stops supporting the cap (or as in your example, schedule a reducing cap).

The third case would have almost certainly bankrupted the SNB.  If they had, as you suggest, let everyone know in advance what was going to happen, then everyone in the world would just arbitrage the situation into the ground.  Everyone would just buy CHF from the SNB at the cheap rate while they support the cap, and sell as soon as the cap is dropped.

The first case is a little dishonest, and would almost certainly get found out (the worst kind of dishonesty!).  As soon as they stopped supporting the cap, the FX rate would drift slowly down from 1.2.  Once people realised that this was not "supposed to happen" and therefore the SNB must have stopped defending it, then it would probably snap anyway.  There are two dubious plus sides to this approach I see though

The SNB could have started offloading some of its 85% holdings before the market realised.  This is called front running and market abuse, and would land a stock trader in jail, but for a central bank trading FX, it would not technically come under any legal challenge (at the moment...).
The reputational damage to the SNB would be huge, which would go some way to undermine investment in the country, causing a weakening in the CHF!

As you can see this would be a rather dubious strategy, but I have often wondered if Thomas Jordan (chairman of SNB) could simply address the world with underpants on his head and his willy hanging out as a way to depress the CHF.

The strategy they opted for was the "ripping off a bandaid" style.  The sudden shock is estimated to have cost the SNB about 13% of GDP due to all those foreign holdings.  Since the SNB made a massive profit in 2014 (see: http://www.bloomberg.com/news/2015-01-09/snb-sees-2014-profit-of-38-billion-francs-resumes-dividend.html) it probably saw this as an opportunity to get out before things got any worse.  Hold out longer and have 100+% GDP in foreign currency, and the bank might not have survived the jolt itself.


Interpretation of regression coefficients with and without logs Say you want to estimate return to education.

Model 1 (no log): assume the DGP is:

$$w_{i} = \alpha + \beta x_{i} + \zeta_{i} + e_{i}$$

where $x$ is years of schooling, $\zeta_{i}$ is unobserved heterogeneity (e.g. capturing ability), and $e$ is an idiosyncratic error. Furthermore, wage is measured in \$ per hour.

Question 1: since the dependent variable is in wage per hour, does this imply that $\alpha, \zeta_{i}$, $e_{i}$ are also in wage per hour? Same for the composite $\beta x_{i}$? If this is the case, then $\beta$ -- the return to education -- is defined as wage per hour, per year of experience.

Model 2 (log): assume the DGP is:

$$\ln{w_{i}} = \alpha + \beta x_{i} + \zeta_{i} + e_{i}$$

where wage, $x$, $\zeta_{i}$ and $e$ are as defined above.

According to answers to this question, the log transformation of a variable is dimensionless. In consequence, $\ln{w_{i}}$ is dimensionless.
Question 2: does this imply that $\alpha, \zeta_{i}$ and $e_{i}$ are also dimensionless? Is the composite $\beta x_{i}$ dimensionless? If so, the dimension of $\beta$ is "1 over years of experience"(!). How it is then that we can interpret $\beta$ as the % change in wage following a extra year of education?

A possible answer if it's not too late.

Q1: Yes, if you mean "per years of schooling" at the end of your question. So, the unit of $\beta x_i$ is $\$/hr$.

Q2: The unit of $\beta$ is $\log(\$/hr)/years$ literally. Then the unit of $\Delta (\beta x_i)$ is $\Delta \log(\$/hr)$, nothing strange, which is approximately the % change times 0.01. This is "dimensionless" if you like to say so, or would "dimension-irrelevant" be better? We interpret $\Delta (\beta x)$ as % change, not $\beta$.


Subgame Perfect Equilibrium in Baye, Shin (1999) The following is taken from Baye, Shin (1999)
Consider a contest over a prize valued at 1 with symmetric players $1$ and $2$ who exert a level of effort $x_1$ and $x_2$ respectively. Effort cannot exceed $2/3$. Profit ($\pi$) of player 1 is
$$\pi_1=\frac{x_1-\frac{x_1x_2}{2}}{x_1+x_2-x_1x_2}-x_1$$
The simultaneous-move equilibrium is (denoted with superscript $*$)
$$x_1^*=x_2^*=1-\frac{\sqrt{2}}{2}$$
The profit for each is
$$\pi_1^*(x_1^*,x_2^*)=\pi_2^*(x_1^*,x_2^*)=\frac{\sqrt{2}-1}{2}$$
And we have that the best response of player $2$
$$R_2(x_1)=\frac{2x_1-\sqrt{(-2x_1^2+4x_1)}}{2(x_1-1)}$$
However, suppose that player $1$ 'moves' before player $2$. Then, player $1$ would deviate (upwards) from $x_1^*$, presumably, because player $2$ would reduce it's level of effort, and it would receive more of the prize. How does one show this?

In the article, Baye and Shin consider the new Stackelberg equilibrium $\pi_1^s$ where they show that $\pi_1^s(x_1^*+\epsilon)>0$ for some $\epsilon>0$. Specifically
$$\pi_1^s(x_1^*+\epsilon)-\pi_1^*(x_1^*+x_2^*)=\frac{\sqrt{1+2\epsilon\sqrt{2}-2\epsilon^2}-1-\epsilon\sqrt{2}+2\epsilon^2}{\sqrt{2}-2\epsilon}>0$$

I've tried replicating their result by seeing how $x_2$ changes with $x_1+\epsilon$ and substituting $x_1+\epsilon$ and the new value of $x_2^s$ into $1$'s profit function, but I fail to reach their result.

True to the saying that a picture is worth a thousand words, let's plot the profit function under the Stackelberg game and see what we're dealing with.

You correctly observed (or copied from the Baye, Shin paper) that the reaction function of player 2 is:

$$
R(x_1)=\frac{2\mathit{x_1}-\sqrt{2}\,\sqrt{2\mathit{x_1}-{{\mathit{x_1}}^{2}}}}{2\mathit{x_1}-2}\
$$

Inserting this reaction function in the profit function of player 1 gives us a complicated expression:

$$
\pi(x_1)=-\frac{{{2}^{\frac{3}{2}}}\,\sqrt{2-\mathit{x_1}}\,{{\mathit{x_1}}^{2}}-2{{\mathit{x_1}}^{\frac{3}{2}}}-3\sqrt{2}\,\sqrt{2-\mathit{x_1}}\,\mathit{x_1}+4\sqrt{\mathit{x_1}}}{{{2}^{\frac{3}{2}}}\,\sqrt{2-\mathit{x_1}}\,\left( \mathit{x_1}-1\right) }
$$

(Perhaps more advanced symbolic math programs can further simplify this, mine won't). In any case this is  a function of one variable $\mathit{x_1}$, and can be plotted. For completeness I have inserted the original equilibrium as well.

As you can see the original NE is no longer a local maximum, and player 1 can increase its profits by increasing their effort.


Short-run price competition with capacity contraints I am doing an undergrad course in Industrial Organization and at the end of the chapter on Short-run price competition (Bertrand and Cournot models mainly), there is a question with which I'm struggling. Here it is:

  Consider a market with two price-setting firms producing a
  homogeneous product. The demand function is q = D(p) = 1 – p,
  which implies the inverse demand p = 1 – q1 – q2. The two firms
  have capacity constraints q1hat and q2hat , where q1hat + q2hat = 3/5. The
  marginal cost of production is zero for qi ≤ qihat and infinite for qi >
  qihat for any i = 1,2. Finally, assume that consumers are rationed according to the efficient rationing rule.

  i. Show that if q1hat = q2hat , there is a unique Bertrand-Nash equilibrium
  where p1 = p2 = p* = 1 – q1hat – q2hat

  ii. Show that when q1hat ≠ q2hat, the equilibrium under part (i) breaks
  down when the firms’ capacities are too dissimilar.

So for part i. I basically adapted part of the material from the chapter and said:

  To show that this is a Nash equilibrium, we need to show that none of the
  firms has an incentive to unilaterally deviate from this equilibrium.

  Is it profitable for firm 1 to set a price lower than p*, given that firm 2 sets price p*? The answer is no. By charging p* firm 1 sells exactly q1hat. Firm 1 cannot produce more than q1hat anyway, so by reducing its price below p* it would simply sell the same quantity at a lower price and would therefore make
  less profit.

  Is it profitable for firm 1 to set a price higher than p*, given that firm 2 sets price p*? The answer is again no, but the argument now is more subtle.
  Suppose that firm 1 sets a price p ≥ p*. Then it has residual demand 1 –
  p – q2hat, because at price p total market demand is given by 1 – p and firm
  2 sells q2hat. Firm 1 makes profit Π = p(1 – p – q2hat). Using the inverse demand function, the expression for profit can be written as (1 – q1 – q2hat)q1, where q1 is the quantity sold by firm 1 at price p. Note that the profit function Π = (1 – q1 – q2hat)q1 is exactly the same as the profit function of a firm that chooses output q given that the rival firm chooses output q2hat. This profit function is concave in q, that is Π''(q1) < 0. Also, ∂Π/∂q1 = 1 – 2q1 – q2hat. Evaluated at q1 = q1hat, this derivative is equal to 1 – 2q1hat – q2hat, which is positive because q1hat + q2hat = 3/5 and q1hat = q2hat so 2q1hat + q2hat = 9/10. In other words, if firm 1 starts from q1hat and marginally reduces its quantity, its profit will fall. This result and the concavity of the profit function ensure that any reduction of q1 below q1hat will reduce profit. Another way of saying this is that if firm 1 starts from p* and increases its price, its profit will fall.

So far so good, the concavity of the profit function implies that when we close in to the maximum marginal profit, the slope (or the derivative of profit with respect to q) will be closer and closer to 0.

Now part ii. gets me and I don't know how to attack it. I thought about making 2 cases, one where q1hat is close to 3/5 and one when it is close to 0. The profit function and its derivative are the same as for i. and the constraint q1hat + q2hat = 3/5 is still applicable from what I can understand, so demand can't be met. For me the part about setting a lower p is still the same as in part i. But the part about setting a p higher than p* is not as clear.

Can anybody help?

If Firm 1 assumes Firm 2 produces and sells the maximum it can produce, i.e. $\hat{q}_2$, then Firm 1 can aim to maximise its revenue and profit $$\Pi_1=q_1p = q_1(1-q_1-\hat{q}_2)$$ which is maximised at $\left(\dfrac{1-\hat{q}_2}{2}\right)^2$ with $q_1=\dfrac{1-\hat{q}_2}{2}$, at least when Firm 1's maximum production exceeds this quantity. If not, then Firm 1 should continue to produce as much as possible.
So if Firm 1 is big enough then both firms producing as much as possible may not be an equilibrium

As an example, suppose $\hat{q}_1=0.5$ and $\hat{q}_2=0.1$, with a sum of $0.6=\frac35$ as required. If both firms produce at maximum capacity then the price will be $1-0.5-0.1=0.4$ making the Firm 1's revenue and profit $0.5\times 0.4=0.2$

But if Firm 2 produces at maximum capacity and Firm 1 were to produce only $0.45$, this would make the price $1-0.45-0.1=0.45$ and the Firm 1 's revenue and profit $0.45\times 0.45=0.2025$ which is higher than $0.2$, and the Firm 2 will also see profits rise due to the price increase, showing that both firms being at maximum production would not be an equilibrium in this case

With the overall maximum production being $\frac35=0.6$, the equilibrium will break down in this way if $\hat{q}_1\gt \frac25 =0.4$ and $\hat{q}_2 \lt \frac15 =0.2$


How is reserve money 'multiplied' by the banking system? I'ma an econ newbie so please forgive my lack of understanding.
I am confused as to how the money multiplier effect works. I get that the money multiplier effect doesn't actually hold true as banks don't loan out all their funds but I don't understand the mechanics behind how the multiplication takes place.
Initially I had thought that when, for example, a bank receives $10,000 from a Fed asset purchase, it is able to use the 10,000 USD to meet its (let's say 10%) reserve requirement, and can thus make 100,000 dollars in new loans. However I've just read an article by the Federal Reserve Bank of Chicago that suggests that this is not how money multiplication occurs, and instead that it occurs indirectly through many transactions (best demonstrated graphically, below). This confuses me, why doesn't the initial 10,000 dollars count as reserve money? Surely the  first bank could use it to loan out 100,000 dollars, creating an asset in the form of a loan and 'creating' a liability in the form of the borrower's deposit - isn't this how money is created?   Thank you in advance.

This overlaps an existing question: Can money multiplier happen within a single bank? The mechanics is described in there, and I think it addresses some of your questions.
My guess as to what is happening in the explanation you found is that there is an added behavioural assumption: banks only make loans up to the size of their excess reserve position. This means that if there is an injection of reserves, there can only be a loan of the same size as the injection, then a sequence of smaller loans. You then end up with diagram result. The reality is that this is not how banks operate, and they could just make a single loan and use up the excess reserves in one shot. (Obviously, could be done in smaller steps.)
The “sequence of small loans” story was probably in an old Economics 101 textbook, and it has been repeated many times. I have not seen a formal version of this model, so I have no idea why the non-existent constraint on loan size is imposed in the money multiplier model explanation.


Can implicit costs make every option not worth doing? I'm new to microeconomics so sorry if this is simplistic, but if an action should only be taken when benefits > costs and opportunity costs are included in cost calculations, how would one deal with situations that arise when implicit costs make either choice not worth doing? For example, if you have the option to see a movie or go bowling at the same time, and the movie ticket is 10 dollars with 12 dollar benefit and the bowling entry is 15 dollars with 17 dollar benefit, wouldn't that make the costs (including opportunity cost) of the movie 27 and bowling 27, both higher than their benefits, so a person should choose to do neither? This seems illogical so I'm sure I am missing something.

As correctly pointed out by @Herr K., the opportunity cost of forgoing a movie (bowling) and going bowling (to a movie) is $2.
Hence, the net payoff from going to a movie = benefit - cost = 12 - (10+2) =0.
Similarly, the net payoff from going bowling is 17-(15+2) = 0
Hence the consumer should be indifferent between bowling and going to a movie.


Can a country's default on internal debt affect the rates of the external debt? If a country is ready to default on internal debt and ready to confiscate their citizen's money to pay external liabilities, does that affect the yields of the external debt?

If yes, does that make it higher or lower?

Probably, but it's not visible because a country is usually already in shambles before a default, and data collection for domestic debt crises is poor.

Here is a list of defaults:

http://www.nber.org/papers/w13946

Here's some rate data:

http://www.statistikbanken.dk/statbank5a/SelectVarVal/saveselections.asp

http://www.tradingeconomics.com/argentina/inflation-cpi

https://en.m.wikipedia.org/wiki/Historical_exchange_rates_of_Argentine_currency

There have been many cases where countries default on only internal debt. Argentina did this. I can't find bond data anywhere. But when it defaulted on domestic debt (1989), inflation went up and the currency fell. Which is pretty much the same as an increase in external interest rates.


How to prove that profit function is convex in price (with smaller price)? According to this site, if output price increases from $p*$ to $p'$ and factor prices remain constant, then a new production bundle chosen must yield at least the same amount of profits as the old bundle, as the old profit would yield at least as much profit in higher output price. The reasoning behind which is understandable.

However, how does it also apply for the case when output price decreases from $p*$ to e.g. $p"$? How does one be sure that the maximum profit at $p"$ would definitely be higher than the one at $p*$ (instead of lower)?

Also what does it mean by "reverse convexity" in "A reverse convexity will be obtained if we plot $\pi (p, w)$ against a particular factor price, $w_i$." in the aforementioned proof on the same site? I can not even find a proper definition of the term on internet.

I don't think it is a case. On a page you linked we have a proof that the profit function is non-decreasing in $p$. If the output price decreases, $p \geq p'$ and factor prices remain constant, $w_i \leq w'_i$ for all inputs, then the profit would be less or equal to the previous one.

Then, in connection to your previous question: How to prove that a concave production imply that the input requirement sets are convex? you can let $\mathbf{y}=(y,-\mathbf{x})$ be maximizing profit at $(p,\mathbf{w})$ so that your profit function becomes $\pi(p,\mathbf{w})=py-\mathbf{wx}$. On page 12. of the Lectures in Microeconomic Theory Fall 2009, Part 3 you have linked, you can see a proof of that (probably the same as on the page you linked just now but not sure as the page does not open properly to me (cannot really see the mathematical equations).

As for your second question - "reverse convexity" is a little bit strange expression, to show what the author meant I will use a picture.

As you can see it is still convex in input prices $w$. However, in comparison to plot with output prices $p$, it is decreasing.

Algebraically, you can see it that way:

Profit function is convex in both prices: $$\frac{\partial^2\pi}{\partial p^2}>0 \;\;\; \textrm{and} \;\;\; \frac{\partial^2\pi}{\partial w^2}>0$$
Profit function is increasing in output prices $p$: $$\frac{\partial\pi}{\partial p}>0 $$
Profit function is decreasing in input prices $w$: $$\frac{\partial\pi}{\partial w}<0 $$


Has there been an applications of search and matching theory in the Neoclassical Growth Model? Specifically, I am looking for the standard neoclassical growth model, but the labour decision is based on either search or matching theory instead of a Walrasian labour mechanism.

Search and matching models are fairly standard in macroeconomics. I guess this is fair to say since Peter Diamond, Dale Mortensen, and Christopher Pissarides won the Nobel prize in 2010. These are the names behind the canonical DMP model that most graduate students have to study in their first year. Although I am not a macroeconomist, I am confident to say that search models recognized as a key ingredient to explain unemployment in equilibrium. I suggest to watch the interview with Per Krusell on the Nobel prize homepage and read the scientific background.


Framing Effect Risk-Aversion Risk-Pursuit I am an economics' graduate seeking to study Law and I want to illustrate the importance of legal certainty. Penalties, Costs are negativelly framed.

I am trying to word.

200 dollars with 50% certainty or 100 dollars with absolute certainty both positevely and negatively.

The negative part is particularly difficult. I am giving nuances I should not.

I tried You find 200 dollars on the street( suppose you are unable to give them back) and after this you either have to pay 100 dollars or 200 with 50% certainty.

I do not know what nuances I give of but I always seem to fail to show people's inconsistency which I necessarily need to illustrate the importance of legal certainty.

How can I word the experiment question so as to best illustrate the Framing Effect?

The following is a slight rewording of an example in Richard Thaler's Misbehaving (1):

  Positive framing of certain outcome

    Imagine you are $300 richer than you are today.  You are given a choice between:

      A. A certain gain of \$100.

      B. A 50% chance to gain \$200 and a 50% chance of losing \$0.

  Negative framing of certain outcome

    Imagine you are $500 richer than you are today.  You are given a choice between:

      A. A certain loss of \$100.

      B. A 50% chance of losing \$200 and a 50% chance of losing \$0.

It can be seen that, under either framing, choice A implies \$400 richer than today while choice B implies a 50% chance of \$500 richer and a 50% chance of \$300 richer.  According to Thaler, however, 72% of subjects chose A when presented with the positive framing and only 36% chose it when presented with the negative framing.

To modify this to fit the terms of your question, the initial figures in both framings could be reduced by \$300. The second would then become "Imagine you are \$200 richer ...".  The first would no longer require any imagining.  My (untested) intuition, however, is that the inclusion of imagining in one framing but not in the other might influence people's responses in some way that Thaler's formulation avoids.

I therefore suggest instead the following, because it retains the symmetry of imagining in both framings:

  Positive framing of certain outcome

    Imagine you are \$50 richer than you are today.  You are given a choice between:

      A. A certain gain of \$50.

      B. A 50% chance to gain \$150 and a 50% chance to lose \$50.

  Negative framing of certain outcome

    Imagine you are \$150 richer than you are today.  You are given a choice between:

      A. A certain loss of \$50.

      B. A 50% chance to gain \$50 and a 50% chance to lose \$150.

Reference

(1) Thaler R (2015) Misbehaving: the Making of Behavioural Economics, republished by Penguin Random House UK in 2016, p 33.


When would prices increase according to Malthusianism? Malthusians and Neo-Malthusians believe that, eventually, the population of the earth will be exceed the number of people able to be sustained by the earth's food production.  As such, they advocated different forms of population control.
However, it appears that an increase in the population beyond that of the food supply would cause an increase in the overall real price for food.
Proponents of Malthusianism, evidently, are not waiting for food prices to rise before advocating population control, but I do not see how we should be worried until the real price of food increases.
If Malthusianism is correct, how soon before the population crash would prices begin to rise?

This question rests on a few assumptions.
So let's dig into them.
What Malthus Said
First, the Malthusian collapse you are referring to is similar to the Malthusian Trap, from whence it derives, so let's look at that.
From Wikipedia:

In accordance with the theory, cross-country evidence indicates that technological superiority and higher land productivity had significant positive effects on population density but insignificant effects on the standard of living, during the time period 1–1500 AD. In addition, scholars have reported on the lack of a significant trend of wages in various places over the world for very long stretches of time. In Babylonia during the period 1800 to 1600 BC, for example, the daily wage for a common laborer was enough to buy about 15 pounds of wheat. In Classical Athens in about 328 BC, the corresponding wage could buy about 24 pounds of wheat. In England in 1800 AD the wage was about 13 pounds of wheat. In spite of the technological developments across these societies, the daily wage hardly varied. In Britain between 1200 and 1800, only relatively minor fluctuations from the mean (less than a factor of two) in real wages occurred in Britain. They peaked at around 1450 and in 1800 they were actually significantly worse.

So to go back to the source, Malthus didn't predict a population explosion at all (or food price rises for that matter). In fact, his theory was specifically that population growth fluctuated with economic development such that the prices of wheat (in terms of wages) remained relatively stable over two millennia.
This was known as the Malthusian Trap, where technological advancement would always be matched by (not exceeded by) population growth, resulting in the stagnation of living conditions.
Since the time of Thomas Malthus, new evidence has emerged that, while the trap may exist, many societies break out of it, and achieve explosive growth in living conditions. This is generally termed, the "breakout". In A Trap At The Escape From The Trap?$^1$, Andrey Korotayev suggests that this breakout leads to social upheaval, and may have played a role in events like the revolutions in Latin America, or possibly even the formation of the US. Unfortunately if we delve too far down the social macroevolution road we wind up having to have the Guns, Germs, and Steel discussion, and that's straying dangerously off topic, though I also want to throw in a reference to Huntington, as another great and accessible read on the really big picture.
But More People...!
But moving back to your assumptions. Let's assume that population and technological growth became uncoupled by the "breakout". Now all of a sudden standards of living are at all time historical highs. Under Malthus we would expect the population growth rate to also be at historical highs.
But it's not.
In fact much of the developed world is at "peak population", facing major demographic shifts as baby-boomers age out of the workforce faster than they are being replaced.
Japan faces a "demographic crisis"$^2$$^3$, the US shows substantial aging and even China's growth rate has slowed dramatically and is now lower than the US's.
In fact, according to the UN, the projected world population over the next several decades looks like this:

Which you may notice is not an explosive growth. For more information on this, I'll defer to the experts at the Population Division of the Department of Economic and Social Affairs, and their technical paper
Cause and also Cause
Lastly, you're assertions rely on the assumption that increased population means food prices go up.
But that's not how numbers work.
Prices are denominated in currency.
More people (without a correlating rise in currency), actually means there's fewer dollars per person. In that scenario, food prices would go down (although probably slower than wages), leading to shortages. Price is a way of rationing scarce resources, but it's not the only way. The other way to ration is queueing, or shortage. This is what we see happen in developing nations. Rice is not more expensive, there just isn't enough rice there.
If everyone only has \$5 a rice merchant can't charge \$6/lb, or he won't sell any.
An Inflationary Theory
In the event that the population increased, and central banks also increased money supply, than standard economic models would predict that the prices of all commodities (not just food) would rise, since the relationship to amount of quantity over the amount money would have changed, or roughly
$$\rho (\Delta P_n, \Delta \frac{M_0}{Q_n})>0$$
where $\rho$ is correlation, and $P_n$ and $Q_n$ are price and quantity of $n$ respectively. Of note, there is some disagreement o whether $M_0$ or another measure of money should be used, but prices in the US (as measured by CPI) have a substantial correlation with $M_0$ ($\rho = 0.46$ for $M_0$ as compared to $0.086$ for $M_1$ from 1985-2013)$^3$
This would be conformant with standard economics, and not reliant on a Malthusian population collapse.
The only way we would expect prices to rise dramatically without central bank intervention would actually be after the collapse, as people accumulated currency, and would trade more currency for food.
TL;DR
In the event of a zombie or post-nuclear apocalypse, cash will decline in value relative to commodities, so stock up on rations and bullets because dollars won't help.$^4$
References
$^1$: Korotayev, A.; et al. (2011). "A Trap At The Escape From The Trap? Demographic-Structural Factors of Political Instability in Modern Africa and West Asia". Cliodynamics 2/2: 1–28.
$^2$: Aging of Japan. (2014, December 9). Retrieved December 18, 2014, from http://en.wikipedia.org/wiki/Aging_of_Japan
$^3$: Current research. You'll have to take my word or pull the data from St Louis Fed and BLS yourself.

$^4$: Fallout: New Vegas. (2010). United States of America: Bethesda Softworks.


Economic policies to decrease obesity (would they be effective?) According to the Center for Disease Control and Prevention, approximately 35% of adults in the United States are obese. I have done much research on the topic of economic policies to reduce obesity (I did a fat tax simulation for my undergraduate capstone thesis). I have run into three proposals:

1) Fat Tax: A fat tax is a tax on fatty foods or on fats themselves. Various papers I read on the topic simulated a tax on certain fatty foods. However, one paper proposed an ad valorem tax on saturated fats which seems like the most effective way to target fats. The biggest problem found with fat taxes is that fatty foods are very inelastic. This means that a tax won't change consumption much, so this doesn't seem like an effective option.

2) Thin Subsidy: A thin subsidy is pretty much the opposite of a fat tax. It subsidizes foods that are considered healthy. In the literature, this option by itself doesn't change behavior much, but a thin subsidy can also be paired with a fat tax. Basically, the government would use all of the revenues from the fat tax to subsidize healthy foods. When paired together, they are more effective than they are separately, but they still are not very effective in reducing calorie intake.

3) Gym Membership Tax Credit: This is a tax credit you can receive if you have a gym membership. I have not seen as much literature on this topic. Intuitively, if the tax credit is equal to or close to being equal to the cost of the membership, then people may have more incentive to get a gym membership. However, if the credit isn't very close to the cost of the membership, it may not cause people to go get memberships. Another problem with this method is that someone may get a membership and simply not go to the gym. I know most gyms have scanners now, so one remedy could be that the tax credit amount could depend on how many days you scan in.

Other than these three policies, are there any other policies being discussed to slow the trend of obesity? How effective can a policy be in reducing obesity rates?

Yes, sugar tax!

This is probably as controversial as tobacco tax was back in the days. If you walk through a supermarket, you will find that half of the food section is food full of sugar. Sugar is what makes you fat, not fat itself. It has been known for a while, at least since the professional sports were invented. Yet the lobby of the enormous sugar industry keeps regulators from labeling it as hazardous and taxing its use. If you are doing a research into obesity I highly recommend devoting two hours to watch That Sugar Film (2014).

I would also recommend taking a multidisciplinary approach and bringing some arguments from biochemical and nutrition fields.


Are Credit Card Points, Airline Miles, and Store Credit representations of M2 money supply? I found a curated shop that heavily relies on store credit (or more accurately stated, a network of stores who rely on this credit)

Is it accurate to call this system mostly M2 money?
Does the depth and reach of the products and services change the classification? (e.g. Amazon points vs a small retailer also with points)

When looking at this from an economic perspective, this seems similar to Credit Card points, Airline Miles, and XBox points.

Question

Is there any authoritative source that explicitly states that store credit is M2 money? (or elaborates on it in a way this question can relate to)

Research

5 years ago I did find such a source, but now I'm at a loss in locating it. Investopedia, Wikipedia, and I've likely looked at many other -pedias and *.stackexchange.com and came up empty handed for my purposes.

Googling "M2 Credit Card points" resulted in me getting 20 advertisements, and will likely haunt me as I surf the net with advertisements for a Capital One card.  <-- if you intend to help, learn from this experience and use an incognito browser ;)

It seems unlikely that any authoritative source would consider credit card points, airline miles or store credit as apart of M2 money supply.

As you have probably read on investopedia:

  What is 'M2'
  M2 is a measure of the money supply that includes all elements of M1 as well as "near money." M1 includes cash and checking deposits, while near money refers to savings deposits, money market securities, mutual funds and other time deposits. These assets are less liquid than M1 and not as suitable as exchange mediums, but they can be quickly converted into cash or checking deposits.

According to this definition, credit card points are not counted to as apart of M2 money because they are not directly tied back to a cash exchange directly,(though there are some firms who will purchase them,) but are tied to specific services provided by the authorizing firms.

Since Credit card points are only usable for a specific services and are viewed  as  "in kind" transfers  rather than actual money.


Finding restrictions on parameters for a demand function I have a question that asks:
Let $x_1$ be the quantity of a good 1, $p_1$ the price of good 1, $p_2$ the price of good 2, and
$M$ is income. Let
$_1(_1, _2, ; ) = _1^_2^^$ Where $$, $$, $$, and $$ are parameters.
If this is a demand function, what restrictions does this impose on the parameters?
I am a bit confused if my understanding of the question is correct, currently what I've gone and done is impose the restriction $x_1 p_1+x_2 p_2≤M$, and then sub in $_1^_2^^$ for $x_1$, resulting in $Ap_1^α p_2^β M^γ (p_1 )+x_2 p_2≤M$. I have then gone and rearranged for the various parameters, resulting in:
$A≤(M-x_2 p_2)/(p_1^(α+1) p_2^β M^γ )$,
$α≤ln((M-x_2 p_2)/(Ap_2^β M^γ ))/ln(p_1 ) -1,Ap_2^β M^γ$,
$β≤ln((M-x_2 p_2)/(Ap_1^(α+1) M^γ ))/ln(p_2 )$,
$γ≤ln((M-x_2 p_2)/(Ap_1^(α+1) p_2^β ))/ln(M) $
I'm not really sure if my approach is correct at all, as this seems more of a maths rearranging formulas answer rather than something related to economics. I was wondering if anyone could help me get on the right track if this is wrong. Thanks

Demand is positive, so $A>0$.
If $p_1$ goes to $\infty$, $x_1$ has to go to 0, since $p_1x_1$ is bounded by $M$. Thus $\alpha < 0$.
If $p_2$ goes to 0, $x_1$ cannot go to $\infty$, since $p_1x_1$ is bounded by $M$. Thus $\beta\ge 0$.
If $M$ goes to 0, $x_1$ has to go to 0, since $p_1x_1$ is bounded by $M$. Thus $\gamma > 0$.
If both prices and income are scaled up by the same factor, then demand doesn't change, so $\alpha+\beta+\gamma=0$.


References for particular definitions of risk and uncertainty I have some doubts about risk vs. uncertainty. I have read the thread "What is the difference between risk, uncertainty and ambiguity" and have skimmed through Knight's "Risk, Uncertainty, and Profit" Chapter VII (starting on p. 197). It seems there exist alternative definitions of these concepts, which is a bit confusing.

I have a particular example that implicitly defines risk and uncertainty. I would like to know if these implicit definitions are in line with any of the established ones.

Example: In a lottery, the probability to win is $p$ and the probability to lose is $1-p$. If I know $p$ and participate in the lottery, I am facing risk. If I do not know $p$ and participate in the lottery, I am facing uncertainty.

Does this match any existing definitions of risk vs. uncertainty?
Could I also get a reference to an academic paper or a textbook?

Edit 1: User 123 notes correctly that there seems to be risk in both cases (whether I know the probabilities or not, I am still participating in the lottery which by itself is a source of risk). Hence, the term uncertainty seems to incorporate risk + the lack of knowledge of the probabilities. This may suggest the terms risk and uncertainty are not mutually exclusive; when we call something uncertain, it might also include an element of risk; but when we identify something as risky, we must know the probabilities, thus it is not uncertain. Yeah, it is convoluted...

Edit 2: Quoting Knight via Wikipedia, a measurable uncertainty, or 'risk' proper, as we shall use the term.... Thus it is enough that the probability be measurable in the above example and is does not have to be known precisely. So I understand that the implicit definitions in the example above are not in line with the Knightian ones.

Knight's 1921 essay was not written in formal mathematics (and trying to formulate a direct translation into modern mathematics may be quite problematic). Since Knight's time, a formal decision theory literature has developed which makes distinctions that are at least reminiscent of Knight's.

Lars P. Hansen (2012), writes "Motivated by the insights of Knight (1921), decision theorists use the terms uncertainty and ambiguity as distinguished from risk." Hansen references Gilboa et. al. (2008) who write:

  In economics, Knight (1921) is typically credited with the distinction
  between situations of "risk” and of “uncertainty.” In his formulation,
  “risk” designates situations in which probabilities are known, or
  knowable in the sense that they can be estimated from past data and
  calculated using the laws of probability. By contrast, “uncertainty”
  refers to situations in which probabilities are neither known, nor can
  they be deduced, calculated, or estimated in an objective way.

Gilboa and Schmeidler (1989) introduced a max-min utility theory where instead of simply maximizing expected utility, agents solve a max-min problem where to model ambiguity aversion, the objective is minimized over different priors. This work has been expanded on by Hansen and Sargent in their work on robustness.

Sliding away from Knight and into the broader topic of decision theory, it would be mandatory to reference Leonard Savage's classic, Foundations of Statistics where he introduces the notion of subjective probability.

Your particular example (in more modern decision theory)

You have a Bernoulli likelihood function for winning the lottery.

To a frequentist statistician, $p$ is a scalar value, a parameter (albeit unknown). There is only one possible outcome for $p$ and so there's no randomness.
If you're a Bayesian in the spirit of Savage, you're willing to extend the tools of probability to model uncertainty in your own mind; you will treat $p$ as a random variable!

If we put a prior on $p$ (eg. the beta distribution is a conjugate prior to the Bernoulli likelihood), we can compute posterior probabilities and make decisions based upon standard expected utility. In terms of how we behave though, there's no difference between a 20% probability that's objective vs. subjective.

Under the ambiguity aversion, max-min model though, we may maximize our control variable over expected utility, taking into account that it will then be minimized over multiple priors: we choose control variable $x$ to maximize utility and then (after observing our choice $x$) a mean guy chooses the prior to minimize utility.

References

Hansen, Lars P., 2012, "Challenges in Identifying and Measuring Systemic Risk", NBER

Hansen, Lars P. and Thomas Sargent, 2001, "Robust Control and Model Uncertainty," American Economic Review

Gilboa, Itzhak and David Schmeidler, 1989, "Maxmin Expected Utility with Non-unique Prior," Journal of Mathematical Economics

Gilboa, Itzhak, Andrew W. Postlewaite, and
David Schmeidler, 2008, "Probability and Uncertainty in
Economic Modeling", Journal of Economic Perspectives

Savage, Leonard Jimmie, 1954, Foundations of Statistics


Has a market labor shortage ever occurred? A true labor shortage is when no labor is available for a task at any price. Surely this occurs all of the time if you consider markets that don't exist or could never exist, but has this ever happened otherwise?

Has there ever been a situation where a particular type of labor existed, and then dissapeared, leading to a situation where none of the labor in that sector was available at any price?

That very narrow definition of labour shortage, "when no labor is available for a task at any price", is rarely used, because it's a very rare phenomenon. Market forces kick in, raising prices sharply enough to suppress even relatively inelastic demand, long before the shortage becomes absolute. So the phrase is much more commonly used to mean that there is a temporary constriction in supply of a particular type of labour, usually leading to a large, rapid increase in its remuneration. Hence, when you hear the phrase, that's much more likely to be the intended meaning.

However, in the very narrow definition, the canonical example given is usually that of many trades in Western Europe, after outbreaks of the Black Death in the Fourteenth Century had halved the population.

However, even that example is problematic, as the evidence is that women were largely prevented from taking men's jobs, so the shortage was as much about culture as about physical limits:

  Labour scarcity should have opened up opportunities for females, but the regulations only added to their geographical and occupational immobility,


What does annualised GDP shrinkage of 75% and growth of 54.6% mean? According to Business Today (India), these are the latest figures for 2020 September 3 for GDP change in World's largest economies.

In simple terms, what do GDP shrinkage of 75% and growth of 54.6% mean?

Update
My question is not about the formal technical definition of GDP, but the meaning of 75% shrinkage in GDP and 54.6% growth in GDP, in layman's language. That is, from the perspective of the history of economies of large human societies, how massive in magnitude are these figures (has 75% GDP meant total economic collapse and has 54.6% growth in GDP meant legendary economic boom)?
For a person who is not trained in economics, these figures are hard to grok.

Growth of GDP is generally reported quarterly on YoY basis in real terms, i.e., the growth rate of 5% means increase of GDP in current quarter by 5% as compared to GDP in same quarter previous year in real terms.
As with most macroeconomic variables, GDP has seasonality and that is why the QoQ is not reported.
For example for india the FY Q1 (Calender Q2) has a less than 1 seasonal factor. So the QoQ of this quarter will always be low and therefore misleading. For Q1 FY 2020-21, India's QoQ growth rate is -27.1%.
Coming to annualized rate: it is the growth rate of GDP if the economy continued to grow (shrink, in this case) at the same pace as the current QoQ growth rate.
So if the QoQ is, say, 2% then annualized rate would be:
$$((1+0.02)^4)-1)*100=8.24$$
In the above example:
$$((1-0.2928)^4)-1)*100=74.98$$
Now in general in Central bank communications and research analysis work, the annualized rate is calculated on deseasonalized QoQ growth, otherwise you ate misleading the reader. The newspaper here seems to have ignored that, perhaps intentionally to magnify the contraction of economy and is most certainly misleading.
On the second part of your question: $75%$ economic of economic contraction does mean collapse. In worst of recessions this does not happen in a period of just one year. In theoretical terms, it is equivalent to everyone's income in the economy to decrease by $75%$.
You can rather think like this: Overall income last year was say $100$. Q1 of India's FY generates income of little less than $25$ (say, $22$ - seasonality effect). Given a negative growth rate of about $23.9%$, actual income generated is about $16.75(=(1-0.239)*22)$. Now as economy opens up, income generated in Q2-Q4 may not be $78$ but somewhere around may be $70$ (or $65$, who knows). So total income would be about $82-87$. Overall, therefore, the annual contraction may come-out to be of around $13-18%$. Certainly not $75%$!!


How can the Fed enforce exit criteria if they begin yield curve control? Over the past year, the notion yield curve control has resurfaced and appeared on FOMC minutes, decades after its last implementation.
According to the Fed's introduction page:

As the U.S. continued to incur debt, the Fed was obligated to keep
buying securities to maintain the targeted rates—forfeiting some
control of its balance sheet and the money stock. The public generally
preferred to hold higher-yielding, longer-term bonds. Consequently,
the Fed purchased a large amount of short-term bills, which also
increased the money supply, to maintain the low interest rate peg.
After the war ended, FOMC members grew more concerned with addressing
the rapid inflation that materialized. However, President Harry S.
Truman and his treasury secretary still favored a policy that
maintained YCC (which also protected the value of wartime bonds by
implying a price floor). By 1947, inflation was over 17%, as measured
by the year-over-year percent change in the consumer price index
(CPI), so the Fed ended the peg on short-term rates in an attempt to
combat developing inflationary pressures.)

This poses an interesting dilemma in configuring the bounds of the program. WW2 was a one-sided victory with rather clear end date. Yet the fact that YCC continued post-WW2 suggests that terminating the program was difficult. It's conceivable that marshaling the political will to end a program that the treasury likely derives massive utility for operating against a high fiscal-deficit backdrop was a major challenge. This phenomenon is sometimes termed "fiscal dominance."
A BIS paper goes into great length on the matter. Condensing one of the themes:

For many, a long period of large fiscal deficits and very high public
debt-to-GDP ratios raises the spectre of fiscal dominance. It will in
any case accentuate the links between fiscal policy, monetary policy
and government debt management.

Question
How can the Fed enforce exit criteria without a massive/dramatic macro impairment (such as double-digit inflation)?

History and Theories of Yield Curve Control (20 pages)
https://www.boj.or.jp/en/announcements/press/koen_2017/data/ko170111a1.pdf

Lastly,  as  the  fourth  issue, I  would  like  to  touch  upon  the  relation  between  fiscal  management  and  yield  curve  control.  As  I  noted,  yield  curve  control  by  the  Bank  differs  from  the  government  bond  price-supporting  policies  once  implemented  in  the  United  Kingdom and the United States. While these policies aimed to minimize financial costs of the government, the Bank's current policy aims to overcome deflation and achieve the price stability  target.  Given  that  the  policy  directly  sets  the  long-term  interest  rates  as  its  operational   target,   however,   it   is   undeniable   that   the   area   deeply   related   to   fiscal   management expands. Not surprisingly, therefore, there are voices of concern and criticism that  the  current  policy  coincides  with  money  finance  or  monetization,  or  that  the  exit strategy of  the  policy  will  be  constrained  by  consideration  for  fiscal  management.  It  is  therefore   important   that   the   Bank,   bearing   in   mind   those   voices   as   well,   gain   the   understanding  of  the  markets  and  the  public  by  releasing  more  carefully  than  ever  the  information on the purpose and ways of thinking about monetary policy implementation.

Quantitative Easing: Entrance and Exit Strategies (16 pages)
https://files.stlouisfed.org/files/htdocs/publications/review/10/11/Blinder.pdf

Because many of the Fed’s unorthodox quantitative easing policies put taxpayer money at risk, these policies constituted quasi-fiscal operations — equivalent to investing government funds in risky assets.

I would argue that there was less spare capacity in the economies after World War 2 due to destruction of assets in many countries and due to wartime restrictions of consumption and investment. Also the household sector in the United States emerged with a relatively clean balance sheet where collateral assets were not saturated with private debt. By contrast the economies with QE today have spare production capacity and assets saturated with greater burden of private debt. I am not aware of any econometric series that compares the private debt to government debt. Rebel economist Steve Keen publishes some charts making these comparisons of private to public debt but I have not drilled down into his sources of data.


Dead Weight Loss (Tax) Problem
Given demand $D(p)=A-ap$, and $A,a>0$ and a fixed price $0<p_1<A/a$ by some company.
My solution so far
CS is
$CS=\int_{p}^{A/a}D(p)dp=\int_{p}^{A/a}(A-ap)dp=\frac{1}{2a}(A-ap)^2=\frac{(A-ap)^2}{2a}$
Problem
Find the CS now with a tax $p_1+t>A/a$
My solution so far
Just let $p_2=p_1+t>A/a$. Insert $p_2$ into the previous result since the integration would be the same and we get
$\frac{(A-a(p+t))^2}{2a}$
Main Problem
Find the DWL
My solution so far
I get the general formulas
$(p_2-p_1)p_1-\int_{p_1}^{p_2}A-ap\;dp$ and $1/2 \cdot (p_2-p_1)\cdot (Q_1-Q_2)$
And then the answer with the second formula that
$1/2*((p+t)-p)*((A-ap)-(A-a*(p+t)))=1/2\cdot t(a(p+t)-ap)$
Is this approach correct throughout the taxation influence on CS and the DWL?

I think you are making it unnecessarily hard for yourself. You can calculate the deadweight loss (DWL) simply as the difference between consumer surplus pre-tax and post tax, and also by adding tax revenue as it is not necessarily wasted if government uses it, so that would be:
$$DWL =  \frac{(A−ap)^2}{2a} -  \frac{(A−a(p+t))^2}{2a} +t(A-a(p+t))= A t - \frac{1}{2} \left( a t (2 p + t) \right) + t(A-a(p+t)) $$
In addition if you have further equations that explicitly model supply you should also add to the deadweight loss the difference between producer surplus pre-tax and post tax but if that is not specified it is common to assume that supply is just flat line (so there is no producer surplus).


How to interpret this regression coefficient? I am performing a simple single variate regression on the variables crime rate (denoted by crrate) and the probability of getting arrested (denoted by prarrest). To be precise, the variables are defined as:

crrate: ratio of the number of crimes committed to county population
prarrest: 100* the ratio of arrests to offenses.

The slope coefficient value I got when I regressed crrate on prarrest is -0.067. How can this coefficient be interpreted?
My attempt:

Ceteris paribus, one percentage point increase in prarrest causes the number of crimes committed per 1000 county residents to go down by 67.

Is this interpretation correct? If not, how can it be improved?

Assuming that from the beginning you made the regression with prarrest with transformation *100 (say you have for example [0.012,0.093] and you transform it into -> [1.2,9.3], I remark this cause its critical to the interpretation).

Ceteris paribus, one percentage point increase in prarrest causes the number of crimes committed per 1000 county residents to go down by 67.

It is correct, you could se this with this approach (assuming its linear regression), taking into account the your hypothesis must have this from:
$crrate=\hat{\beta_0}+\hat{\beta_1}(prarrest)\;\;\;\;\;$where $\hat{\beta_1}=-0.067$
$\frac{\Delta(crrate)}{\Delta(prarrest)}=-0.067 \implies \Delta(crrate)=-0.067\Delta(prarrerst)$
Now, if $\Delta(prarrest)=1$ then $\Delta(crrate)=-0.067$.
Since prarrest is in the terms clarified from the beginning, this $\Delta(prarrest)=1$ means a whole percentage point increase (e.g. from 34(%) to 35(%)), then looking at the terms or the $crrate$ variable (#crimes/population, so for one individual of the population how many crimes are committed), a -0.067 change means a decrease in the order of 0.067 per each person, so multiplying this by 1000, would give us decrease of 67 per 1000 people. Yes, your try is correct.


Editing formula for finding Marshallian Demand with Cobb-Douglas utility function Suppose a utility function $u=x_1^ax_2^b$ with $a+b=1$. The following formula finds the values for $x$:

$x_1 = \frac{am}{p_1}\\
x_2 = \frac{bm}{p_2}$

But what if the utility function looks like $u=cx_1^adx_2^b$ so has additional factors bevore $x_i$? Can the formula above be edited accordingly?

$u=cx_1^adx_2^b$ is equivalent to $u=(cd)x_1^ax_2^b$
the values of $c$ and $d$ do not impact the optimal bundles. I'll provide complete working on your other question (Marshallian Demand for Cobb-Douglas).


University course references for Market Structure/Industrial Organization Are there any books that are used in University-level courses that contain a detailed analysis of market structure ( Perfect competition , Monopoly and so on)?

The standard, if somewhat aged textbook for graduate study of industrial organization is

The Theory of Industrial Organization by Jean Tirole.

Tirole has the merit of tacking issues around market structure in a quite direct fashion. A slightly more modern text is

Industrial Organization: Markets and Strategies by Paul Bellflamme and Martin Peitz

A less advanced text that can be downloaded for free is

Industrial Organization: A Strategic Approach by Jeffrey R Church and Roger Ware

It's worth mentioning that Industrial Organization is typically not encountered as a stand-alone course until the late stages of an undergraduate degree or until graduate level, so books on this subject will typically be more advanced than a standard econ101 text.


Prove that $h(p,u) = \nabla_p e(p,u)$ is implied by Roy's identity I am struggling a bit with the math in my first graduate microeconomics course. I'm not sure if this belongs here. If it doesn't, please direct me to a more appropriate place.

Below is one question along the with provided solution. The red part is the part I don't follow.

I don't understand how the derivative of $v(p, e(p,\overline{u}))$ w.r.t. the price vector can evaluate to the LHS of the given equation.

Perhaps I'm confused by the vector notation, so any step explaining this equation would be very much appreciated.

a) The convention, when differentiating a real valued function $v$ wrt to a column vector $p$ of dimension $(G \times 1)$, is that:
$$
\nabla _{p}v\left( p,w\right) \equiv \frac{\partial v}{\partial p}\left(
p,w\right) =\left(
\begin{array}{c}
\frac{\partial v}{\partial p_{1}}\left( p,w\right)  \\
\vdots  \\
\frac{\partial v}{\partial p_{G}}\left( p,w\right)
\end{array}%
\right).
$$

b) When expenditures $w$ are not constant, the column vector $p$ with respect to which we take the derivative occurs twice in $v(p, e(p,\overline{u}))$, and the chain rule has to be applied in order to obtain the total effect of the price change on the indirect utility: the first partial effect on utility is due to the price changes, and the second effect is through the adjustment in expenditures implied by the price change. Hence the expression:
\begin{eqnarray*}
&&\frac{\partial v}{\partial p}\left( p,e\left( p,u\right) \right) +\frac{%
\partial v}{\partial w}\left( p,e\left( p,u\right) \right) \frac{\partial e}{%
\partial p}\left( p,u\right)  \\
&=&\left(
\begin{array}{c}
\frac{\partial v}{\partial p_{1}}\left( p,e(p,u)\right)  \\
\vdots  \\
\frac{\partial v}{\partial p_{G}}\left( p,e(p,u)\right)
\end{array}%
\right) +\frac{\partial v}{\partial w}\left( p,e(p,u)\right) \left(
\begin{array}{c}
\frac{\partial e}{\partial p_{1}}\left( p,u\right)  \\
\vdots  \\
\frac{\partial e}{\partial p_{G}}\left( p,u\right)
\end{array}%
\right).
\end{eqnarray*}


Why slope is constant in demand/supply curve? I was reading Mankiw and it showed variation of demand/supply curve with external factors. However, in all the cases the curves only shifted but didn't change in shape. What I am wondering is why the slope of these curves don't change?

Well, it's just a simplification. You can make a demand curve non-linear if you want to, but it doesn't serve any particular pedagogical function to do so and Mankiw is just trying to make the reader understand the intuition behind basic concepts.

I think you also want to know why a shock only shifts the curve, not its slope. Well, slopes of these curves have a certain meaning. The slope of a demand curve is related with consumer preferences, for example. An income shock is not particularly relevant to consumer preferences (not in the simple models Mankiw presents, at least, it's not like you can't model preferences like that), so it shouldn't change the demand curve's slope, only shift it. That is, people consume more (or less, depending on the shock) of a certain good at the same price.

The slope of a supply curve has an intimate relation with the economy's cost structure. Why should a supply shock - such as an earthquake - alter the curve's slope?


Federal Reserve Open Market Operations I am trying to understand how the Fed effects the fed funds rate. Here it says:

  Once the Federal Open Market Committee deems that economic conditions
  warrant a change in the money supply through specific open market
  operation, the command to buy or sell a specific amount of U.S.
  Treasury securities is passed down through the New York Fed President
  to what is called the Domestic Trading Desk of the New York Federal
  Reserve Bank. The Domestic Trading Desk is then responsible for
  implementing the conducting the actually trades. It does this sending
  messages to a selected group of about 30 securities dealers who
  specializing in the U.S. Treasury securities. These dealers have 15
  minutes to respond back with a indication of their willingness to buy
  participate in the exchange of securities. Some dealers are willing,
  others are not. In fact, the "open" part of open market operations
  means that the trades are open to any of the securities dealers
  willing to participant. The Domestic Trading Desk then has 5 minutes
  to respond back to the each of dealers that the terms of the exchange
  is acceptable.

  Once all parties have agreed on the exchange terms, the resulting
  transactions work much like any other. If the Fed buys, then it
  collects the securities from the dealers in exchange for checks. If
  the Fed sells, then the dealers collect the securities from the Fed in
  exchange for checks. In both cases, the checks are cleared much like
  any of the millions of checks process each day.

So the Fed manipulates the reserves of banks in order to increase or decrease fed funds, and it uses open market operations to do this. I am curious, though: what if in the case of "raising rates", the Fed wants to sell securities but no bank wants to buy them? And, why wouldn't a bank buy securities anywhere else?

Thanks,

The actual details of the auction and so on are interesting, but in principle there is no magic. Its just demand and supply:

There is a number of agents that can supply or demand treasury bonds as well as other bonds. There's the government that issues the treasuries, the Fed that sometimes holds them, sometimes sells them, investors of all kinds( brokers, pension funds, individuals, money market funds, etc). All these agents want to sell more if they deem the price high(rates too low) and they want to buy if they deem the price is low (rates too high).

When supply shrinks, then agents that want to buy these assets bid up their prices (bid down the rates). similarly, when supply expands then the price falls (the rate rises) as the buyers bid down the  prices after observing the quantity.

To push up an interest rate, the fed will sell bonds. This will increase supply, until the price falls (i.e. until the rate rises).  To push down an interest rate, the fed will buy bonds. This will decrease supply, until the price increases (i.e. until the rate falls).

  I am curious, though: what if in the case of "raising rates", the Fed wants to sell securities but no bank wants to buy them? And, why wouldn't a bank buy securities anywhere else?

If no bank wants to buy the securities, but the fed is trying to sell them, then their price would go down, down, down, increasing the rate, until somebody wants them. If this rate is too high for the Fed, then it can instead buy these securities, lowering the market rate. In principle, if nobody wants to buy it means they are willing to sell, if nobody wants to sell it means they are willing to buy.

The banks can buy securities wherever they want, but the rates of all securities are closely related to each other. If the fed lowers rates on Treasuries, the rates on corporates, munies, etc, are all going to follow suit, at least to some extent. This is because the securities are all close substitutes of each other, so if you were thinking of buying a treasury, but its price increases, you go and, for example, you try to buy a muni, thereby increasing its price too.


Violating WARP or not? If the only information we had about Goldie were that she chooses the bundle (6, 6) when prices are (6, 7) and she chooses the bundle (10, 0) when prices are (5, 5), then we could conclude that

a.
the bundle (6, 6) is revealed preferred to (10, 0) but there is no evidence that she violates WARP.

b.
Goldie violates WARP.

c.
the bundle (10, 0) is revealed preferred to (6, 6) and she violates WARP.

d.
neither bundle is revealed preferred to the other.

e.
the bundle (10, 0) is revealed preferred to (6, 6) but there is no evidence that she violates WARP.

My attempt:
Obvious conclusion to this question is that (6,6) bundle is preferred to (10,0) bundle when prices are (6,7) but when the prices are (5,5) everything is the other way round thus it violates the WARP whereas the correct answer as stated in the questionbank is A why is that?

When she chooses the bundle (6,6) when the prices are (6,7), she spends
\begin{equation*}
6*6+6*7=78
\end{equation*}
The total price of the bundle (10,0) given this price system is
\begin{equation*}
10*6+0*7=60<78
\end{equation*}
Therefore she could afford the bundle (10,0) if she wanted to. The fact that she chooses (6,6) reveals that she prefers (6,6) to (10,0).

Given the price system (5,5), when she chooses the bundle (10,0) she spends
\begin{equation*}
10*5+0*5=50
\end{equation*}
And the price of the bundle (6,6) would be
\begin{equation*}
6*5+6*5=60
\end{equation*}
Therefore (6,6) is not necessarily affordable if her budget is comprised between 50 and 59. This is why (10,0) is not revealed preferred to (6,6) in that case, and thus there is no evidence that she violates WARP.


Rothschild-Stiglitz working paper? I recently rediscovered Rothschild and Stiglitz's classic paper, "Equilibrium in Competitive Insurance Markets".

In footnote 7, they refer to an earlier version of their paper for details on the robustness of their results to their assumptions. Does anyone know how to track that version down? Many different Google search queries haven't worked.

The complete citation for the working paper is

  Rothschild, M., and J. E. Stiglitz, "Equilibrium in Competitive Insurance Markets," Technical Report No. 170, IMSSS Stanford University, 1975.

On a separate note, the published version of their paper is beautifully written. You would be remiss to not have read it.

(Edited)
Here is the working paper. Enjoy.

Rothschild, M., and J. E. Stiglitz, "Equilibrium in Competitive Insurance Markets," Technical Report No. 170, IMSSS Stanford University, 1975.

https://drive.google.com/file/d/1MXb3OcOQc_lxNYC4CzsNTTax9_3Q_4UN/view?usp=sharing