What makes statistics economical reports so varied and different? Search for Iran's GDP in Google, and what you will see is an image representing GDP of Iran, compared to other neighbor countries. It gives us the value of 393.4 billion USD (2015).

Now in that page simply open some results. From Wikipedia, from World Economics, and other sources. You see values from 300 to 1.3 trillion Dollars.

Values are not coherent with each other. As an engineer who is not an economist but understands figures and diagrams, I think these values are so varied that they can not be used in researches as reliable information.

I'm working on a proposal, and I need information that can be trusted. What makes such a bold and universally known economical value so varied across data sources?

Regarding the general question in the title, the reasons why "the same" variable vary across sources depends very much on the particular variable you are talking about. Personally, one of my first shocks when I started working after my undergraduate was the high number of ways the same conceptual variable studied theoretically (e.g. inflation) could be measured in practice. These alternative definitions might refer to slightly different phenomena, or might reflect different set of assumptions by those computing the statistics. Depending on your ontological position when it comes to economic concepts (e.g. is there such a thing as "inflation" out there?), you can argue that some assumptions are better than others. But this does not deny the fact that there are potentially many ways to measure the same variable, and different institutions/individual might prefer one over the other.

Focusing in the case of GDP for Iran in particular, there is the "original" GDP (as coming from official or primary sources) in local currency (notice there are several definitions of GDP too, and in the case of Iran, one with and without oil production). For international comparison purposes, this metric needs to be transformed into e.g. current US\$ or PPP US\$, process which involves some assumptions (e.g. which exchange rate to use?). Again, different institutions might use different metrics and prefer different assumptions. As said below, for data coming from countries using the Islamic calendar, there are further complications when translating to the Gregorian calendar.

Let us dig deeper in the case of Iran's GDP. First, you need to start with the official data (or primary source), available in the website of the Statistical Center of Iran. If you select the file for GDP at current prices (this file), you get the quarterly data for GDP in current Iranian currency. Notice however, that this data corresponds to the Islamic year, which is different from the Gregorian calendar used in most of the world (and used in the websites you mention). The former starts around the 21st of March of the latter. This is not exactly the end of the first quarter of the Gregorian calendar. Since quarterly data is the minimum frequency of the Iranian GDP, there is no exact way to convert quarterly Islamic-based GDP into annual Gregorian-based GDP. This tells you immediately that the translation exercise is by definition an approximation.

One reasonable approximation is to use the last quarter of an Iranian year and the first three quarters of the next Iranian year to produce a metric of the Gregorian-based year GDP. For 2015, this is:

Quarter     GDP
-----------------
1393_4    439,687
1394_1    432,264
1394_2    450,158
1394_3    433,799

Which add up to 1,755,908 billion Rials (this includes Oil production).

To translate this into $USD, which is the metric of the World Bank data, you would need to assume something about the exchange rate. Do you use the average over the quarter? Over the year?

For example, the same official statistics website above offer a measure of GDP in USD for the Gregorian calendar (see here):

Unfortunately, they do not mention which exchange rate conversion was used.

Meanwhile, the World Bank offers a slightly different one:

The notes for the latter states:

  Dollar figures for GDP are converted from domestic currencies using single year official exchange rates.

Did they use a different conversion rate? It's very likely.

Regarding the IMF data, which is reported in the Wikipedia article (particularly in the graph here), this is measured in PPP terms (and the data is highly consistent with World Bank data of GDP in PPP; see here). PPP adjusts GDP figures not only by the exchange rate but also by a measure of the relative cost of living of Iran with respect to the US. This inflates the GDP of Iran (see PPP rates here).

There are plenty of questions in this site about PPP. For example, see here and here.


Is the locus of consumption in Ramsey growth model a vertical line? In almost all documents I have read on the internet, the locus of consumption where $C_{t} = C_{t+1}$ seems to be a vertical line as shown below. However, my teacher said it could well be not a vertical line. I really don't know why it should be different. Thank you for all your help.

In the standard/canonical Ramsey model for discrete time, the Euler equation is of the form (notation is standard here, I won't write the whole model),

$$\beta (1+r_{t+1})u'(c_{t+1}) = u'(c_{t})$$

To obtain a zero-change locus for consumption, we must satisfy

$$c_{t+1} = c_t \implies u'(c_{t+1}) = u'(c_{t}) \implies \beta (1+r_{t+1}) = 1$$

$$ \implies r = (1/\beta)-1$$

-irrespective of the form of the utility function assumed (as long as it does not change, as a function, from period to period), and irrespective of the level of consumption. The locus  therefore cannot have a slope in the consumption-capital space but it has to be vertical to the capital axis at a level of capital for which $r$ (which equals the marginal product of capital) equals the above constant.


Utility maximimization for unusual Leontief utility function The problem is basic utility maximization subject to a budget constraint with
$$u(x,y) = min\{x+y,4\sqrt{x},4\sqrt{y}\}$$
$$p_x = 1, p_y = 1, M = 4$$

I will have to first plot the Indifference Curves.

I am able to figure out the following:

If $x < y: u(x,y) = min\{x+y, 4\sqrt x\}$,  else $u(x,y) = min\{x+y, 4\sqrt y\}$.

But I get stuck here. For ex: if I am in the region where $x<y$, I can't find the sub-region where $x+y < 4 \sqrt x$ or $x+y > 4 \sqrt x$.

Cheers!

Above is a plot of the indifference curves for $U=1,2,...,8$ and also for $U=8.5$ that I made in MATLAB. For $P_x=P_y=1$ and $m=4$, the budget constraint is simply the the line $y=4-x$ (not pictured here, but easy to visualize).

Notice this budget constraint overlaps the $U=4$ indifference curve (fourth contour from the origin) on the line segment connecting $(1,3)$ and $(3,1)$. Any other point on the budget line would yield $U<4$, hence consuming on the line segment connecting $(1,3)$ and $(3,1)$ is optimal. But since all of these bundles correspond to $U=4$, the optimal bundle is not unique, but could be any bundle on this line segment.

Here is the MATLAB code that generated the plot:

u=zeros(60,60);
for i=1:60;
    for j=1:60
        u(i,j)=min([(i+j)/10 4*sqrt(i/10) 4*sqrt(j/10)]);
    end
end
figure
contour(u,[1 2 3 4 5 6 7 8 8.5]);
ylabel('Good Y')
xlabel('Good X')
grid on
grid minor
xt = get(gca, 'XTick');                                 % 'XTick' Values
set(gca, 'XTick', xt, 'XTickLabel', xt/10)
yt = get(gca, 'YTick');                                 % 'XTick' Values
set(gca, 'YTick', yt, 'YTickLabel', yt/10)


What does 'continuation' as in continuation games, strategies, plays, etc. exactly mean? I am in my first course in grad level game theory. While I was reading through Fudenberg and Tirole's Game Theory, I constantly come into contact with the word 'continuation' to describe some games and strategies but I was never able to find where the authors exactly define what they are referring to. Some sources say continuation game is a game starting at a given information set and including all edges and vertices/nodes until the terminal nodes. But isn't a subgame defined as a part of game tree which starts at a single node and contains all the succeeding nodes and wholly containing the information sets associated with them? Any help in understanding the term would be highly appreciated.

Consider a game with private information such as a privately known willingness-to-pay or any other type. We usually model this as a game in which at first "Nature" draws the type and then players make their moves. Such games do not have proper subgames because a proper subgame never splits up an information set and Nature's first move connects the entire game that follows into a subgame. That is why in such games we do not look for subgame perfect equilibrium, but a perfect Bayesian or sequential equilibrium.
A continuation game is kind of like a subgame that can start at an information set larger that just one decision node and it also assigns beliefs (probabilities) about at which decision node the player is.


Marginal productivity, wages, and profits in neoclassical economics In neoclassical economics a worker is paid the marginal product of what they produce. If this is true then what is the source of profits?

Recall the profit function.

$$\pi=pf(x)-wx$$

where $x$ is a set of inputs, and $w$ is a set of input prices.

A firm is profit maximizing when $MC=MR$ or in a competitive case where $MC=p$. If a worker is paid his marginal product (where $MPL=w$) we only pay what he produces.

If  marginal cost is constant and marginal revenues are constant across all production sets, then the firms profits will be zero.

However if there are diminishing returns from the inputs then every worker is paid less, thus allowing for profits to exist in the short run.

Bottom line: In the short run, through the diminishing returns from labor that profit for the firm comes into existence.

In the long run however, new firms enter capturing more and more of the profits until they are reduced to zero.


A general formulation to capture price stickiness In Wickens' macro book, page 227 (1st edition), the author states

where $p^*_t$ is the optimal price at time $t$.
The three theories he is referring to are: Taylor Model of Overlapping contracts, Calvo pricing model, and Optimal Dynamic adjustment. He says that all can be encompassed in this reformulation. The author then proceeds to show why this general formulation of inflation exhibits price stickiness, and this is the part which I don't understand what he does, specifically what he calls the partial adjustment model:

How can he deduce that equations (9.29) and (9.30) exhibit price stickiness?

I will answer the first question, I believe the second one can be found in the book's appendix.

"Price stickiness" is defined with respect to the optimal price level for the period (here denoted by a star) or equivalently in inflation terms. We do not have price stickiness if the current inflation equals the optimal inflation:

$$\pi_t = \pi^*_t$$

Looking at eq. $(9.26)$, written

$$\pi_t = \alpha\pi^*_t + \beta \pi^e_{t+1}$$

to allow for any expectations formation hypothesis (we will need this flexibility), here are the only two scenarios under which we do not have price stickiness, while also Wickens' "general formulation" holds:

A. Assume $\beta = 1-\alpha$ and $\pi^e_{t+1} = \pi^*_t$. Then we get $\pi_t = \pi^*_t$. Now, $\pi^e_{t+1} = \pi^*_t$ can be observed, it may be the case under Rational Expectations to expect next period inflation to equal the current optimal inflation. But assuming $\beta = 1-\alpha$ is a very special and uninteresting case.

B. Impose immediate and full adjustment, $\pi_t = \pi^*_t$, while respecting equation $(9.26)$: we get a very specific rule for expectations formation:

$$\pi^*_t = \alpha\pi^*_t + \beta \pi^e_{t+1} \implies \pi^e_{t+1} = \frac {1-\alpha}{\beta}\pi^*_t$$

This is clearly an ad hoc expectations formation assumption.

It follows that in any other case, eq. $(9.26)$ implies that $\pi_t \neq \pi^*_t$, i.e. we have partial adjustment. It is perhaps more illuminating to perform the above "what ifs" using eq. $(9.27)$ of the book that is written in terms of the price level (starting in long-run equilibrium, i.e. assuming $p_{t+1} = p^*_{t+1}$).


Optimization problem with Kuhn-Tucker conditions Consider a game with two players where each player $i=1,2$ has preferences $u_i=s_i^a c_i^{1−a}$, where $c_i$ is consumption and $s_i$ is social interaction. $s_i$ is given by $s_i=t_i+t_{ij}\times t_{ji}$ , where $t_i$ is the time spent by player $i$ alone and $t_{ij}$ is the time player $i$ spends with player $j$. Player $i$ has to decide how much of his or her time $T$ to allocate between work, having time alone, $t_i$, and social interaction $t_{ij}$. Assume that for each hour, player $i$ works, that he or she earns the wage $w$ and assume that the price of the consumption good $c_i$ is normalized to $p=1$.

  Carefully define the optimization problem for player 1. Write down the Kuhn-Tucker conditions and discuss these conditions. Explain why player 1 faces a strategic situation. Find the best-response functions for player 1 and 2. Graph these functions.

My solution :

$L = s_i^a c_i^{1-a}  - \lambda(c_i + s_i - (T-s_i)w) + \mu (c_i + s_i - T)$

FOC:

$\frac{\partial L}{\partial \lambda} =  c_i + s_i - (T - s_i)w = 0$

$\frac{\partial L}{\partial s_i} = a s_i^{a-1} c_i^{1-a} - \lambda(1+w) +\mu = 0$

$\frac{\partial L}{\partial c_i} = (1-a) s_i^a c_i^{-a} - \lambda +\mu = 0$

$\frac{\partial L}{\partial \mu} = c_i + s_i - T  = 0 $

By following this procedure, I cannot come to the solution.
Please share your ideas with me.

Solving that I obtain :

Player $1$'s utility maximization problem is the following :

$$\max_{0 \leq t_{12} \leq T} \ \ \left(T-t_{12} + t_{12}t_{21}\right)^a \left(w(T-t_{12})\right)^{1-a}$$

An equivalent way to solve the above problem is maximizing the $\log$ of the objective i.e. one can solve

$$\max_{0 \leq t_{12} \leq T} \ \ a\ln\left(T-t_{12} + t_{12}t_{21}\right) +(1-a)\ln  \left(w\right) + (1-a)\ln  \left(T-t_{12}\right) $$

Solving it we get the best response function of player 1 as

\begin{eqnarray*} t_{12} = \begin{cases} 0 & \text{if } t_{21} \leq\frac{1}{a} \\ \frac{T(at_{21}-1)}{(t_{21}-1)} & \text{if } t_{21} > \frac{1}{a} \end{cases} \end{eqnarray*}

Likewise, the best response function of player 2 is

\begin{eqnarray*} t_{21} = \begin{cases} 0 & \text{if } t_{12} \leq  \frac{1}{a} \\ \frac{T(at_{12}-1)}{(t_{12}-1)} & \text{if } t_{12} \geq  \frac{1}{a} \end{cases} \end{eqnarray*}

Now you can solve the best responses to get the Nash Equilibria.


Question about maintaining fixed exchange rates In my textbook, borrowing from abroad is listed as one of the method to increase the value of a currency by shifting its demand curve to the right.

"If the country borrows from abroad, its loans will come in the form of foreign exchange, which when converted into [its currency] will cause an increase in the demand for [it] and hence a rightward shift in the demand curve toward D1."

I (and a group of friends) am not quite sure how this works, given that borrowing from another country and converting the funds to their own currency should increase the supply of it, leading to a rightward shift of the supply curve instead.

Please help us out by clarifying the explanation from the textbook. Thanks!

In my textbook, borrowing from abroad is listed as one of the method to increase the value of a currency

The textbook is wrong. Borrowing from abroad tends to impact the exchange rate in a way that purchase power of the domestic currency decreases. A lower purchase power is the opposite of increased value.


How and when did the public learn of monetary policy changes before FOMC announcements and press conferences? I've been reading about the Federal Open Market Committee's announcements of monetary policy decisions, specifically the time at which the announcements are made and then how the markets somewhat immediately respond. However, FOMC announcements are a relatively recent thing, as they appear to have only started regularly in ~95 or so (press conferences are even more recent). It seems like from 1996-2013 they made an announcement after the end of every meeting at 2:15, and from 2013-present they changed it to 2:00 for some reason.

What about before 1994/5 though? How did the public learn of the monetary policy changes, and how soon after the FOMC meetings did a majority of people learn what the policy changes, if any, were?

The operating procedures for the Federal Reserve have changed drastically over the years. For example, interest rates were pegged during the early post-war era. Later on, the Volcker Fed attempted to target money supply growth, and "Fed Watchers" scoured the money data. (I do not have any references for this earlier history.)

Once money supply targeting was abandoned, operating procedures were roughly similar to the situation after 1994. The Dallas Fed has discussions of Fed Communications (written by Mark A. wynne) that has a brief summary of this period.

During that era, reserves paid no interest. The Fed did open market operationa to add/subtract reserves to match the demand for required reserves; the Fed Funds rate is the "price" banks were willing to pay to borrow reserves. If they supplied too much reserves, the Fed Funds reserves would drop towards 0%; supply too little, and banks would pay a lot to meet reserve requirements. The open market desk attempted to estimate the demand for reserves, and calibrate the size of the operations based on the market fed funds rate.

From the other side, banks could see the operations undertaken by the open market desk. They tried to reverse engineer the Fed's reserve supply function, so that they could tell what the target was (and of course, they could observe the market rate on Fed Funds).

As a result, banks roughly could tell what the target was. They would then adjust the prime rate on loans. I believe that "the public" would find out as a result of banks announcing changes to their prime rates, although presumably investors with a particular interest in interest rates would be watching what was happening in the money markets (which would adjust more rapidly).


What is the difference between "aggregation" and a "representative agent?" What is the difference between "aggregation" and a "representative agent?" I'm sorry if I'm not entirely clear on this question, but that's why I ask. It seems to me as if a representative agent is defined as a situation in which a competitive equilibrium can be reached by maximizing the utility of an object that can be interpreted as a "representative agent" whereas "aggregation" refers to a related situation where in competitive equilibrium prices don't depend on the distribution of an initial endowment. (Something to this effect.)

Could somebody clarify what these two concepts are and how they are related and/or different?

(I cannot say if my answer will respond to your questions, which indeed, are a bit unclear).

If one browses through many-many economic papers, one will get the impression that "representative" just means identical. Indeed in large chunks of literature this is the case, for historical reasons.

The drive behind the adoption of the "representative consumer" modelling framework came from the Lucas critique on the previous-generation macro-models, and the requirement that macroeconomic models are "micro-founded". But true theoretical aggregation (with heterogeneity present) requires some skill and knowledge and the bulk of the discipline appeared to have quickly settled for the "representative means identical" framework.

The problem is that in such a case, you don't really have a macro-model, just a blown-up version of a micro-model (note: here the words micro/macro are not to be mapped to the partial/general equilibrium concepts). There is nothing to "aggregate" here: the whole point of aggregation is to see whether the behavior of the collective differs from the behavior of the individual. And in the "representative means identical" approach, no such thing can happen, by construction: Instead of micro-founded macro-models, we ended up having blown-up micro-models posing as macro-ones (this is not opinion, I am just describing).

There are some models where the term "representative" obtains some intuition -especially in models with more than one classes of agents (say, labor owners and capital owners). Here we model two agents, and each is "representative" of its class. In-class are all identical, but here it sounds more appropriate to call the two individuals "representative".

The funny thing is, the concept "representative consumer" (RC) does have a special meaning: the representative consumer represents all consumers as regards basic structure, not measurement or quantities. E.g. "all individual maximize utility from consumption ("same structure"), but their utility parameters may differ("different measure"). All consumers have wealth, but the level of wealth may differ. Etc. RC is still a modelling abstraction, but it does leave room for heterogeneity.

A good source on the matter is

Caselli, F., & Ventura, J. (2000). A representative consumer theory of distribution. American Economic Review, 909-926.

Apart from their focus on developing a theory of distribution in the context of an RC model, they make a good job in presenting what can be done in an RC framework and what not. An excerpt:

  The RC is a fictional consumer whose utility maximization problem when
  facing aggregate resource constraints generates the economy's
  aggregate demand functions. The RC assumption does not rule out
  consumer heterogeneity, but only requires that potential sources of
  consumer heterogeneity have sufficient structure to ensure that the
  sum of all consumers behaves as if it were a single consumer.


Detecting Multicolinearity Are high R square and low t-stats a signal for multicollinearity? What is the nature of this problem and correction? Also, how do you generally decide if the problem is high enough to be corrected?

It’s an indicator but I personally would never decide based on them.

$t$- statistics tests the null that individual coefficient $\beta_i$ is 0 against alternative that it is statistically different from 0.

$F$-test which is increasing function of $R^2$:

$$F=\frac{R^2/k}{(1-R^2)/(n-k-1)}$$

Which tests the hypothesis that all $\beta$ coefficients are 0 against alternative that some of them aren’t.

$F$-test is not affected by multicollinearity and it will be high if $R^2$ is high. Hence if all your $t$-tests say all variables are insignificant but $F$-test (based on high $R^2$) says some of them should be significant it’s an indicator for multicollinearity. However, it could be also due to other problems so it’s always best to do some direct test - calculate correlation between independent regressors or even better something like calculating variance inflation factor (VIF) or some more fancy model.

Generally the rule of thumb is to remove variable if it’s VIF is above 5 some sources say 10.


Stock Markets and Monetary Policies Assuming we're dealing with rational investors, the stock price is equal to the present value of all future dividends(supposedly discounting at the nominal or real interest rates should give the same present value).

Imagine the Central Bank increases the real money supply, from an initial state of equilibrium, and this increase is unexpected by the investors of the stock market.

Now we have the consequences of monetary expansion in the 'physical' economy:

In the short run, the expansion causes the nominal interest rate to decrease and the output to increase. However, in the medium run, the output reverts back to the natural level, and assuming for simplicity that the output growth rate is zero, the nominal interest rate also increases when compared to initial medium run equilibrium.
In the short run, real interest rate decrease. In the medium run it increases to the natural level, and remains equal to initial levels.

In a book I'm reading on macroeconomics, it's stated that since in the short run the output (and dividends) increase, and the nominal interest rate decreases, the stock prices will go up, because the monetary expansion was unexpected.

My question is: shouldn't the rational investor know that changes in the nominal interest rate are only short term, with the longer term effect being in the opposite direction, and hence it's not clear cut that stocks' price should go up? Or should they always go up? Is it due to expected inflation that counteracts the higher expected nominal interest rate?

I think at the outset you have to make the distinction between the real interest rate and the nominal interest rate. The nominal interest rate is the real interest rate less inflation. Assuming the money supple curve is a vertical line in M-r space, then a shift of the line to the right (as indicated by a monetary expansion) implies a decrease in the nominal interest rate. Some books make the distinction between money demand being dependent on nominal interest rates, but it makes intuitively more sense that money demand be a function of real interest rate rather than nominal. The real interest rate decreases as the nominal return on assets stays constant but the price level increases (increase in inflation as a result of the monetary expansion). Remember that the price of a stock in a perfect world is the net present value of all future dividends, discounted by real interest rate. As this interest rate decreases, we discount stocks less, and hence price increases. This is the intuition behind the inverse relationship between asset prices and interest rates. This however, is a short run effect, so stock prices increase in the short run. When the real interest rate returns to its original level in the medium run, the stock prices decrease again. In short, the fluctuations in stock prices reflect fluctuations in interest rate. (the illustration is simplest for a fixed coupon bond that pays C every period). Basically, it all depends when you examine the price.


What portion of our annual deficit is financed by bonds? What portion of our annual deficit is financed by bonds?  Compared to say, treasury notes (such as checks and printed currency), or private lending?

Unfortunately, there doesn't appear to be a single site that clearly identifies the data you seek. However, that information does appear in a couple of different sources, (in a couple of different formats):

This source from the Treasury gives a list of the values of all different types of securities auctioned off at every recent treasury auction in Excel spreadsheets

This source gives the relative holdings for domestic and foreign agents, however it doesn't break down the data into as clear specifics for tyeps of debt held.

Finally, these presentations give overviews (in the "Financing" section of each presentation) of the total value of each type of bond that was issued, and the corresponding value of each typoe that matured.

Hope that helps a bit!


Under what conditions is a monopoly undesirable? First of all, I realize that "undesirable" is an ambiguous term. So, to clarify, when is a monopoly undesirable under the following metrics?

Pareto efficiency
Reduces consumer surplus
Social Welfare (could this possibly be different from the pareto efficiency criterion?)

Are there any criteria that I'm missing? Also, if we take into account potential general equilibrium effects (like the effect on wages), does the analysis change?

Firstly, suppose we take a utilitarian welfare standard that is linear in money. That is to say, suppose that both utility and profits are linear in the amount of money that consumers and firms have (but not necessarily linear in anything else). In that case, the Pareto standard and the utilitarian social welfare criterion coincide exactly! You can see a nice video of Jeff Ely talking about the intuition for this result here (look at the video titled "efficiency"). Intuitively, if both the utility and profits are linear in money then we can always maximise utilitarian welfare by implementing the Pareto optimum and then constructing side-payments to support it.

Now, the answer to the question of when a monopolist is undesirable depends on the richness of the model that one has in mind. In a very basic textbook model of a monopolist, FooBar's criterion is a good one. We know that an ordinary competitive market equilibrium maximises total welfare (the shaded area in the below figure) with price equal to marginal cost (n.b. the supply curve and the marginal cost curve are essentially the same thing):

Since the profit that a monopolist makes from a unit is equal to difference between its price and its marginal cost, the monopolist will tend to set price above marginal cost. This results in a higher price (the green $p$) and a reduction in total welfare (given by the shaded area in this figure) and consumer surplus (the triangle between the price line and the demand curve):

Since this kind of analysis is standard, it makes sense to think of the case in which a monopolist reduces consumer surplus and welfare as being a kind of 'default' and instead ask "when might a monopolist be desirable"? Here are some situations in which having a monopolist might be better than having very intense competition:

As Jyotirmoy Bhattacharya noted in a comment, First Degree Price Discrimination. This describes the situation in which the monopolist can charge each consumer an individualised price that is exactly equal to that consumer's willingness to pay. Thus, the monopolist captures all consumer surplus so that
$$\text{Social welfare}=\underbrace{\text{Consumer surplus}}_{=0}+\text{Producer surplus}=\text{Producer surplus}.$$
Since producer surplus and social welfare coincide, when the monopolist acts to maximise its own surplus it is also maximising social welfare! However, whilst this is good for welfare, it is very bad for consumers. It also requires that the monopolist has enough information about consumers to accurately estimate their willingness to pay, that such discrimination is not illegal, and that consumers are willing to tolerate it (i.e. there is no PR backlash--see, e.g., here).
Large economies of scale. Sometimes the fixed costs of establishing a business are massive. For example, to set up a rail/telephone network requires that you lay train tacks/phone lines across the entire country. Once this cost is incurred, the infrastructure can be used at close-to-zero marginal cost. In this kind of environment it doesn't make sense for society to incur the fixed cost more than once. The infrastructure company is then called a natural monopolist. In these kinds of industries a monopolist is usually allowed to operate and is either (i) owned by the government, or (ii) heavily regulated to ensure that price is not set far above marginal cost.
Network externalities. Some products are only valuable to you is other people also use them. For example, Facebook and telephones (and Stack Exchange!) are only useful because they can be used to contact other people. The more people you can contact, the more valuable to the product becomes. If everybody uses a single monopoly social network then that network will be more valuable than if people are divided across a large number of competing social networks. Network effects are sometimes call demand-side economies of scale.
Innovation and investment. Firms invest in R&D to develop new products (or new production technologies). Why bother? Presumably, firms do this because they anticipate earning a profit selling those new products (or from the reduced cost of the new technology). But their ability to earn this profit will depend on how much competition the firm faces. Thus, one might think that competition should reduce the incentive to innovate by eroding the associated profits. In fact, a famous paper by Aghion and coauthors shows that adding competition first reduces innovation and then, once competition gets fierce enough, increases it again. Thus, if the choice is between a monopolist and a few firms then a monopolist might result in more innovation.
It's perhaps worth mentioning that this last point is closely related to the idea of intellectual property. Since most intellectual property (i.e. creative works like books, songs, or movies; and inventions) are information goods, they can be duplicated or imitated at zero marginal cost. That means that if we allowed competition we should expect there to be many competitors and it will be very hard for anyone (including the original creator) to make any profit whatsoever. In order to ensure that creators and inventors have an incentive to create new works or new inventions, the state therefore grants them a temporary monopoly in the form of either copyright protection or patent protection.

Those are a few of the most common ways in which a monopolist might be preferable to competition. I am sure there are others that don't come to mind right now. The main message is that you have to look at the specific market context to evaluate whether there might be any problems associated with intense competition. Most often the answer will be that there are not, and the usual assumption is therefore that monopolists are undesirable unless we have good reason to think otherwise.


Interpretation of Demand and Cost Curves I am currently starting on the topic of monopolies in school and I encountered the following scenario:
A monopolist faces a demand curve given by $Q = \frac {100} p$ and a cost function given by $C = 4Q$. I need to find the price elasticity of demand (PED) as well as the optimal level of output for the monopolist.
I was taught that $MR = P(1 + \frac 1 \epsilon) = MC$, where $\epsilon$ = PED.
I know that any producer produces at the point where $MR = MC$, but before I could even proceed with solving for the PED, I am wondering how, in this case, can $MR = MC$?
If I am not wrong, by my calculations, $MR = 0$ and $MC = 4$. How do I interpret this?
Then, since $MR \neq MC$, how can I proceed with this question?
And any intuitive explanations on how I can calculate the PED and optimal level of output will be greatly appreciated :)

Your calculation is not wrong. First a more easy and more intuitive way of calculating marginal revenue is just to take derivative of total revenue.
Total revenue is price times quantity $TR=P (Q) Q$ where price is still function of quantity as at higher price people demand lower quantity of goods (I am expressing everything in terms of Q since that is the choice variable in your model). Substituting for quantity we get:
$$TR=  (100/Q)Q \implies MR = \frac{dTR}{dq} = 0$$
Hence in this case they are indeed zero. Furthermore, in this case the profit maximization problem of monopolist does not even have a solution. Profit is given as total revenue minus total costs so:
$$\Pi = TR-TC = (100/Q)Q -4Q$$
If we would try to derive the first order conditions for maximization we would just get that 0=4 which means there is no solution. To make that clear I even programmed a visualization of your problem in R, this is how it looks like where green curve is demand, red line is marginal revenue and blue line is marginal cost.

So there are three options I see here:

This is a trick question and you teacher expects correct answer to be that there is no solution (no solution in standard non-negative real numbers that is as it could be argued that quantity produced should be as small as possible but not zero (infinitesimal) from right side - however thats not a standard real number).
You misread the problem or made mistake in part of the problem which asked you to first create cost function or demand from some text.
Your teacher made a mistake when making up the problem.

Hence my advice is first make sure you read the set up thoroughly, if there is no mistake there then contact your teacher and ask if its possible that the teacher made a mistake since MR is zero in your case. If there is no mistake then its a correct solution.

response to question in comments:
Price elasticity of demand is defined as:
$$\epsilon = \frac{d Q}{dp}\frac{p}{Q}$$
So in your case it will be:
$$\epsilon = -\frac{100}{p^2} \frac{p}{\frac{100}{p}}= -\frac{100}{p^2} \frac{p^2}{100} = -1$$

Addendum: In response to comments I also added simulation for profits of the monopolist in this situation assuming that the profit function is:
a) $\Pi = \frac{100}{Q} Q -4Q$  - in red color
b) $\Pi = 100 - 4Q$ - in blue color


Monopoly/Monopolistic Competition Productively Efficient or Inefficient? I know both market structures are allocatively inefficient as P > MC. But,

Since monopolistic competitive firms produce on the downward sloping part of their AC curves, there is excess capacity which implies productive inefficiency. To achieve productive efficiency, they have to produce on the lowest point of their ATC curve. Since monopolies also do not operate on this lowest point of their AC, they are also productively inefficient.

However, the total cost curve shows the least cost method of producing each output level as it is derived from the tangent of the isocost to isoquant, which implies that all points on the total cost curve is productively efficient since cost is minimised. Since AC = TC/Q, it also implies that all points on the AC curve is productively efficient - all points on the LRAC are productively efficient.

Since all points on the total cost curve and average cost curves are productively efficient, monopolies and monopolistic competitions, who operate on their AC curves, are productively efficient.

Both of this concepts contradict one another. One claims both are inefficient while the other says they are efficient. Am i confused or is one of them wrong?

If productive efficiency is achieved when goods are produced at the lowest cost possible, are all points on the LRAC are productively efficient since the LRAC shows the lowest cost of producing at each output?

Productively efficiency is only achieved on the lowest point of LRAC/SRAC?

No contradiction. All points in the AC curve indeed reflect the production of the corresponding quantity at minimum cost. This is conditional efficiency, conditional on arbitrarily specifying an output level.

Then we ask: what is the output level for which this product is produced at an average cost that it is lower than the average cost for all other output levels, the minimum minimorun, the least of all minima?

And we get the minimum of the Average Cost curve. At this output level we cannot do better by varying the quantity (either increase it or decrease it). So it is this quantity that achieves "universal" efficiency.


MRS for quasi-linear preferences I'm having difficultly understanding what my professor taught in class.

I thought, like cobb-douglas, when finding $U_1$ we take partial derivative with respect to $q_1$ and hold everything else constant. Why does gamma($q_2$) disappear? Same with $U_2$. and what is gamma? a variable?

Well going through the derivatives, simply put. View $U$ as a function. A.K.A $U=U(q_1,q_2)$ and let $U_1=U(q_1)$ and $U_2=U(q_2)$. So to find $U_1$ and $U_2$ respectively, just take the partial derivatives in respect to the  given variables

$$U_1=\frac{\partial U(q_1,q_2)}{\partial q_1 }=(1-\beta)q_1^{-\beta}+ \frac{\partial}{\partial q_1} \gamma q_2=(1-\beta)q_1^{-\beta}$$

Since $\frac{\partial}{\partial q_1}\gamma q_2=0$

Similarly,
$$U_2=\frac{\partial U(q_1,q_2)}{\partial q_2}= \frac{\partial}{\partial q_2}q_1^{1-\beta}+\gamma=\gamma$$

since $\frac{\partial}{\partial q_2} q_1^{1-\beta}=0$

Hope this helps


What is an estimate of the value of the world's assets? Gross world product is on the order of 80E12 $ per year (PPP). Where can I find an estimate of the net value of the world's assets (companies, properties, infrastructure...)? Preferably with some more granular statistics.

One place that estimates the world's wealth (measured as net value of assets) is the Credit Suisse Global Wealth Report.
According to the report their estimation of worlds net assets is 361 trillion of USD in 2019. Their site has also statistics for other years. They also offer some country level statistics in their reports (not sure if that's granular enough).


Pure and Mixed Nash Equilibrium algorithm gives different results I have a game represented by following table:

It is clear that there is a pure Nash equilibrium at 4,2 (both players do not cooperate, player 1 awarded 4 points and player 2 awarded 2 points).

Now if I used mixed strategy Nash equlibrium algorithm I get a = 1 and b = -1 as the probability of player 1 plays Cooperate and player 2 plays Cooperate respectively. To my understanding, a and b should be equal to 0 so that both players should play the above pure equilibrium strategy.

Why is there such a difference in pure and mixed strategy?

Edit 1: mixed strategy Nash equlibrium algorithm:

The expected ultility for player 2 playing cooperate is: a*2 + (1-a)*1 (This means that some of the time player 1 plays Cooperate, so the probability is a).
The expected ultility for player 2 playing non-cooperate is: a*2 + (1-a)*2.
By equating the two formuala I have (1-a) = 2*(1-a) so a = 1.
Simmilarly, the expected ultility for player 1 playing cooperate is: 6*b + 3*(1 - b).
The expected ultility for player 1 playing non-cooperate is: 8*b + 4*(1 - b).
By equating the two formuala I have 0 = 2*b + (1-b) so b = -1.

Mixed strategy Nash equilibrium cannot involve strictly dominated strategies. In particular, Cooperate is strictly dominated for player 1 ($6<8$ and $3<4$). Therefore, no $b\in[0,1]$ can make player 1 indifferent between Cooperate and Non-cooperate. You made a mistake by trying to solve for $b$ by equating player 1's expected payoffs from his two pure strategies.


What's the relation between economic growth and buying power? If a country had economic growth last year (2015) does that mean that the average citizen had a better buying power in that year (2015) than in the previous year (2014)?
For example with their monthly wage they could buy 800 kilos of rice in 2015 up from 700 kilos in 2014.

Or to put it in other words: can an country have economic growth while in the same time the average citizen face a reduced buying power (for example by increased prices of commodities) in the same period of time?

Probably no, not in the same year. But maybe in the year after.

If you're talking about the average citizen, the intensity of this expansion of buying power depends on wealth distribution, the importance of those industries which had grown and whether those industries are more labor intensive or capital intensive.

Also, this expansion doesn't happen instantly; don't expect that the whole nation will realize this growth in the same year that it happened. It takes time for the money to flow from the main industries to industries of the same network and than to other firms not related.

That process is even slower through the employee chain. One of the reasons is that frequently employee and employer negotiate salary for long periods (there's some "stickiness"). When a type of workforce is unionized, it takes even more time for them to negotiate wages as a group.

The pathway you're asking about is like this: More production means the industries needs to increase their capital, inputs and workforce. They buy more capital, more inputs and hire more workers. This increase in demand means those other industries and workers are able to negotiate better salaries than in the year before. To be able to satisfy this new demand, the industries that produce capital and input need to increase their production as well, by hiring more workers, buying capital and inputs. And this goes on and on till it,theoretically, affects the lower paying jobs. Of course it all depends on how much the links in the chain pass the wage increase to the next link.


Free alternative to EViews for ARIMA modelling Can someone guide me in acquiring an application similar to EViews? I need a free application where I can incorporate the ARIMA model.

The standard open source statistical language is R. The R-Project homepage is here. Here is a page about ARIMA in R. If you want to try using R without having to install anything, then I would recommend DataJoy, which provides a free web-based R environment.

Note that R is an entire statistical computing language, so you may find that there is quite a big overhead for learning the language before you can start doing your ARIMA analysis.


What is the actual numerical value of the velocity of money? All the discussions of the velocity of money that I've come across (e.g. here, here, and here) only display relative changes in the velocity of the money (e.g. by normalizing it by an unspecified value). I've never seen any source report an actual numerical value (with the units of inverse time) for a given point in time, for any choice of money supply. Does anyone have a reference for such a value?

(It appears that the answer was supplied in the original question. The third link was to the time series for the M2 velocity for the United States. This answer is just taking text out of the comments.)

The linked chart link to FRED website is of the ratio: (nominal GDP at an annual rate) divided by M2 (for the United States).

The units for annualised GDP are \$ per year, and the units for M2 are \$; the \$ cancels and we end up with 1/years as units. (This is tracking units the way that is done in the physical sciences.) If we took non-annualised quarterly GDP, the ratio would be 1/4 as large.

Some economics charts can be confusing from the perspective of physical sciences, because the inverse time units for flows are suppressed. This is a convention that has held for decades; you just have to know what is being done. It probably causes problems because people often look at mixes of stock and flow variables, such as the infamous debt-to-GDP ratio.


Matching Theory: Search Time Consider the standard Diamonds coconut economy. One could imagine that people who search longer, have a different likelihood of matching someone to trade with.

Has there been something done akin this (in any part of matching theory)?

Second Example Say, we want to match liver transplants between donors $d$ and recipients $r$. The longer anyone waits, the higher the likelihood of being matched with someone from the other side.

Hence, we would have a distribution of $r$ and $d$ w.r.t the time that they have already been waiting. And instead of an aggregate matching function $M(r, d)$ we would have something that takes into account these distributions.

What has been done in this area so far?

The paper is a couple of years old by now, but I believe the first people to look seriously at the issues you're thinking of are Akbarpour, et al.

It might be useful to look at that paper and the handful of others that cite it. The paper was originally called 'Dynamic Matching Market Design', so it may have more citations under that name.


Why do different product-markets record different rates of return if the assumption of competitive markets hold? I'm a new economics student, and have become fascinated by the field of Industrial Organization. To that end, I'm reading through the Carlton and Perloff Modern Industrial Organization text book. In doing so, I have come upon a question I was hoping to ask the group here. If all product markets are perfectly competitive (to a reasonable approximation), shouldn't the returns to invested capital (a way of measuring 'economic profit') in every product market, whether the market be for cement or GPS integrated circuits, be equivalent after adjusting for risk? Or put in a equivalent way, do the differences that are seen (in reality) between the rates of return in different businesses/industries reflect purely differences in risk borne by shareholders/capital-owners?
The reason I ask is because it seems (to my untrained eye) as if the assumption that all markets have equal risk-adjusted rates of return is just manifestly not true (see  the graph below).  Different product-markets and indeed different firms within a particular market empirically show wide variance in profits and returns (can provide some sources if needed). If the difference is not driven merely by risk, what explains this difference and what are the welfare implications of that explanation?
This leads me to the true question I'm interested in answering. If high returns in certain markets are not explainable by risk, then are they entirely ascribable to market power (with its attendant losses to overall welfare and efficiency)? Or could there be other factors at play? If there are other factors at play, what are they and can you point or direct me to models/theories/papers which describe them? One factor that some people throw around colloquially is "efficiency"; a firm might be more efficient than its competitors. What models explicitly model the process of a more efficient firm and its attend effects on returns, profits and welfare?
Of course, I might be missing something huge. I am new to this and am asking what I realize to be very naive questions. Happy to be educated :)
Edit: I realized that there might have been some confusion. I was referring to differences in rates of return between and within different product markets, not different countries. So the phenomenon I'm interested in understanding is the following graph, which is taken from here

Edit: after OP made changes to his question and clarification this answer became less relevant. I am still keeping it here because OP said some parts of it and references are still useful.
There are several reasons why even if all markets were perfect rates of return would not equalize. I will just focus on some major ones.

Many countries have some capital controls in place. This means that even if markets were perfect the rate of return would be prevented to equalize by the lack of capital mobility. In fact assumption of perfect capital mobility is necessary assumption for rate of return equalization between different markets.

If capital is heterogeneous it might not necessary be easily transferable between countries which mean that capital poor countries will get less capital inflows. For example, some capital such as some computer for some production processes such as programming might require skilled workforce. If some country does not have skilled workforce then not all capital from capital rich country will be allowed to flow from capital rich country to capital poor country.

If places differ with aspects such as infrastructure or geography in general rates of returns might be different just due to differences in these factors as they would again prevent equalization of rates of returns and capital flows (for example country with no roads and harbor cannot really sustain any modern industrial complexes).

Note that you have to also take broader view of risk which encompasses also risks of nationalizations, some institutional risks (countries might be expected to adopt worse institutions in future) and so on. Risk should be not viewed as simply just the entrepreneurial risk.

In fact the reasons above is why you get Lucas paradox (see this question). Lucas paradox is the paradox that nowadays we observe that instead of capital flowing from capital rich countries to capital poor countries (which would equalize rates of return), the capital actually flows from capital poor countries to capital rich countries. The arguments above are more formally presented in Montiel (2006), Schularick & Steger(2008), Azémar & Desbordes (2013), Akhtaruzzaman, Hajzler & Owen (2018).
Also note that if you are wondering why the rates of return are different between different places you have to venture outside pure industrial organization to international macroeconomics or international economics. Industrial organization focuses mainly on explaining how firms compete on given market and while many models from IO are heavily used in international economics or international macroeconomics pure IO will not really discuss much differences between rates of returns in different countries. Hence if you want to pursue this topic further you should also have look at some international macro or international economics textbook. Most of these will discuss international capital flows (on which the equalization of rate of return depends) in decent detail.
Furthermore, of course you are right in assuming that many markets are imperfect and that is also why rates of returns are not equalized.


Higher order beliefs and coherency in game theory I am reading about the higher order beliefs. Before getting into the formal definitions, I will define some common terminology which I will need for the formal definitions.

  If $X$ and $Y$ are two spaces, denote the set of probabilities over $X$ as $\Delta(X)$, and for $\delta\in \Delta(X\times Y)$ define the marginal probability measure of $\delta$ on $X$
  $$
marg(\delta;X)(E)=\delta(E\times Y)
$$
  for every measurable subset of $E$ of $X$.

The formal definition of higher order order is as follows:

  Let $N=\{1,2,\dots, n\}$ be the set of players. For each $i\in N$, $A_i\neq\emptyset$ is the finite set of actions available to player $i$. Denote the set of mixed strategies for  the player $i$ as $\Sigma_i=\Delta(A_i)$. As usual define $\Sigma_{-i}=\times_{j\neq i} \Sigma_i$ and $\Sigma=\times_i \Sigma_i$. Define the se set of first order beliefs $B_i^1=\Delta(\Sigma_{-i})$ and $B_{-i}^1=\times_{j\neq i} B_j^1$, and $B^1=\times_i B_i^1$. Define inductively, for each $k\geq 1$
  $$
B_i^{k+1}=\Delta(\Sigma_{-i}\times B_{-i}^1\times \dots B_{i}^k)\\
B_{-i}^{k+1}=\times_{j\neq i} B_j^{k+1}\quad B^{k+1}=\times_i B_i^k
$$
  Finally, $B_i=\times_{k=1}^\infty B_i^k $

The coherent belief is described in the following way:

  $b_i=(b_i^1,b_i^2,\dots)\in\times_i B_i^k$ is coherent if for each $k\geq 1$ $marg(b_i^{k+1},\Sigma_{-i}\times B_{-i}^1\times\dots\times B_{-i}^k)=b_i^k$ where $marg$ is the marginal probability measure.

Now according to this definition for $E\subset \Sigma_{-i}$ we have $marg(b_i^2;\Sigma_{-i})(E)=b_i^1(E)$.

I try to understand this definition. So I tried to consider a game in which there are two players $i$ and $j$ and two actions for each player. So

$$
\Sigma_i=\{(p,1-p):p\in[0,1]\}\quad \Sigma_j=\{(q,1-q):q\in[0,1]\}
$$
and $b_i^1\in\Delta(\Sigma_j)$ and $b_i^2\in\Delta(\Sigma_j\times B_j^1)$. So $b_i^1$ is a probability measure over $q$, and $b_i^2$ is a joint probability measure over $q$ and the first order beliefs of $j$. Suppose $E$ is the collection of $(q,1-q)$ such that $q\leq 0.5$, which is a subset of $\Sigma_j$.
I could not convince myself why $marg(b_i^2;\Sigma_j)=b_i^1(E)$. Apologies for the length of the question and any help is greatly appreciated.

The way hierarchies of beliefs are specified, beliefs on the same events are encoded in different places.

The basic idea is actually quite simple. You have two players, Ann and Bob, say. Ann's first order beliefs specify how likely she thinks each strategy choice of Bob. Ann's second order beliefs specify how likely she thinks each combination of a strategy choice of Bob and a belief of Bob on Ann's strategy choices. Second order beliefs are joint probabilities.

Now suppose Ann's first order beliefs specify that she believes that Bob plays the strategies C and D with probability $1/2$ each.

Suppose also that Ann believes with probability $1/4$ that "Bob plays C and believes with probability 1 that Ann plays D for sure" and believes with probability $3/4$ that "Bob plays D and believes Ann plays D for sure".

If you ask someone who knows only Ann's first order beliefs how likely Ann thinks it is that Bob will play C, that person will answer with $1/2$. If you ask someone who knows only Ann's second order beliefs how likely Ann thinks it is that Bob will play C, that person will answer with $1/4$. Indeed, that is what the marginal of her second order belief on the space of strategies says.

This is absurd and makes no sense. Ann's beliefs on how likely it is that Bob plays C should be the same according to her first order beliefs as to her second order beliefs. Now coherency is exactly the condition that guarantees that. If some belief on an event E is specified in more than one level of the hierarchy of beliefs, each hierarchy should specify that the same belief on the event E.

In terms of the formalism: The marginal of a probability measure is again a probability measure, so $marg(b_i^2;\Sigma_j)=b_i^1(E)$ is comparing apples and oranges; on the left is a probability measure, on the right a number. What you want is $marg(b_i^2;\Sigma_j)(E)=b_i^1(E)$, as prescribed by coherency- and indeed by common sense.


How to prove the WPBE is SE in signaling game? The definition of a signaling game:

A signaling game is an extensive game with the following structure:

(i) A move of chance first determines a state of the world/type $t ∈ T$, which is drawn from T according to a probability distribution $π ∈ ∆T$,

(ii) The first player, referred to as the sender (player s), observes the true state/his type $t ∈ T$, and chooses a signal/message $m ∈ M$ to send to the second player, referred to as the receiver (player r),

(iii) The receiver observes the sender’s message m (but not the sender’s type t), and chooses an action $a ∈ A$,

(iv) The players’ payoffs are given by functions $u_i: T × M × A → R$, where $i ∈ {s, r}$.

I need to prove:

  If the sets $T$, $M$, and $A$ are finite, then an assessment $<\beta_s, \beta_r, \mu>$ is a WPBE if and only if it is an SE.

The SE must be a WPBE, this is trivial. But I'm struggling with proving WPBE is SE in this game.

I wanna define a strictly mixed strategy sequence and the corresponding belief system to prove that when the receiver's information set cannot be reached, the belief is still consistent. But I'm stuck here.

Can anyone please give me some hints about how to prove this? And how to define such a sequence?

Claim: If choice sets $T, M,$ and $A$ are finite, then an assessment $\{\beta^*_{r}, \beta^*_{s}, \mu^*\}$ is a WPBE (weak perfect Bayesian equilibrium) of the two-stage signalling game between receiver $r$ and sender $s$ if and only if it is a SE (sequential equilibrium).

Proof: SE $\implies$ WPBE is trivial since SEs are PBEs by construction, and thus are also WPBEs.

To prove that a WPBE is also a SE for this signalling game over finite choice sets $T, M,$ and $A$, we must demonstrate that there exists a tuple $(\beta^n_r, \beta^n_s, \mu^n)$ such that $\{\beta^*_{r}, \beta^*_{s}, \mu^*\} = \lim\limits_{n \to \infty} (\beta^n_r, \beta^n_s, \mu^n)$ for some totally mixed strategy $\beta^n$ such that, for all $n$,

$$
\begin{align}
\mu^n(t|m) = \frac{\pi(t)\beta^n_s(m|t)}{\sum_{t' \in T}\pi(t')\beta^n_s(m|t')} &&\text{whenever} \sum_{t' \in T} \pi(t')\beta^n_{s}(m|t') > 0
\end{align}
$$

since this is a two-player game between players $r$ and $s$. The condition on $\mu^n$ above is known as weak (Bayesian) consistency.

To construct such a totally mixed strategy profile, $\beta^n$, consider first the following message-sending strategy profile for player $s$ as a function of $n$ conditional on the state of the world $t$:

$$
\beta^n_{s}(m|t) =
\small{
\begin{cases}
\frac{n-1}{n} \left(\frac{n-1}{n}\right) \beta^*_s(m|t) && \text{if } \beta^*_s(m|t) > 0 \text{ and } \sum_{t' \in T} \pi(t')\beta^*_{s}(m|t') > 0 \\
\frac{n-1}{n} \left(\frac{1}{n \mathcal{N_s}(t)}\right) && \text{if } \beta^*_s(m|t) = 0 \text{ and } \sum_{t' \in T} \pi(t')\beta^*_{s}(m|t') > 0 \\
\frac{n-1}{n} \left(\frac{\pi(m) \mu^*(t|m)}{n\pi(t)} \right) && \text{if } \mu^*(t|m) > 0 \text{ and } \sum_{t' \in T} \pi(t')\beta^*_{s}(m|t') = 0 \\
\frac{1}{n} \left[1 - \sum\limits_{m' \in M} \left(\frac{n-1}{n} \frac{\pi(m') \mu^*(t|m')}{\pi(t)}\right) \right]&& \text{otherwise}
\end{cases}
}
$$

where, borrowing notation from Fudenberg and Tirole (1991),

$$\mathcal{N_s}(t) \equiv \#\{m \in M\ |\ \beta^*_s(m|t) = 0 \text{ and } \sum_{t' \in T} \pi(t')\beta^*_{s}(m|t') > 0 \}.$$

The finiteness of $M$ is invoked here so as to provide a well-defined domain over $\#\{\cdot\}$. These four cases span the parameter-space of $\beta_s^*$ and $\mu^*$ in this game. Thus $\sum_{m \in M} \beta^n_{s}(m|t) = 1$ and $\beta^n_{s}(m|t) > 0$ for all $n$ and for all $m \in M$, establishing that $\beta^n_s$ is a totally mixed strategy profile for player $s$. By construction of the asymptotic behavior of $\beta^n_{s}(m|t)$, it is easy to verify that $\beta^n_{s} \to \beta^*_s$ as $n \to \infty$.

The residual strategy profile for player $r$, $\beta_r^n(a|m)$, can be simply constructed by assigning probabilities only across the parameter-space of $\beta^*_r$ since the belief $\mu^*$ is just-identified by $\beta^*_s$:

$$
\beta^n_r(a|m) =
\begin{cases}
\left(1 - \frac{1}{n}\right)\beta^*_r(a|m) && \text{if } \beta^*_r(a|m) > 0 \\
\frac{1}{n\mathcal{N_r}(m)} && \text{if } \beta^*_r(a|m) = 0,
\end{cases}
$$
where $\mathcal{N_r}(m) \equiv \#\{a \in A\ |\ \beta^*_r(a|m) = 0\}$. Clearly $\beta^n_r \to \beta^*_r$ as $n \to \infty$.

Lastly, by construction of $\beta^n_s(m|t)$, it is straightforward to verify that the sequence
$$
\begin{gather}
\mu^n(t|m) = \frac{\pi(t)\beta^n_s(m|t)}{\sum_{t' \in T}\pi(t')\beta^n_s(m|t')} \to \mu^*(t|m) \text{ as } n \to \infty
\end{gather}
$$

and thus consistency is demonstrated. Hence the WPBE is also a SE for this game.$\ \blacksquare$


Credit Frictions as the source of Business Cycles Many papers look at the impact of credit frictions onto business cycles, and they almost unambiguously find that credit frictions work as an amplification mechanism of other shocks.

For example, given a stronger negative total factor productivity shock, the existence of borrowing frictions will lead to higher firm death, devaluation of capital and in general stronger impact on the real economy.

A lot of these models (in the tradition of Kiyotaki and Moore) have finite periods and just illustrate the amplification mechanisms. Have there been attempts that actually tries to look at credit frictions themselves as the source of business cycles?

Yes credit frictions do have an amplifying effect on supply shocks while they often attenuate demand shocks and they also give increased persistent to the effects of the supply shocks in many models.

Once you have a specified DSGE model you can choose exactly where the shock originates from and the strength of the shock. See for instance Gerali et. al. 2010. Credit and Banking in a DSGE model of the Euro Area. They incorporate a banking sector into a traditional DSGE model. Their variance decomposition shows that it is mostly shocks originating in the banking sector which explain the fall in GDP during the financial crisis. However that is empirical estimation.

What you can do and what they do is to shock bank capital so as to simulate a loss. They show that this loss in bank capital has effects on output, consumption, inflation, investment and so on. So by incorporating financial and/or credit frictions you can simulate shocks to these which in turn should have real effects in your model.

The paper can be found here: http://www.bancaditalia.it/pubblicazioni/econo/temidi/td10/td740_10/td_740_10/en_tema_740.pdf

EDIT:
There are actually papers that are examining the question at hand in even more details than the Gerali et. al paper mentioned above. Two of these are Iacoviello, M. 2014. "Financial Business Cycles" where he examines a recession whcih is initiated by losses suffered from banks. Another paper is Jensen et. al. 2013. "Changing Credit Limits Changing Business Cycles" where they examine financial liberalization in a DSGE model. They find that financial liberalization leads to higher macroeconomic volatility.


Demand correspondence is both upper and lower hemi-continuous; is the preference continuous? $\succsim$ is a weak order over $\mathbb R^L$.

For a closed budget set $B\subset\mathbb R^L$, define demand correspondence: $$D(B)=\{x\in B|x\succsim y\forall y\in B\}$$.

We know that $D$ is always none empty and both upper and lower hemi-continuous, can we conclude that $\succsim$ is continuous? Can we conclude that $D$ is rationalizable by a utility function?

My approach: For the first question, I guess we can first show that $D$ is rationalizable by a utility function $u$. Secondly, since $D$ is continuous, $u$ must be continuous, and $\succsim$ is continuous. But I doubt this approach will work, because the second step seems not work.

For the second part, if $\succsim$ is continuous then it is represented by a continuous utility function. Even if $\succsim$ is not continous, it must be upper-semi continuous and we can still find a upper semi-continuous utility rationalization for $D$ by Rader theorem.

We could consider a simpler version of the problem: Let the demand function be continuous, is the preference relation also continuous? (This is proved by Mas-Colell in 1978, I think)

I think that you should proceed by contradiction assume D is continuous, but $\succsim$ is not, then for a bundle either the more preferred than or the less preferred than sets are not closed. Choose the problematic set and choose a set B appropriately to get a contradiction of the existence of a maximum (remember that not closed sets might not admit a maximum), this will give you the desired contradiction. Once preferences are continuous, remains to check completeness of preferences to use the classic theorem that if preferences are complete, transitive and continuous, then a utility function representation exists.


Market behavior when consumer must choose product before knowing price? What forces influence the price in a market, wherein the consumer must choose a good before knowing the price, and afterwards only knows the price of the good purchased, not that of any competing goods? For instance, in the US healthcare industry, a patient wanting to assess the cost associated with treating a particular condition - historically, at least - cannot receive quotes for the treatment.

Yes, we can model this as a choice under uncertainty, where the distribution is over the set of prices the consumer may face. The consumer could have an expected budget with expected demands and you would need to allow the consumer to go into debt if prices are higher than their wealth (think a quasilinear environment).

The second part, where the consumer doesn't know the other competing firms can also be modeled with uninformed consumers vs informed consumers, where firms compete on price over those kinds of consumers. The informed choose better option, the uninformed just choose the same regardless.


Europe Quantitative Easing Okay, this is from latest events.

Countries like USA & Japan have successfully used QE to stimulate the economy, but what stops European Central Bank from implementing it?

If they decide to use it what will happen to stocks and bonds? How will the investors react? Most economists also say that it wont work well in Europe, why?

Europe is a banking based continent, in contrast to the US where financial markets play a prominent role. As a result, wealth effects in Europe are much smaller than in the US. QE thus has a smaller favorable effect on the economy.

You are right, they should implement it given the low inflation level present for an extended period. But as shown by history, the ECB always reacts later and less agressive than the FED. This is because the ECB has a sole objective of keeping inflation close but below 2% (imposed by the Germans having experienced periodes of hyperinflation). Even today, the germans and some other hawks are still reluctant to pull out the big canon.

QE leads to an increase in bond prices, and supports equities as well. However, whether or not equities go up, depends more on how people react.


If a rational preference relation over simple lotteries $\succsim$ are convex then they satisfy independence? Let´s say there is an uncertain situation with $N$ possible consequences $C = \{C_1, . . . C_N\}$. Assume that
there is a rational preference relation $\succsim$  over simple lotteries.
I know that if $\succsim$ satisfies independence, then it is also convex, but is it true if $\succsim$ are convex then they satisfy independence? How can I show this (if the implication is true)

It's well known that if $\succsim$ satisfies independence, then it is also convex.

Since $\succsim$ satisfies independence,
$L\succsim L^{'} \iff \alpha L+(1-\alpha)L^{''}\succsim \alpha L^{'}+(1-\alpha)L^{''}$ for all $\alpha \in [0,1]$ and $ L, L^{'}, L^{''}\in \mathfrak{L} $
Convexity requires:
$L\succsim L^{''}$ and  $L^{'}\succsim L^{''} \Longrightarrow \alpha L$ + $(1-\alpha)L^{'} \succsim L^{''}$ for all $\alpha \in \left[0,1\right]$  and $ L, L^{'}, L^{''}\in \mathfrak{L} $
Pick any $ L, L^{'}, L^{''}\in \mathfrak{L} $  with $L \succsim L^{''}$  and $L^{'} \succsim L^{''}$. By completeness, $L \succsim L^{'}$ or $L^{'} \succsim L$ or both. Without loss of generality, assume $L \succsim L^{'}$. Then, by independence, for all $\alpha \in [0,1]:$
$ \alpha L$ + $( 1- \alpha) L^{'} \succsim \alpha L^{'} + (1-\alpha)L^{'}  = L^{'} \succsim L^{''} $, which we wanted to show.

Is it true if $\succsim$ are convex then they satisfy independence?

On the other side, convexity does not imply independence. To see this, take a look
at Figure (see below). Triangles are indifference curves and arrows show the direction in which
utility increases. It is convex, but not independent.


Does only "supply/demand" rule justify different prices for a digital good? Provided the network infrastructure costs the same for the seller (if things going on with net neutrality weren't to effect that), certainly considering the fact that an average citizen of a given "low average $ income" country would have less money available for digital products than say someone from Germany or U.S.A.

What are the mechanisms that justify large price differences between different countries (3x ratios or more) ?

Edit: Thanks for your answers.
As real life examples, what struck me is any app here https://steamdb.info/apps/ but as you suggested it applies for various digital goods on amazon and other sellers.

One explanation would be price discrimination.

Some people are willing to pay more for software than others. (Typically, we would expect such people to live in richer countries.) As a result, it will be in the interest of software seller with monopoly power to charge different people different prices.

In case this isn't clear, here is an illustrative example. Suppose that Microsoft is deciding how much to charge users for a digital copy of Microsoft Office. Legally, it is the only entity that is permitted to sell Office, so it has some monopoly power. Since we are considering digital copies of Office, its marginal cost will be essentially zero. Suppose that:

In Country A, all inhabitants would pay at most £10 for one copy of Office.
In Country B, all inhabitants would pay at most £200 for one copy of Office.

(Assume that no inhabitant wants more than one copy.)

What prices should Microsoft charge (to maximise profits)? Obviously, it should charge £10 in Country A (or £9.99 if you prefer) and £200 in Country B. Thus, even though the cost of production are the same in both countries, prices will vary greatly between them.

Note that this explanation only works if Microsoft can prevent resale - which it can, since it has a patent for Microsoft Office. Otherwise, someone might start buying copies of Office in Country A and re-selling them in Country B, a strategy which will render Microsoft bankrupt unless it changes its pricing.

Of course, it also assumes that price discrimination is legal.


Log-linear ordinary least squares specification coefficient loses its interpretation when we change an explanatory variable by a unit? Ok, so something that's common to the econometrics literature is that we interpret the coefficients in OLS log-linear models like such.
To spell it out in the main body:
$ln(y_i)=\beta_0+\beta_1X+u_i \Rightarrow \text{if } \Delta x = 1, \text{then } \text{%}\Delta y \approx 100\beta_1 $
I think that this is a very bad approximation, although my reasoning is probably incorrect (although I do understand the derivation of why this approx holds).
Ok, so an aside:
$\frac{\dot{y(t)}}{y(t)} = g \Rightarrow ln(y_t) = gt + c $
It also follow that:
$y_{t+1} \approx y_t (1+g \Delta t) $
So here, if I plug in a change of t = 1, and let g = 1, y would be doubling with each unit change in t, and so we should approx y as 2^x instead of something of the form e^x. Of course, large-ish changes in x mess up the calculus.
However, isn't plugging in a unit change in t (in the econometrics textbook, x is t) what the econometrics textbooks are doing? A unit change in x -> 100% change in y (g and beta_1 are analogous, so g = 1 -> beta_1 =1) -> y approx doubles with each change in x -> y should be modelled as something of the form 2^x, not e^x, and there's a sizeable difference between the two, and so this contradicts that fact that the specification implies that y is in the form e^x (rather than 2^x).
I hope this makes sense.

When
$$\ln y = \beta_0 + \beta_1 x + u \implies y = \exp\{ \beta_0 + \beta_1 x + u\}$$
$$\implies \partial y / \partial x = \beta_1 y \implies \frac{\partial y / \partial x}{y} = \beta_1.$$
So we see that $\beta_1$ is the marginal change in $y$ due to infinitesimal changes in $x$ as a proportion of its level. Therefore the accuracy of the approximation
$$\beta_1 = \frac{\partial y / \partial x}{y} \approx \frac{\Delta y / \Delta x }{y}$$
$$\implies \Delta x = 1: \beta_1 \approx \frac{\Delta y  }{y}$$
is nothing else than the general approximation inaccuracy issue that arises when we replace a derivative (infinitesimal change) with a disrete-interval proportional change.
In the specific case we have
$$y(x+1) - y (x) = \exp\{ \beta_0 + \beta_1 x + \beta_1 +u\} - \exp\{ \beta_0 + \beta_1 x + u\}$$
$$ = y(x)\cdot (e^{\beta_1 -1}) \implies \frac{\Delta y(x+1)}{y(x)} = (e^{\beta_1} -1).$$
We get

and we verify the folk wisdom that the approximation is accurate enough for purpose of economic analysis if $\beta_1 \in [-0.1,\; 0.1]$, and maybe for a larger interval, if one percentage point is not critical for the purposes of the specific research.


advanced mathematical treatement of revealed preference and utility theory? I am looking for a textbook that treats revealed preference and utility theory much more thoroughly than does Mas-Collel.

What would be suggestions for this? Specifically I'm interested in conditions under which utility functions are characterized uniquely up to monotonic or linear transformations.

Here is a good, thorough book on revealed preference theory. I copied the bibliographic information from my Kindle copy.
Title: Revealed preference theory / Christopher P. Chambers, Federico Echenique. Description: New York : Cambridge University Press, [2016]

Chambers, Christopher P.; Echenique, Federico. Revealed Preference Theory (Econometric Society Monographs) . Cambridge University Press. Kindle Edition.

There is also the 1988 classic by David M. Kreps, Notes on the Theory of Choice (Westview publishers) and the 2013 Microeconomic Foundations I, also by Kreps (Princeton University Press) has quite a thorough discussion.


What's the opposite of a Pareto improvement called? Wikipedia defines a Pareto Improvement, "given a certain initial allocation of goods among a set of individuals" as:

  a change to a different allocation that makes at least one individual or preference criterion better off without making any other individual or preference criterion worse off

Given this definition, then, the opposite of a Pareto Improvement should be:

  a change to a different allocation that makes at least one individual or preference criterion worse off without making any other individual or preference criterion better off.

What's the correct way to refer to this? Does it have a name?

I usually use the phrase "Pareto worsening". It is not really widespread, in fact I am not sure I have ever heard anyone else use it. However now I googled it and people seem to use it in connection with Hart's 1975 paper wherein he shows that the opening of some new markets can make every agent worse off. Hart himself did not call this Pareto worsening, but other scholars do. An example is on page 230 of volume II of General Equilibrium, Growth, and Trade. Here is the same phrase used in Information and Securities: A Note on Pareto Dominance and the Second Best.


How can people save in a equilibrium economy? Two people on a desert island:

John produces 100kg potatoes and sells them to Paul for \$100. Paul catches 100kg fish and sells it to John for \$100. GDP is \$200\$, right?
Next year, they improve their techniques and produce 150kg of potatoes and fish, respectively.
Now, John would love to sell 150kg potatoes to Paul for \$150 and buy only 100kg of fish for \$100, so he can save apart \$50. Unfortunately, Paul has the same wish!
It seems there is no way they can both save. If both transact \$100, the GDP will be like last year. If both transact \$150 the GDP will be \$300.
In both cases, the economy is at equilibrium. It can grow or stay the same. But no saving is possible!
It seems that, in order for John to save \$50, Paul must consume more than his income (or the other way around).

How then is saving in the real economy possible?

Is it a zero sum game, that is, for every John saving, there must be a Paul that consumes more than he can afford?

The question is belied by some basic misconceptions. Just to list a few:

The comparison of GDP in nominal terms and implied statements about growth.
The definition/measurement of GDP (where saving is apparently not part of GDP).
The (completely) arbitrary prices of goods being prescribed for this economy.
The meaning of equilibrium.

  John produces 100kg potatoes...Paul
  catches 100kg fish...
  Next year, they improve their techniques and produce 150kg of potatoes
  and fish, respectively.

In this example, there is real GDP growth, due to technological innovation.
There are more goods in the economy---more potatoes and more fish. Therefore GDP increases.
This has nothing to do with trade between John and Paul or whether money (some medium of exchange called $---e.g. rocks) is being used to intermediate trade in this economy.

Macroeconomic growth is measured in real terms, not nominal terms.

As already pointed out by other answers, saving in the macroeconomy is simply output that is not consumed. If John and Paul barter (no money) and at the end consume 100kg fish and 80kg potatoes between the two of them, then aggregate saving is 20kg potatoes. That 20kg potatoes is still part of GDP.

(The money you put in your savings account is part of your country's GDP.)

Next, consider the proposed scenario:

  Now, John would love to sell 150kg potatoes to Paul for \$150 and buy
  only 100kg of fish for \$100, so he can save apart \$50. Unfortunately,
  Paul has the same wish!

Ok, suppose money, say rocks, is being used in this economy.
(The answer by @1muflon1 touches upon monetary policy by a monetary authority---e.g. there is a central bank on this island that sets the interest rate.)

Where do these prices ( \$1/kg for potatoes and fish) and the demand for saving \$50 you assume come from?

Suppose for the moment there's no saving technology---e.g. John cannot put his money under his bed.
If price of potatoes and fish are $\$P_p$ and $\$P_f$ per kg.
Then John has $ \$150 P_p $ and based on this budget he would choose some quantity
$Q_p$ and $Q_f$ of potatoes and fish so that his budget balances:
$$
Q_p P_p + Q_f P_f = 150 P_p.
$$
Same goes for Paul.

The prices $P_p$ and $P_f$ that actually realize in the economy are such that the potato and fish markets clear, i.e. total amount of potatoes demanded equal to total supply 100 kg, same for fish.

If at price $\$ P_p'$ per kg, John and Paul are willing to purchase only 90 kg of potatoes between them, then $\$ P_p'$ is too high a price, and in equilibrium you would never see potatoes priced at $\$ P_p'$ per kg.

Now suppose there is a saving technology---e.g. John can put money under his bed to spend next year.

Saving means shifting consumption from today to tomorrow. The amount John chooses to save depends on what \$1 represents in real terms tomorrow, which in turn is determined by price. John wants to save \$X today because \$X will buy him certain amount of potatoes and fish tomorrow.

If, at the prevailing price \$1/kg for potato and fish, John would choose to save
\$50, this means John would optimally like to have 50kg of, say, potatoes tomorrow.

However, if there are excess supply of potatoes and fish at the prevailing price of \$1/kg (as in the proposed scenario), prices will decrease, in order to clear the market. As today's potato and fish prices decrease, it becomes more attractive for John to consume today rather than save.
Or the lower prices today leads him to expect lower prices tomorrow and thus he would need to save less \$. His optimal saving choice would change accordingly.

Therefore the above scenario would not occur in this economy:

  Now, John would love to sell 150kg potatoes to Paul for \$150 and buy
  only 100kg of fish for \$100, so he can save apart $50. Unfortunately,
  Paul has the same wish!

If saving $50 by John is infeasible in this economy, then it cannot be an optimal saving choice for John.
In equilibrium, prices equilibriate so that optimal choices of economic agents are jointly feasible.

  In both cases, the economy is at equilibrium.

No, what "equilibrium"?

  How then is saving in the real economy possible?

It should be clear that this question is based on several strands of incorrect reasoning.

  Is it a zero sum game, that is, for every John saving, there must be a
  Paul that consumes more than he can afford?

As pointed out by @1muflon1, there are certain macroeconomic scenarios where saving becomes something like a zero-sum game. Not in the sense you describe, but in the sense that saving by one agent translates to loss of potential wealth for another agent.

Suppose there's a central bank on the island that sets interest rate on saving. The raising and lowering of interest rate would influence John's (and Paul's) consumption/saving decision. Lowering interest rate induces John to consume more today, which increases his demand for fish, which increases price of fish, therefore more wealth for Paul. Vice versa. This is a simplistic version of the central bank lowering rates to stimulate the economy/generate inflation.

However, if rates are sufficiently low ("zero lower bound", as you can find in macro texts), John and Paul might prefer to hoard cash, i.e. liquidity, rather than spend.
This is the Keynesian liquidity trap where monetary policy becomes ineffective and there is excessive saving.

(The liquidity-hoarding instead of spending on fish/potatoes story is awkward for two people on an island. In the actual macroeconomy, people hoard liquidity because return on bonds, which are less liquid than cash, is less than the liquidity premium.)


Independence of price and wealth in Walras' Law The following theorem from Mas-Collel, Whinston and Green's Microeconomic Theory (3rd Edition) assumes $\frac {\partial {w}}{\partial {p}}$ to be zero. I would to like to know the reason behind such assumption.

Notation:

$p$ = price

$w$ = wealth

$x$ = Walrasian demand function

$D$ = derivative matrix

The answer is that $w$, like $p$, is treated as a parameter in this model. It can only be changed by exogenous external forces that are not part of the mechanism included in the model. In contrast, the demand $a$ is a variable that is entirely determined (endogenously) within the model given the prevailing values of the parameters.

Suppose that $p\cdot a=w$. You are correct to think that if we increase the price, $p$, then we break the budget constraint ($p\cdot a> w$). Within the scope of this particular model, only $a$ is variable and therefore the budget constraint must be restored to equality by a decrease in (some elements of) $a$.

Now, the question why is it so is somewhat philosophical because one could, indeed, build an alternative model that includes some mechanism for determining $w$. For example, we could allow consumers not only to buy goods, but also to supply labour and to negotiate wage rates with their employer. Such models exist within the domain of general equilibrium (a basic treatment of which can also be found in your copy of Mas Collel et al.).

However, there are at least a few reasons to think that the model in question is interesting and relevant despite providing no explanation for the determination of $w$:

Incomes might change in response to the overall price level (i.e. in an inflationary environment salaries are likely to increase). But they are much less likely to change in response to isolated or temporary changes in relative price. For example, the price of fruits changes on an regular cycle depending on when and where they are in season. It would be odd to think that people's income changes in response to this cyclic behaviour. But it would also be odd to think that people's consumption plans did not respond to these price changes. this model allows us to study how people vary demand in the face of such isolated price fluctuations.
At least in the short-run, most consumers are much more able to change their consumption decisions (i.e. to vary $a$) than to change their income. Affecting the latter will often require negotiations, change of job, or even retraining—all of which take time. Thus, the model is likely to be informative about the immediate and short-run effects of a price change. In the data, consumption usually reacts relatively quickly to the economic cycle, whereas wages tend to be "sticky".
In modelling we face a constant trade-off between building a model that is realistic and building one that is tractable/parsimonious. The simple consumer demand model has the virtue of yielding a striking number of sensible predictions from a model that is comparatively straightforward. This has various payoffs (easier to communicate to policy makers, easier to use for empirical work, easier to teach to students, easier to use as the foundation for more applied modelling, etc.)
There are many mechanisms by which $w$ could be determined. For example, it could be union-firm bargaining. Or perhaps firms have all the bargaining power and workers are paid only their marginal product. Or perhaps the consumers are entrepreneurs whose income comes from profits/investments rather than labour. Each alternative would require a different model, whereas this model is agnostic on these points and allows us to focus on another dimension of the problem.


Why does Mascolell define second-order stochastic dominance as such? Is not Mascolell's definition in his microeconomic theory of the second-order stochastic dominance narrower? He defines for distribution functions with the same mean only. Although he gives some motivation for doing this, somehow I do not get his motivation.

The motivation is I believe clearly stated in p. 197 beginning of the section, where they write that they want to use Second-order stochastic dominance to reflect comparisons related to "riskiness/dispersion".

To make this prominent, they use distributions with the same mean, so that it is obvious that we compare them not w.r.t their means, but w.r.t. riskiness/dispersion. In fact, the authors use the concept as equivalent to the stochastic dominance over mean-preserving spreads (see proposition 6.D.2 p. 199).

Using the general definition (which is defined by what they provide as property 6.D.2 p. 198) would not have offered them something more, in view of the reasons they want to use the concept.


Why didn't other oil pricing benchmarks such as Brent go negative? This question is asking why the oil (in this case, WTI) price is  negative.

While I think I have broadly understood why WTI collapsed, I don't really understand why other oil pricing benchmarks didn't suffer the same fate. Brent oil, for example, to take the most famous one, suffered losses but was still around $20 per barrel.

What explains the fact that WTI and Brent acted in such different ways?
Is it that that Brent can be better stored? Transported? Refined?
Are the shut-in clauses or future contracts different?

What major factors explain why WTI went negative, while Brent did not?

The Brent price is for oil physically delivered in the UK. The price that went negative if for oil delivered in West Texas, US. The physical and economic conditions at the two places are different - volume available, flexibility of that volume, demand, storage, and so on. This leads to different prices.


Multidimensional product differentiation and density functions I’m having trouble with a model (link) I’m working on for a review.
The author uses a two firms hotelling model with a multidimensional product space (x,y)with orthogonal characteristics, which are uniformly distributed over the unit square. Preferences are standard:
$$ U_i = V - p_i -t |x-x_i| - t |y-y_i| $$
I understand the mechanics of the model (find indifferent consumer, derive demand, find profits, best response, and eq.), but I have a problem with the math behind some profit functions and consumer surplus functions. In particular, the integrals over the densities and cdf really bug me.
In the proof (eq. 31) the author finds the  demand in the case when $p_1 > p_2$ through an integral like the following:
$$ D_1 = \int_0^\hat{x} F(y \leq \tilde y(x)) f(x) dx$$
$\hat{x}$ is the intercept of the locus of indifferent consumers. $\tilde{y}$ is firm 1’s marginal consumer. F() should be the CDF and f(x) the marginal density. My understanding is that $$F(y \leq \tilde y(x)) = \int_0^{\tilde{y}} f(y) dy = y ]_0^\tilde{y} $$
Is this correct?
Then, I don’t understand what $f(x)$ is... given that x is the standard uniform, shouldn’t this be just 1 that after integration would become $x]_0^\hat{x}$?
Sorry, it’s very late and my brain is out of energy. I have to ask since I am very far from my comfort zone... hoping that you could help a bit.

Probably, the author probably is assuming $x_i$ and $y_i$ are independent in addition to the stated assumption on pg. 7 that types "are orthogonal" (which merely means uncorrelated.) (However, since they are also uniformly distributed, we have, $f_{X,Y}(x,y)=f_X(x)f_Y(y)\equiv 1, \forall x,y$, meaning they are independent.)
Assuming independence,
$$
\iint_{\{(x,y):0\le y\le \tilde y(x),0\le x\le 1\}} f_{X,Y}(x,y)\,dydx = \int_0^1 f_X(x)\left[\int_0^{\tilde y(x)} f_Y(y)\,dy\right]dx.
$$


Prediction market based on LMSR: Sell, or buy other side? Consider a prediction market with two outcomes (Yes and No) and a scoring rule based on Hansons’s LMSR, i.e. ln(ea+eb), where a and b are the number of Yes resp. No shares sold.

Assume that I have previously bought 10 Yes shares, but now I changed my mind and want to bet on the other side. I have the option to either sell my 10 yes shares, or buy 10 no shares.

When should I choose one or the other option? Is it always the same, or does it depend on, say, the current market?

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

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


Are Terms of Trade reciprocal? I am trying to learn the meaning of Terms of Trade, but I'm confused.
From the wikipedia article, it says that TOT is the ratio of the value of exports over imports,
and since for the other country these are reversed the TOT of the other country is the inverse,
but I don't understand how that works.

Suppose country X with currency symbol \$ trades with country Y with currency symbol ¥.
(I am using an exchange rate of \$1 = ¥5, but it is not relevant.)

We consider two commodities, A and B.  Companies buy inputs and sell output either buying wholesale and selling retail,
or buying inputs to industry and selling the product of that industry.

Input A can be bought in Y at ¥10.  Since in X it costs \$2.20 to buy it, company XA buys 3 million units from the market in Y.
Conversely B can be bought in X at $2, but it costs ¥12 in Y, so company YB buys 3 million units from the market in X.

Since country X exports 3M units of A, which in X are valued at \$2.20, the value of its exports is \$6.6M.
Since it imports 3M units of B valued at \$2, the value of its imports is $6M and 1.1 is its TOT.

Country Y exports 3M units of B valued at ¥12, imports 3M units of A valued at ¥10 for 1.2 as its TOT.

I don't understand why TOT should be reciprocal when they are 1.1 and 1.2.

EDIT: Maybe I am doing it wrong.  What is the meaning of "value" as in the value of exports and value of imports.  I assumed it is the cost if someone bought it locally.

Terms of trade is a measure of relative prices, and prices only. There are no quantities involved. As a recent review paper puts it:

"with exceptions that I will note below, most trade economists have defined a country’s terms of trade as the price of its exports divided by the price of
its imports, $p_X/p_M$" (p.2).

Therefore, by definition, in a two country model, they are reciprocal. In a model with more countries, there can be differences, as some countries could import or export different goods.

Actually, I don't know which Wikipedia you are looking at, but in the English version, the first line states:

"Terms of trade (TOT) refers to the relative price of exports in terms of imports and is defined as the ratio of export prices to import prices."

For future reference, Wikipedia is an unreliable source. If you are in an educational institution, it is likely you have access to the New Palgrave Dictionary of Economics (the terms of trade article is here). If not, you can google "terms of trade pdf" and hopefully get the slides of a generous professor who is sharing his/her knowledge with the world.


Given fractional banking and the multiplier effect, for every dollar in circulation, how many dollars in spendable money exist? The fractional banking system, in a nutshell, allows banks to invest the money deposited in them, and then for whoever ends up with that invested money to deposit the money back into the bank, which can then reinvest it and so on. For example, let's say Mike puts \$1000 into a bank. The bank might invest \$800 of those dollars into a factory, which then pays the \$800 to its workers that themselves deposit their \$800 into the bank. So while Mike's bank account balance still reads \$1000, the workers' bank accounts include \$800 of those same dollars that have been paid out on loan from the bank, meaning the bank has effectively turned Mike's \$1000 into \$1800, and can loan out that same \$800 to triple dip, quadruple dip, and so on ad infinitum.

In practice, in the world and the United States, how many spendable dollars are created for each actual dollar in circulation, M0 to M1?

The initial statements about fractional reserve banking are not a question. The simplified example you give does not reflect the complexity of bank lending. The article "Money Creation in the Modern Economy," by Michael McLeay, Amar Radia and Ryland Thomas of the Bank of England link to paper is one place to start to get a more realistic discussion of money creation.

  In practice, in the world and the United States, how many spendable
  dollars are created for each actual dollar in circulation, M0 to M1?

For the United States, these data are available at FRED, a service run by the St. Louis Fed. link to FRED

The relationship changes over time; the policy of quantitative easing greatly affected money supply numbers, and the relationship between them.

If you are interested in multiple countries, you will probably need to track down data from central banks or statistical agencies, or you may be able to find an aggregate source. I am unaware of any free data suppliers that cover money supply data.


Econometrics: Is elasticity meaningful in my, or any, regression? A few months ago I interned at this organization; and, as a going away present, I decided to spend my last week, with whatever off time I had, to investigate the factors that affect teacher salaries. One problem that I ran into with teacher salaries was that the distribution for the given state was skewed. I had a lot of observations that clung to the lower end of the wage spectrum. I tried resolving this by incorporating a Comparable Wage Index into my dependent variable (teacher wages), but the results I found were completely out of date for the scope of my project. I instead decided to log my dependent variable. This was nice because now my wages had a normal distribution and it just looked perfect in the histogram. When I started testing down, I got to the point where I was left with one last independent variable, property tax returns. The problem with my normative wages was also apparent in my property tax return observations. I had a huge skew of property tax return numbers towards the lower end of the spectrum. So, I logged this variable as well and it still passed the null hypothesis test just fine.

I am not sure if this is precisely correct, but by comparing the change of one logged variable to another logged variable gave me the elasticity. Assuming that this is correct, my regression equation (something like LogWages = B0 + B1(LogPropertyTaxReturns)) shows the elasticity between the two variables. Is this meaningful though? If my goal was to see which variable most affected teacher salaries in any given county of my state, then is showing the elasticity between the two variables helpful? We want to raise the counties with the lowest teacher salaries up higher to increase their living standards, but I fear that I've extrapolated so far away from the real observations that my concluding regression equation is meaningless.

Edit: One of my bigger fears is that I should have used a non-linear model to show the relationship. I feel that forcing both the dependent and independent variable to cooperate in a this linear regression is misleading in some way.

The answer to the question is yes, it is indeed meaningful (at least mathematically speaking). If you estimate the linear equation

$$ W = \beta_0 + \beta_1 PTR, $$

then $\beta_1=\frac{\partial W }{\partial PTR}$, meaning that $\beta_1$ represents the marginal change of $PTR$ over $W$. Now, if you estimate

$$ log(W) = \beta_0 + \beta_1 log(PTR), $$

then $\beta_1=\frac{\partial W}{\partial PTR}\cdot\frac{PTR}{W}$, which is the very definition of elasticity.

Generally speaking, linear transformations only affect the interpretation given to the coefficients, but the validity of the regression itself (in broad economic terms) is given by the model's assumptions and the economic phenomena being analyzed.