Monopoly: Demand Curve and Marginal Revenue Curve Intercepts I'm doing an introductory economics course, having never done economics before. In our topics, we covered monopoly and the principle that the marginal revenue slope is twice that of the demand slope. I have also seen it stated elsewhere that the y-intercept of the two is also the same. However, if I calculate the marginal revenue equation and if I graph it, I get a different y-intercept to that of the demand slope (see below). As a result, I am always 0.5 units away from the given solution.
If the demand equation is as follows: $P = k + aQ$, then $MR = Q\times(k+aQ) - (Q-1)(k+a(Q-1))$. This simplifies to $MR = (k-a) + 2aQ$. (Note, a is normally negative, so $-a$ would essentially be adding to $k$).
Can anyone explain to me what I'm doing wrong?
The demand curve of one example was given as: $P = 120 - 2Q$
Here are my calculations:
$MR = Q \times (120 - 2Q) - (Q - 1) \times (120 - 2(Q - 1))$
$MR = 120 Q - 2Q^2 - (Q - 1) \times (122 - 2Q)$
$MR = 120Q - 2Q^2 - (122Q - 2Q^2 - 122 + 2Q)$
$MR = 120Q - 2Q^2 - 124Q + 2Q^2 + 122$
$MR = 122 - 4Q$

Your marginal revenue is not calculated correctly. Marginal revenue $(MR)$ is the derivate of total revenue which is equal price times quantity $TR=PQ$.
In your case $TR$ should be:
$$TR=(k+aQ)Q \implies MR = \frac{dTR}{dQ} = k+2aQ$$
If the demand is given as: $P = 120−2Q$ then:
$$TR= (120-2Q)Q \implies MR = \frac{dTR}{dQ} = 120-4Q $$
Also made a graph for you by simulating the $MR$ (red) and demand (blue) in R


Contribution by each factor Must admit it has been many years since I have done advanced calculations or anything remotely like it, so please bear with me.
I have problem that I hope to get some help with. Say I have below dataset:

|   Quarter |   Exposure |   Loss Given   |   Probability of  |   Estimated Loss  |
|           |            |   Default (%)  |   Default (%)     |                   |
|-----------|------------|----------------|-------------------|-------------------|
|       Q1  |   100,000  |          3.0%  |             5.0%  |            150.0  |
|       Q2  |   150,000  |          2.8%  |             5.5%  |            231.0  |

Where Estimated Loss = Exposure x Loss Given Default x Probability of Default.

My problem now is, I would like to be able to explain the difference between Estimated Loss in Q2 and Q1, by explaining how much of the delta is due to the change in each parameter, or how much each parameter contributes of the change - if that makes sense?

Ideally I would like to be able to say something like below:

231 - 150 = 81, of which:
+76 due to increase in Exposure
-10 due to decrease in Loss Given Default
+15 due to increase in Probability of Default

The reason behind showing it like this, is to make it more "understandable" for the reader who is not aware of the mechanics behind the numbers.

My initial thinking was to see what effect it had on Estimated Loss by changing only one parameter at a time; but I will miss some multiplier-effect, since the parameters are not independent.

Also if done this way - the order of how I show the change affects the outcome. Say I first change Exposure and see the result, next up LGD and lastly PD - then, because they are dependent, the effect is larger in PD than in Exposure - and other way around if I change the order. That was when I realised that I should probably have brushed up on my math skills.

1) Would it even be possible/make sense to explain the delta as above, where it can be determined how much each paramter contributes of the delta?

2) If it is possible; I assume that I need to do some sort of Partial Differential equation?

Thanks for you help :-)

The easiest consistent explanation is using multiplication: The Q2 estimated loss of $231$ is $\frac{231}{150}=1.54$ times the Q1 estimated loss of $150$.  This is a combination of

The exposure being $1.5$ times the previous figure
The loss given default being about $0.933$ times the previous figure
The probability of default being $1.1$ times the previous figure

and this is consistent with $1.5\times 0.933 \times 1.1 \approx 1.54$ - it does not matter which order you do the multiplication

It is not that far away from saying $50\% -6.7\% + 10\%$ is about $54\%$, except that that is not precise (they actually add up to $53.3\%$ and other examples could be worse) but this would be talking about percentage changes in percentages, which is often confusing

If you looked at the effect on the old estimated loss of $150$ of each change if the others had not changed, you would have got $+75$ (not $+76$), $-10$, $+15$ which add up to $+80$ rather than the actual $+81$, and other examples could be worse


Is there a term for the indirect sponsorship of large corporates by the state? For example, unemployment welfare payments could be argued to be ameliorating the negative externalities of large corporates hiring newly arrived unskilled migrants.

Is there a term that covers this?

In European Union's nomenclature this is called 'State aid' (see glossary on EU's legislation site for a quick summary).
The idea behind this term is to cover all direct and indirect aid, including economic policy. If the measure is selective and it distorts the competition, it constitutes 'incompatible State aid'.

Besides the EU, I think the word you are looking for is 'subsidy', which covers both direct and indirect aid, or more generally, 'aid measure'.

Hope this helps, if still relevant to you :)


What are the consequences of government spending by imposing tax? The question is "If the government of country Z increases spending by \$12 million dollars and raises tax collections by the same amount, then what will be the overall impact of theses moves on real GDP in country Z." The official solution is that real GDP will increase by \$12 million because it is a balanced budget move.

However, I think it depends. Increased tax collection will discourage production while the spending would encourage production. Any suggestions will be appreciated.

Your professor want probably that you compute the keynesian multiplicator (hint: once you have the general formula, replace dT by dG and see what you get).

Intuition: if you raise G, you will raise your GDP. As Y increases, your consumption increases. But the taxes (T, lump sum) increase also, so the consumption decreases (it depends of the disposable income). The overall effect is a 1 to 1 increase of your GDP.


Pro and cons to finding coal I found some Anthracite coal. I know a coal bed of this quality is worth money? I also know that there is a "no pun intended" carbon foot print if I decide to share my findings to others.

Economics wise would the coal be worth more now or 20 years from now at our current consumption?

I could not find a SE for Ethics, but I wander is this something I should buy and sit one for environmental sake?

It's highly likely that the coal will be pretty much worthless in 20 years from now.

That's because we've got far more fossil fuels than we can burn safely: the negative externalities far exceed the consumer's private benefit.

The world is on the edge of rejecting coal forever. Several countries have already done so, and that number is growing steadily.


Is it considered acceptable or unacceptable to use currency as a measure of utility? There will always exist at least one economist who condones measuring utility in US dollars and another who does not. However, I am wondering which way the majority of contemporary economists lean.
Would it be safe to say that at least 75% of author of academic papers published between the years 2000 and 2020 measured utility in terms of US dollars? Is it standard practice, or not standard practice?
I took many economic courses in college, but I have no idea what is done in contemporary economics research.

One potential drawback to approximating utility with currency is that currency is associated with diminishing marginal utility per unit of currency.
Suppose that Bob is stranded in the desert with two bottles of water.
Sarah is stranded in a similar desert with six bottles of water.
If all other contributing factors are the same, then it hurts Bob more to lose one bottle of water than it hurts Sarah to lose one bottle of water.
If someone who made 10,000 USD last year earns 9,000 USD this year, their decrease in personal happiness (utility) might be greater than if someone who made 101,000 USD last year year earns 100,000 USD this year.

Statistically speaking, in the United States, wealthy parents tend to spend more hours playing with their children than poor parents. I once read an economics textbook where the author expressed incredulity as to why that might be.
If you make 300 USD per hour as an attorney at law, the opportunity cost of spending 4 hours with your kid(s) is 1,200 USD.
If a poor person spends the same amount of time with their children, then the opportunity cost might be $40 in forgone wages.
The opportunity cost, in US currency, of a wealthy parent spending time with their children is greater for the wealthy parent than for a poor parent. The author of the textbook went as far as to deem the phenomenon "a paradox."
The solution is simple to me: The poor person would lose more utility, yet less money. The wealthy person would give up a great deal of money, but very little utility, to play with their children  for 4 hours.
If a wealthy attorney plays with their kids one more day per week on average, then the family might own 3 cars instead of 4. However, if the poor American parent plays with their kids one more day per week on average, then family might forgo new shoes for the children and the family might eat soup made from water and stolen ketchup packets every Friday. Having 3 cars instead of 4 cars hurts less, relatively speaking, than having uncomfortable shoes and eating badly. The poor person stands to lose quite a lot of utility when small financial losses occur. The wealthy individual loses very little utility when small financial losses occur.
Is currency is a poor quality measure of utility/happiness?

Utility functions as ordinarily used are not a measure of well-being comparable among people, but a representation of preferences. Moreover, preferences could principally be elicited from choice experiments.
A utility function assigns real numbers to alternatives so that one alternative is preferred to the other if and only if it is assigned a higher number.
Now in many situations, one can use so-called "money metric utility functions." Start by holding prices fixed (this should already tell you a fundamental limitation of the idea.) For each commodity bundle $x$, let $u(x)$ be the price of the cheapest commodity bundle at least as good as $x$ according to the preferences. Under some assumptions, this gives you a genuine utility function $u$ representing preferences and it gives you actual dollar values. But the natural interpretation depends crucially on prices being fixed.


Capital stock depreciation rate, how to calculate? I am trying to work out the depreciation rate using the following information, it is an extract from a longer data set on capital stock:

Just wanted to find out what the rate of depreciation is for 2000. I used $K_t=K_{t-1}+I-\delta K_{t-1}$ to calculate the rate of depreciation $\delta$ but I am not satisfied with the result. Any help is appreciated! Note, this is not a homework.

Rate of depreciation  = depreciation/gross stock in the current year. So 1.7%. Strictly speaking there is no way to calculate depreciation because the timing of capital formation is unknown, but capital begins depreciating as soon as it is formed.


How to prove that a function is a positive montone transformation Consider the utility function

$$
U(x_1,x_2) = x_1^\alpha x_2^\beta
$$
for $0 < \alpha, \beta < 1$. How do I then show that
$$
V(x_1,x_2) = F(U(x_1,x_2)) = \frac{\alpha}{\beta} \ln(x_1) + \ln(x_2)
$$
is a positive, monotone transformation of $U(x_1,x_2)$. I thought about showing that MRS for both functions is the same. Is this approach alright? I also thought about taking $\ln(x)$ on $U(x_1,x_2)$ and see what happens:

$$\ln(x_1^\alpha x_2^\beta) = a \ln(x_1) + \beta \ln(x_2)$$
but I am not sure here if I am allowed to divide with $\frac{1}{\beta}$ now to get the desired result?

Thanks for your help in advance.

Other people have already hinted at the correct answer. Here is a complete justification:

Note that $V(x,y) = g(U(x,y))$ where $g$ is the function defined by $$g(u) = \dfrac{1}{\beta} \cdot \log(u).$$ Assuming that only positve levels of consumption are allowed (otherwise $V$ is not well defined), $g$ is continuously differentiable on the image of $U$ and satisfies
$$
g'(u) = \dfrac{1}{\beta u} > 0
$$
Therefore, $g$ is a monotone transformation. $\blacksquare$


What does it mean to say that deficits are financed by debt issue? Let $B_t$ be real net government debt, let $G_t$ be public spending, let $T$ be net tax revenue (i.e, tax income minus transfers), and ignore everything else. One can show, $$B_{t+1} = (1+r)B_t + G - T$$

If I say that deficits are financed by debt issuance, what does this mean? How would I represent that in the formula?

Your formula can be simply reaaranged to

$$(G+rB_t)-T=B_{t+1}-B_t.$$

The left-hand side of this equation is the deficit (the difference between public spending—including the spending needed to pay interest on existing debt—and public revenue from taxation). The right-hand side is the amount of new debt issued. Thus, this equation tells you that you must issue enough new debt to pay the deficit—in other words, deficits are financed by debt issuance.


Basic question on S=I Consider the identity:
$$
Y=C+I+G+X-M
$$
 where $Y$ is defined either as value-added output, or income, or
total expenditure. Now, consider private individuals, who decide to
save money, as opposed to spending it. Aggregate demand decreases,
and so output follows, due to the Keyensian cross logic. However,
income that is not consumed, is saved. If savings increase, so does
investment. As such, why is it not the case that if consumption goes
down, investment goes up by the same amount? And if so, aggregate
output should remain unchanged, regardless of the decision of the
consumers after they receive their income?

The reason for that is that if you check carefully the model an important assumption is that investment is fixed $I=\bar{I}$ once you relax this assumption and allow $I$ be some variable function of interest the paradox of thrift disappears in long run.
This does not meant that fixing $I$ in the short run is incorrect assumptions as during recession you will get liquidity trap in a short run. Banks are scared to borrow money because they can’t distinguish good lenders from bad. So in short run all the excess savings during recession get absorbed into banks hoarding liquidity and no matter how much you save $I$ is fixed. Even without recession another way of thinking about it is that in short run it’s hard for companies to change their investment profile.
However, in long run once the $I$ is some variable function of interest rate and of course it has to equal public and private saving  $I=S+ T-G$ the paradox of thrift disappears ($I=S$ only if you assume government runs balanced budget $T=G$ which is fine but I wanted to point out that you should not forget about public saving).
Also I basically took the answer to this one from Blanchard et al. Macroeconomics an European Perspective. If you want to understand this deeper I really recommend checking the book, it’s in my opinion the best undergraduate macro book on the market. If you google hard enough you can even find a free pdf version...


For linear quadratic approximation of RBC model, why does matrix $P$ of value function $V = F^TPF$ has to be negative semi-definite matrix? In http://www.compmacro.com/makoto/note/note_rbc_lq.pdf page 5, it is said that for value function $V = F^TPF$ (Bellman equation) $P$ has to be negative semi-definite matrix. Why does it have to be negative semi-definite?

P being negative semi-definite would imply that V is a concave function. The reason you would restrict P so that V would be a concave function is because of some of the assumptions you've made about about the model previously tell you that V must be concave.

In general, some of the typical assumptions that imply that the value function must be concave are something like the following:

the graph of the constraint correspondence is convex,
the period return function is concave,
other assumptions about the stochastic transition function having the Feller property and being monotone,
etc...

Sorry I'm not giving the full details, but you can read more about them in chapters 4 and 9 of "Recursive Methods in Economic Dynamics" by Stokey, Lucas, and Prescott. The point that I'm making is that the assumptions of these kinds of models usually imply that the value function is concave. Therefore, if you check the assumptions and they indeed do so restrict the value function, then you can restrict your search to look only for matrices P that are negative semi-definite.


Question on returns of scale in isoquants What does the dotted line in the diagram show and what are they called?

I am also wondering why the steepness of the isoquants changes at Q=3 for the third diagram.

Thanks

I've computed this in WolframAlpha and I think it'll help you understand just what exactly a production function is. Remember, the production function $Y=f(K,L)$ is defined by $f:\mathbb{R}^2 \to \mathbb{R}$. When you see a graph with axis in $K$ and $L$, you`re seeing a part of a 3D object, the surface that a function with domain in $\mathbb{R}^2$ generates. The isoquants are just contour lines of it.

The change in the isoquant's steepness is a consequence of the shape a Cobb-Douglas Produtcion Function's surface. The non-linear nature of Cobb-Douglas model makes its contour lines change steepness as $f(K,L)$ gets bigger, as production goes up. There's an interesting economic intuition behind it. The more inputs a firm employs in its production process, the smaller the marginal rate of technical substitution of the optimal plant is because of diminishing marginal returns. As a firm employs more of an input, the smaller is that input`s marginal productvity. As a firms employs more and more of two inputs, capital and labor, both the marginal productivity of capital and labor get smaller, meaning a smaller marginal rate of technical substitution.


How does inflation affect the value of savings? Well, I got basically a question about economics of our world, I hope I'm wrong in my assumptions, because it's pretty ugly and I'm really hope it's more about me being wrong than it's actually the truth. So...:

What does inflation actually means when we talk about savings? For example, If Joe works his ass off and makes some savings in US dollars and puts them in the bank. So say Joe's savings are about \$100,000 and he decides to transfer them to his kid's bank account so when his kid grows up his kid could take the money. But, as I understand it, this \$100,000 won't be the same \$100,000 in about 20 years, when Joe's kid has grown up and wants to take the money. Instead he would get much less than \$100,000, because each year the inflation will eat out by at least 1.5% (avg. for my opinion for Western countries) of this money. Is this really how it is?

I don't know what tags to put, if you may, please help with this too.

It's not so grim: interest rates on savings tend to be higher than inflation, because lenders factor in expected inflation and won't lend unless they're compensated for the risks they face and the fact that they can't use the money in the meantime. So while Joe isn't likely to be lending directly, by saving money in a bank, he's lending money to the bank that the bank will then lend to others, and all Joe needs to do is make sure that his money is in an account that will pay him a decent rate of return (i.e., one that is higher than inflation).

If Joe put \$100,000 in a mattress or in a bank account that pays a 0% rate, then yes, in 20 years if inflation has risen by 1.5% annually, then the money will only be worth about \$74,000 in today's dollars. But if he saves the money in an account that pays a higher interest rate than inflation (or buys a financial instrument like TIPS, a type of government bond that pays an inflation-adjusted return), his kids will have an amount of money equal to more than \$100,000 in today's dollars.

The yield to maturity on a TIPS bond maturing in 2040 is currently about 0.9%, which isn't very high, but that's a nearly risk-free investment that is protected against inflation. If Joe bought one of these, his kids would have about \$100,900 in today's dollars. If he instead took on a certain amount of risk, his kids could have potentially much more.


In the event of a company's bankruptcy, how does a SPV continue operations if it can no longer collect payments on collateral Let's say a company sells car loans (or mortgages or credit cards, I don't think it really matters). The company sells the loans to an SPV, who then issues securities backed by the cash flows the SPV receives from the loan repayments, which, as far as I understand, come through the initial company (as it is the entity that services the car loans and repossesses them in the event that a car purchaser cannot make payments).

If the company goes bankrupt, and must discontinue operations, I understand that the SPV is legally separate, and as such the company's creditors have no claim on the assets held by the SPV.

But how is the SPV going to collect/ repossess the car loans/ cars? It's not set up to do that. Would the SPV not also end up defaulting on its obligations at this point?

Servicing and origination don't have to be done by the same firm. It is quite common that the financing company contracts out the servicing rights on the loans they originate.
Servicers, like many other kinds of firms, can continue to operate after bankruptcy. Bankruptcy is what happens when a firm can't pay its bills which includes debt, it doesn't mean that the firm needs to be liquidated. For example, existing debt holders are not getting paid and sue to put the firm into bankruptcy. The equity holders are wiped out, the debt holders become the new equity holders, and with the reduced debt costs the firm can often cover its costs and be profitable (even though the debt holders took a loss on their investment).
Servicing can be reassigned after servicer bankruptcy. In fact, not only does this happen but it is common for a servicer to change when a loan is sold. So transfer of servicing rights is commonplace.


Existence of Symmetric Pure Strategy Equilibrium I have 2 symmetric players $A$ and $B$.

Each of them has 2 decision variables $x_i\in[0, \beta]$ and $y_i\in[0,1]$, where $i\in\{A,B\}$.

Their payoff functions are symmetric, i.e., if you swap the label $A$ and $B$, you get the other player's payoff function. And the payoff function is continuous in both $x$ and $y$.

My question is: for this type of game, does it always have symmetric pure strategy equilibrium? In general, what are the conditions to guarantee the existence of symmetric pure strategy equilibrium?

There is no guarantee that symmetric games have symmetric equilibria.
See this paper for concrete examples.
There is also no guarantee that symmetric games have pure-strategy equilibria. For example,  the following game is symmetric and has no pure-strategy equilibria
$$
\begin{array}{cccc}
& \mathrm{a} & \mathrm{b} & \mathrm{c}\\
\mathrm{a} & 1,1 & 0,2 & 5,0\\
\mathrm{b} & 2,0 & 3,3 & 0,4\\
\mathrm{c} & 0,5 & 4,0 & 1,1\\
\end{array}
$$
There are two special kinds of games that are known to always have pure strategy equilibria: supermodular games and potential games.


What is the equilibrium price in this case? From the Review Questions to Chapter 1: The Market in Hal Varian's Intermediate Microeconomics with Calculus, 9th ed.:

Suppose that there are 25 people who had a reservation price of $\\\$500$, and the 26th person had a reservation price of $\\\$200$. What would the demand curve look like?
In the above example, what would be the equilibrium price if there were 24 apartments to rent? What if there were 26 apartments to rent? What if there were 25 apartments to rent?

Please note that in this chapter, the supply of apartments is taken to be fixed.
I have drawn the demand curve, and attempted to solve the first two cases in the second question in the following way:
If there are 24 apartments, they go to the 24 people with the highest reservation price. This happens to be $\\\$500$, so that is the equilibrium price in this case.
When there are 26 apartments, we can imagine 25 landlords successfully leasing their property for $\\\$500$, and one landlord who is unable to net the $\\\$500$ lowering his price until he reaches $\\\$200$. This prompts a surge of potential tenants at his doorstep, but the apartment does not necessarily go to the tenant who had a reservation of price of $\\\$200$; it goes to whomever spends most time bargaining with the landlord, has the best connections, etc. Since this apartment generally goes to someone who had a reservation price of $\\\$500$, the new tenant vacates an apartment in her wake, which is then leased for $\\\$200$, and so on until everybody is living in a $\\\$200$ apartment.
The third case is confusing. The answer at the end of the book says that the equilibrium price would be "any price between $\\\$200$ and $\\\$500$" when there are 25 apartments. Why is this true? It seems to me that since the supply of apartments is fixed, the price of one apartment would depend only on the reservation price of tenants. If the equilibrium price is anything lower than $\\\$500$, landlords would have an incentive to arbitrarily increase the rent to the highest the market can absorb, i.e., $\\\$500$. What's keeping the equilibrium price below $\\\$500$?
Please also tell me if my reasoning about the other two cases is flawed, or there are other, better ways to reason about them.

I have quickly skimmed the chapter and there does not seem to be much about bargaining models so as the question says you have to solve this using supply and demand.
We know that an equilibrium price on the market will occur when supply intersect demand. Given that the supply is fixed at $24$ and $25$ apartments respectively it will be just straight vertical line in each case. Now when it comes to demand, if we assume each person wants only one single apartment the demand will be given in step-wise fashion, with two steps given by reservation prices ${\\\$}500$ and ${\\\$}200$ respectively. So this situation will look like shown on the tikz picture I made below (supply is blue, demand is red):

At point where supply is equal to $24$ the equilibrium price given by intersection of supply and demand ($S=D$) is clearly ${\\\$}500$. However, when supply is equal to $25$, supply and demand will intersect at a whole range of different prices $[200,500]$.
Consequently, in this case using this simple supply and demand model we cannot say anything more that price will be something between ${\\\$}200$ and ${\\\$}500$. There are more advanced ways how we could model this situation which might yield unique price instead of range (maybe some models with explicitly modeled bargaining process or some matching models), but here the author of the book gives you hints by asking how demand would look like etc., that you are supposed to use this solution concept (also the first chapter uses only simple supply and demand models so that is another hint).


What determines a new cryptocurrency's initial value? I understand that a cryptocurrency has no intrinisc value, and that therefore its value is determined strictly by market forces, i.e. supply and demand.

I "get" (more or less) that this is how it works for cryptocurrencies that are already "up and running", but what I don't get is how a cryptocurrency's market gets started. I mean, there are over 800 cryptocurrencies already, with a couple dozen pretty well-known, right? So apparently starting one isn't very difficult. But when someone starts a cryptocurrency, how does his first (and his second, third, etc.) "coin" acquire any value in terms of traditional money? I mean, I understand that the first transaction gets the cryptocurrency's "market" going, but that transaction is internal to the currency, right? It does not establish a value relative to a traditional currency.

I also don't get who would enter into that first transaction anyway. If some person tells me "Hey I started a new cryptocurrency, so far I've mined 1 unit of it. Can I use it to buy a can of beer from you?", why would I ever say yes, given that there is no way to determine what is a reasonable "starting value" for his currency?

(I did read up on a bit ICO's, but I don't quite get that either. OK, some "company" proposes to create a bitcurrency, and investors can buy into it prior to its creation. Does that mean they buy a certain number of the yet-to-be-created currency? In that case, again I don't understand what possible basis there could be for assinging a specific value.)

A cryptocurrency's initial value is set at the same way as an established cryptocurrency.

It's the price that people are willing to pay, when they believe the hype told to them by the crypto's promoters.

As such, the price is a measure of the promoters' marketing skills, and the gullibility of the buyers.

I completely understand that you feel it ought to be different. But for an intrinsically worthless thing, what I've written above, applies both to a new crypto and an existing one. It's worthless. Therefore its price is whatever the owner can fool someone into paying for it.

As for what number the promoters actually pick, they will play a guessing game. There's a story about how opticians price the pair of a new glasses. When they tell a new customer the price, they say, it will be £60. And they pause, and watch the customer's reaction. If they don't blink, they add "per lens". Pause, and if no blink again, "and £120 for the frame". If the customer looks scared, they can then add "but with your discount, the frame will be half price".

Pricing worthless assets is similar, but far worse. The seller make a pretty fairy story about the total value of the market, works out how many tokens there will be, throws in a big "get in at the ground floor" discount, and then plucks the asking price out of thin air.


What activity or event(s) marks the point at which an economic "bubble" burst? What general activity or event(s) mark the time at which an economic "bubble" bursts? e.g. the dot-com bubble, etc.

Would it be considered to have "burst" when intrinsic value is less than price?
What about when this drop in intrinsic value might be due to some news event, etc...

Is it simply when prices go down? When speculators exit the market, etc. or is it when "the something" happens that causes the drop in prices or the mass exodus from the market? Or something else altogether?

An economic "bubble" bursts when the buyers in the market deem the good or service to be overpriced.

At a certain point, the price of whatever is causing the bubble will reach a certain "threshold price."

It is at this "threshold price" that the corresponding amount of "threshold buyers" is reached.  These buyers will stop buying (or continue not to buy) the good or service offered.

In an attempt to incentivize the buyers to continue buying their product, the sellers will lower their price.  Of course, certain sellers will lower their prices further to out maneuver each other in order to sell more of their product.  This is the burst.

At this point, some of the buyers will recognize the "burst" of the "bubble market" and will become sellers to move their product.  This, simultaneously, increases the amount of supply and decreases the demand, further lowering price.

This cycle will continue until a new (lower) equilibrium is reached.


Pure-Strategy Bayesian Nash equilibrium with general common prior I'm doing a problem set on the subject of Bayesian Nash equilibrium. I'm asked to find the pure-strategy BNE of the following. I've calculated to matrix shown below. My first concern is if I've calculated the expected payoff matrix correctly, and second how do I find all of the pure-strategy BNE when the common prior is not concrete.

Matrix looks correct. To final all pure strategy BNEs, you'll have to discuss cases based on the value of $p$.
For example, if $p\in(0,1)$, then $FT$ is player 2's unique best response to $F$. Thus, to have a BNE, you'd want $F$ to be player 1's best response to $FT$ as well, meaning that you'd require $3p>1-p$, or $p>\frac14$. Hence, $(F,FT)$ is a BNE if $p\in(\frac14,1)$.
You should be able to find other BNEs following a similar line of reasoning. (Hint: don't forget the edge cases where $p=0$ and $p=1$.)


Is there any statistics available on forecasting failures? Like what percentage of financial/economical forecast fail?
Or how often do politicians create bad policies based on wrong forecasts?

Like what percentage of financial/economical forecast fail?

Well it depends on what you call a forecast.

Considering that there is a large uncountable number of people who are called (or call themselves) financial,economic and policy analysts all over the world who together make what one would think millions of forecasts made everyday, there is probably a number which fail and a number which succeed.

So where are the numbers on it?

I would suspect no general statistic exists because its measurement does not have a practical use from a policy perspective. I say this in the sense, that it is a concern exclusively of private businesses and companies to care how well their forecasts work. providing statistics on their forecasting success would be exclusively for marketing purposes.

  Or how often do politicians create bad policies based on wrong forecasts?

This part of the question I recommend for Politics SE as it is  more political than economic.

Hope this helps


Notation conventions for superscripts and subscripts I want to establish a consistent notation in my work, however, I struggle with the correct notation when more than one condition is present.

First, I am wondering what to put in the superscripts and what in subscripts.

I figured that the following is often in superscripts:

denoting that something is optimal, e.g., $p^*$
describing that something is a special condition, e.g., $p^{\alpha=1}$
denoting critical values, e.g., $b^{crit}$

I figured that the following is often in subscripts:

denoting an individuum, firm, combination, $p_i$, $\pi_j$, $p_{ij}$
numbers of different solutions $c_1$, $c_2$

Some cases were not very consistent

"states" or strategic alternatives are sometimes sub/subscripted, $\pi_M$ and $\pi^M$

So my first question is: Is there a rule, guideline or best practice for what to put where?

Second, I am wondering how to correctly write combinations of different subscripts or superscripts.

As an example, one could take the first derivative of the optimal price. Would that be ${\pi^*}^{'}$  ({\pi^*}^{'}) or is it better to write $\pi^{'*}$ (\pi^{'*}) or $\pi^{*'}$ (\pi^{*'})?
Similarly, how do we combine for example special conditions and optimal values $p^{\alpha=1,*}$ or $p^{*,\alpha=1}$, ${p^{\alpha=1}}^{*}$ or ${p^{*}}^{\alpha=1}$?
Where do we place numbered solutions for specific conditions when both are used in subscripts (e.g., $c_1$ in $\pi_M$)? is it  $c_{1M}$, $c_{M1}$,  $c_{M,1}$,  $c_{1,M}$?

So my second question is: Is there a rule, guideline or best practice of how to combine different subscripts vs. superscripts

This is only partial answer since your question is quite broad but in my work I had similar problems.

When ti comes to optimal values and derivatives I choose to use Leibniz's notation as it does the job quite nicely:

instead of writing this $\pi^{'*}$, I would write this $\frac{\partial \pi^*}{\partial x}$ or if you like it more  $\frac{\partial }{\partial x}(\pi^*)$, sure it takes some time to type out but in my humble opinion it looks quite good. I try to use Leibniz's notation any time there are some other superscripts or subscripts (as with multivariate function even derivatives with subscripts can be problematic).

For conditions consider maybe notation borrowed from statistics so instead of $p^{*,\alpha =1} $ I would use $[p^*|\alpha=1]$

Regarding those numbered solutions, I was once told by older scientist, during my internship at one research institute, that when  you have one letter subscripts you can just put them without comma but if one of the subscripts has multiple letters always put comma so for example $x_{itj}$ is fine but when I need to put $t-1$ I would put it as $x_{ij,t-1}$ (to be honest I have no idea to this day if there could be some issue with this but so far nobody complained - not even at  conferences/workshops where I was presenting my work, nor any referee - although I dont have that many published work yet as I am very young researcher, so maybe take that as a caveat regarding my suggestions).


What percentage of UK imports/exports were with the EU in the economic year 2015-2016? With the referendum over whether or not the UK should leave the EU or not I am interested to know what percentage of UK trade is made up of trade within the EU (Imports & exports).

I am aware that the UK Government currently runs a trade deficit with the EU, and a ultimately a trade deficit in general.

My question is, how much of UK trade is within the EU, and how much of this is imports/exports in the economic year 2015-2016?
An objective link proving this would be excellent.

Apologies for the 'trade deficit with EU' link being far from ideal, but as you can imagine, it is hard to find solid fact among the propaganda.

& To clarify, I do not want people's opinion on whether the UK should remain or not. I am in the process of forming my own opinion based on the objective information I come across.

And as always, thank you to those that take the time to answer!

UK Exports 2015:

  The United Kingdom shipped US$460.1 billion worth of products around the globe in 2015. [...] From a continental perspective, 53.6% of UK exports by value are delivered to European trade partners while 22.5% are sold to Asian importers. United Kingdom ships another 16.1% to North America but just 2.6% to Africa.

While the total value of exports is a useful piece of information, here Europe means the continent, not the EU. Thus Norway, Switzerland and several Balkan countries are also included. It is not clear where Russia would fall under such a categorization so it is better to look at Eurostat's statistics.

In 2015 the UK's intra-EU trade share was lowest among the member states  but it was still 50%.


In the Ricardian model, why are two out of 3 cases invalid? I am considering the Ricardian model.

There is an economy with two countries $S,T$. Two goods $a,b$. Each country has linear production technology with labor ($\ell$) as only factor of production.
$$y_i^j=\alpha_i^j\ell$$
where $i \in \lbrace a,b\rbrace$ and $j \in \lbrace S,T \rbrace$.

$$\ell_S + \ell_T = 1$$

The firm's maximization problem is

$$\max_{\lbrace \ell \rbrace} \pi^j_i = \alpha_i^j\ell p_i-w^j \ell$$

There are 3 cases to this problem

Case 1: $p_i^j \alpha_i^j <w^j$

$\ell = 0$

$y_i^j = 0$

Case 2: $p_i^j \alpha_i^j > w^j$

$\ell = 1$

$y_i^j = \alpha_i^j$

Case 3: $p_i^j \alpha_i^j = w^j$

$\ell \in [0,1]$

$y_i^j = [0,\alpha^j_i]$

My Question

Apparently, cases 1 and 2 aren't valid. I'm not sure why. Can someone explain?

The logic is supposed to be

  "if there is complete specialization then $\ell_S = 1, \ell_T = 0, y_T = 0$ or $L_S = 0, L_T = 1, y_S = 0$, so therefore cases 1 and cases 2 fail"

I just don't understand this explanation at all and would like a better explanation. What does it mean to "specialize completely"?

To "specialize completely" means a country only produces one of the two goods.

Given your firms' (there seem to be four, one for each good in each country) profit maximization problems their optimality conditions are
$$
p_i \cdot \alpha_i^j \leq w^j
$$
with equality if $l_i^j > 0$. From this, you can easily derive what parameter combinations of $p_i$ and $\alpha_i^j$ will result in conditions when a country specializes completely.

I am not sure what you mean by 'fail', and the indices in your workforce notation seem a little off. Perhaps my detailed discussion of the Ricardian model can be of benefit. Beware it is not the exact same model as yours. For example, prices are not given exogenously, but they result from a supply and demand equilibrium.


max{x1,x2} where P1not=p2 I have seen min{x1,x2} functions representing perfect compliments but have never seen a max{x1,x2} function anywhere in my book or lectures, I also have never seen anything about p1 not equaling p2. can anybody give me some insight to this problem.

Consider a consumer with a utility function U = max{x1,x2} the consumer faces prices p1 and p2 for goods 1 and 2, respectively, and has an income of m dollars. (assume throughout p1 dne p2).  His optimal consumption solves the standard problem.

a)Find the optimal levels of consumption for goods 1 and 2 as a function of income and prices.
b) is good 1 a normal good?
c) Are goods 1 and 2 complements or substitutes?
any help would be much appreciated

Here is my suggestion:

I would say the optimal level of consumption is $\frac{m}{p_1}$ if $p_1 < p_2$ and $\frac{m}{p_2}$ if $p_2 < p_1$. So the individual consumes only whichever good is cheaper. Since utility is just the maximum of whichever two amounts you could consume, you would maximize that by consuming the highest amount possible.
Good 1 is a normal good if it is cheaper than Good 2, then the amount consumed rises with income.
I would say these goods are perfect substitutes, since you consume as much of the cheaper good as possible with no further constraints.
EDIT: This wrong, they are not perfect substitutes, since they are not substitutable - if you consume only Good 1, you wouldn't want to exchange any for Good 2, except if you then had more of Good 2 than of Good 1.


Normalise historic values given in different currencies I have historic monetary values given in different currencies and stemming from different points in time. I want to be able to compare them, and for that all must be given in the same currency, and inflation between the points in time must be considered as well. Eventually, all values should be given, for example, in US Dollar 2018.

What is the right way of achieving comparability in the above mentioned way? Does the base currency and the base year impact the method and/or the result, or are those independent of the choice of base currency and base year?

If you have a single country, using the CPI to deflate values does not create a serious issue with the base year. Changing the base just changes the levels of the numbers, but they are are multiplied by the same amount. This means that rankings of prices are the same.

If you convert to a single currency, which one you pick does not matter for ordering the prices. For example, it does not matter whether you choose to convert all prices to Canadian dollars or US dollars, if the price is more expensive in one country in one currency, it will also be more expensive in the other.

This equivalence breaks down when you want to inflation adjust across countries. The choice of the currency for the inflation index affects the comparability. For example, imagine that the exchange rate between two countries in unchanged between two periods, yet the inflation rate is different. The scaling ratio between the two time periods depends on which country’s inflation index you choose. (I don’t think the choice of base year matters other than by applying a scaling factor.)

(If exchange rates followed relative inflation exactly, the country for the inflation index would not matter.)

There are different approaches you could try. I’ve never run into this kind of comparison before, so I have no idea what the accepted practice is. I would look at what you are trying to compare, and see what the best basis of comparison is. One approach is to not use a CPI index, and instead use a particular price to scale quantities, such as an average hourly wage. (This would imply that all prices are converted to the equivalent number of hours of wages that the price represents.) This converts prices to a meaningful unit, and not some arbitrary CPI indexation factor.


Preferences where wealth effect dominates King-Plosser-Rebelo preferences satisfy balanced growth requirements, we have that income and substitution effects of labor cancel. Labor does not respond to a change in the wage level.
Greenwood-Hercowitz-Huffman preferences shut off the wealth channel: There is only a substitution effect left, hence labor co-moves with wages.
Jaimovich-Rebelo create the nested case with a wealth effect within the two aforementioned.

Is there any commonly used preference specification for which the wealth effect dominates the substitution effect, and hence labor supply reduces as a response to an increase in wages?

In open macroeconomic models some cases of logarithmic preferences cause the wealth effect to dominate the intertemporal substitution effect.

If I recall correctly, at least Vegh's book "Open Economy Macroeconomics in Developing Countries" (2013, MIT Press) presents this case.


How to specify a Diff-In-Diff Regression with multiple time periods? I'm working on analysing experimental data for a thesis project. The data consists of subjects performing the same task over five rounds, and I'm interested in the difference in trends between subjects in two different treatments. The two treatments are identical until round 3.

I planned on using a diff-in-diff model to estimate the difference of Effort levels of subjects across these treatments. The problem is, I have five rounds, two of which are before-treatment and three of which are after-treatment. Currently, I'm using this specification, but I'm not sure if it's correct:

$$
Effort_{it}=\beta _{0} + \beta_{1}Treatment_{i}+\sum_{n=2}^{5}\beta _{n}Roundn_t+\beta_6Treatment*After_{it}
$$

Where treatment is a dummy for being in the treatment groub, Roundn is a dummy for being in Round N, and Treatment*After is an interaction dummy for being in the treatment group after round 2 (when the treatment "begins").

I'm confused mostly on what to do with the different time periods. Would it be best to use dummies for each round like above, or to just include a Round variable that is equal to the number of the round. Also should I just include one interaction term, or one for each round?

I am a bit confused because you said there are two treatments. I presume that one "treatment" group is the control group and the other is the treatment group. (I don't think you have a separate control group.) I am also confused because you said the treatment is identical until round 3 but then the treatment begins in round 2. I presume that there is no treatment in rounds 1 and 2, and the treatment group is treated differently thereafter in rounds 3, 4 and 5.

Your $Roundn$ dummy variables for $n=2,\ldots 5$ make sure that you handle the "round effects" (for the control group) properly in a nonparametric way. This looks fine to me. If you include only the $After$ dummy, it means that there is no trend within each of the "before" and "after" periods. You would not want that.

A single $round$ variable means that there is a linear trend in $Effort$ in the control group. You could try that, but I would wonder where the linearity belief comes from. Also, you lose only 3 more degrees of freedom by including the round dummies comparing to the linear trend model. That's not a big deal unless you have a really small sample. I would be happy with the full round dummies.

Your model assumes that the treatment effects (measured by diff-in-diff) are identical in all rounds 3, 4 and 5 (because you have only one interaction term). If you believe it is true, that's fine. If you believe otherwise, you can include three interaction terms $Treatment * Round3$, $Treatment * Round4$ and $Treatment * Round5$ instead of the single interaction term. If you want, you can test if those treatment effects are identical across rounds.


Effect of a subsidy on a monopoly I'm trying to understand how a subsidy on a monopoly would affect the deadweight loss. I know a subsidy shifts the marginal cost curve downwards, creating a new equilibrium price (price decreases) and quantity (quantity increases), but my question is if the deadweight loss is going to be bigger than before the subsidy?

The deadweight loss from the monopoly decreases. This is because the deadweight loss comes from the price being too high (higher than the marginal cost), which leads to not enough goods being consumed in equilibrium. Since the subsidy redices the price, the deadweight loss decreases. The subsidy itself does not increase the deadweight loss, because the only thing it does is reduce the price and there are no other effects. One issue may be that additional deadweight loss is caused by the taxes required to finance the subsidy. If these are lump-sum taxes then they do not affect the deadweight loss as they are non-distortionary and do not affect prices.

In fact it is possible to completely remove the deadweight loss with a subsidy. This requires lump sum taxes to be an available tax instrument, so that raising the money for the subsidy doesn't cause deadweight loss itself. This is an old result that goes back to Robinson (1934). However, although she first noticed the result, she did not advocate that this would be a good policy, unless the subsidy was financed by taxing the monopolist's rents. This is because of concerns such a policy would have on income distribution.


Why don't Burgers cost 5 cents? In this blog post, economist Bob Murphy raises a puzzle involving the principle that in a competitive market, the price equals the marginal cost:

  There’s a general principle from intro to microeconomics that says in
  a competitive industry, in equilibrium P=MC. So how would we actually
  apply that in practice to the fast food industry? At the point at
  which the burgers are already made and sitting on the back warmer,
  what’s the marginal cost to the firm of the worker picking up the
  burger and handing it to a customer? 5 cents? So, in an efficient fast
  food industry, burgers should be priced at 5 cents. Don’t you dare say
  that the firm needs to charge at least enough to cover average costs,
  because (as David points out) that involves a sunk cost fallacy…
  Something is obviously not right in the above. But I’m curious to see
  how you guys would unpack it. If you want to say, “I don’t trust them
  there textbooks with their funny graphs!” OK fine, but ideally I’d
  like you to solve it within the world of standard textbook micro,
  since presumably that can be done.

What he's saying is that once the burger is already made, the cost of making the burger is a sunk cost, and thus the marginal cost of the burger is just the cost of the tiny labor involved in picking it up and selling it to the customer.

So why is it that in the fast food industry, the price of a burger takes into account the cost of making the burger and not just the cost of handing it over to the customer?  Is it because the fast food industry is far away from the conditions of perfect competition, or can this be explained using a perfect competition model?

What he's saying is that once the burger is already made, the cost of making the burger is a sunk cost, and thus the marginal cost of the burger is just the cost of the tiny labor involved in picking it up and selling it to the customer.

That's sort of an odd position to take.

Obviously once the burger is cooked you can't recuperate the costs, but in the aggregate, the decision to cook some number of burgers in such and such a time period is made before actually cooking them. So the cost of making a burger (including labor) isn't a sunk cost; it's a prospective cost.

Additionally, just because the monetary cost of making the burger is the same for each burger doesn't make it a sunk cost, just fixed (perhaps). But more to the point, there's a time cost which varies the more burgers you cook. We pay for convenience. Part of the marginal cost of cooking the burger is the opportunity cost of that time that could be spent not running a nice little fast food restaurant.


Did JP Morgan mitigate the effects of the Great Depression? I had heard that, at the start of the Great Depression, JP Morgan and other bankers attempted to prevent the depression by purchasing some of the overpriced stock.
Did the actions of JP Morgan and the other bankers have any effect on the US economy at the time?  Were the effects of the Great Depression mitigated by their actions?

Not really. While it's possible that the Morgan intervention softened the initial stock market decline, the vast majority of the ultimate collapse in securities prices, commodity prices, industrial production, and the banking sector took place after the purchases had been liquidated.

First some history: the bankers' pool intended to lift the stock market was assembled at the J.P. Morgan & Co. offices on October 24, 1929, "Black Thursday", the initial day of market chaos. They pooled their resources and directed broker Richard Whitney to place high bids on blue chip stocks at the NYSE to lift the confidence of the markets. This stemmed the crash on Thursday and led to a rally that continued the next two days. Indeed, the following Sunday's New York Times lauded the "carefully arranged" plan to boost the market, and mentioned that the inclusion of the First National Bank in the buyers' pool the next day confirmed to Wall Street that "the danger of panic had been averted". Some history of these events is provided in the Wikipedia article on the crash.

Alas, the Monday and Tuesday immediately following this confident appraisal - October 28 and 29, 1929 - are known as Black Monday and Tuesday, respectively. They experienced the second and fourth largest daily percentage DJIA declines in history, combining for easily the largest two-day percentage decline in history. Most newspapers at the time described the bankers' pool as waiting to intervene until late Tuesday, when they cut margin requirements and placed buying orders (see AP article). An AP article describing the crash on Monday opened with "powerful financial interests stepped aside today and let the stock market drop...". Finally, on Wednesday the bankers' pool entered with strong buying orders, leading to the third highest daily percentage DJIA increase in history. The next day the pool apparently stepped away from the markets once more.

It kept going like this for a little while, with some more volatility in markets over the next few weeks but eventual stabilization and partial recovery. Finally, the banking group quietly wrapped up its activities in February 1930, with press accounts mentioning that it "come out about even".

Given all this, it's possible that the bankers' pool offered some initial stabilization of the markets. (Although even that's not clear: from press accounts, it seems just as likely that volatility was increased by the erratic day-to-day decisions of the pool.) But again, any significant effect seems unlikely, because the vast majority of the carnage in the Great Depression took place after the pool had been liquidated in February 1930. To convey some sense of this, the following graph shows (in log points) the fall of the DJIA, industrial production index, and wholesale price index in the US starting in September 1929. As you can see, the initial declines in late 1929 and early 1930 - although substantial - are far smaller than the eventual ones. This is in line with the modern consensus view on the Great Depression, which emphasizes the role of the gold standard and its propagation of adverse monetary and banking shocks, rather than the initial market crash itself.

This is all an interesting contrast with the more famous and successful case of intervention, performed in the Panic of 1907 by J.P. Morgan himself. (The original J.P. Morgan was long dead by 1929, though his eponymous son and firm lived on.) In 1907, Morgan engineered a wide variety of rescue measures, making large deposits in struggling banks and large call loans to brokers. These measures are thought to have helped end the panic.

The key difference, I think, is that the 1907 panic was a fairly conventional acute crisis in the banks and money markets: recent nominal growth and seasonal demand for currency meant that interest rates were already high, and then a run on banks and trust companies led to more hoarding of currency and extremely high interest rates. Extremely expensive margin borrowing led to a collapse in securities prices, which endangered the banks further (they were more exposed to stocks, through various channels, than they are now), leading to more run pressure, and so on. In this environment, where banks and firms were sound - and money markets would loosen - if only the panic would stop, it was possible for a few decisive interventions to swing momentum in the other direction.

The Depression was much different. Thanks to the Federal Reserve, seasonal fluctuations in currency demand and (to an extent) panicked currency hoarding did not lead to a spike in money market rates, which actually fell drastically in late 1929 and 1930 rather than spiking as they did in 1907. Also unlike 1907, the banking crisis did not coincide with the initial stock market collapse - instead, it only started with the Bank of United States failure in December 1930, and in the initial stages was arguably due to fundamental insolvency rather than illiquidity. (Since both nominal real estate prices and food prices collapsed, mortgage default rates - residential, commercial, and farm - were all extremely high.)

Bottom line: the crisis of 1929-33 was different enough from the crisis of 1907 that similar measures no longer worked.


What's the minimum number of datapoints in order to run a diff-in-diff? I was thinking about running a diff-in-diff with fixed effect in order to deal with a panel data experiment. The problem is that I don't know how many datapoints I need in order to the experiment be reliable.
This is the thing: I want to see how my customers react to a change in price. An AB test doesn't look like a good alternative, due to cannibalization. So I would like to change the price of a bundle of products in some cities. Let's say for cities A, B, C and D, cleaning products will be 10% cheaper. Then I would run a diff-in-diff with fixed effects using each city datapoint. The question is: how many cities do I need in order to run this experiment? How many sales each city would have to have in order to the experiment be reliable?

Diff-in-Diff is a parametric model. A rule of thumb for parametric models is that you should have at least 25-30 observations (different authors might disagree but it is around 30) per independent regressor used in your model (see discussion in Verbeek A Guide to Modern Econometrics pp 36). However, note this is a rule of thumb and as Verbeek points out (my comments are in []):

Unfortunately, there is no unambiguous definition of what is ‘sufficiently large’ [talking about sample sizes to justify asymptotic properties]. In
simple circumstances a sample size of 30 may be sufficient, whereas in more complicated or extreme cases a sample of 1000 may still be insufficient for the asymptotic
approximation to be reasonably accurate.

This being said getting precise number for every individual case would be too difficult (it would involve Monte Carlo simulations) so often people  follow the rules of thumb unless they have suspicion something is awry.
Consequently, if you would just follow the rule of thumb in a diff-in-diff model with 5 independent regressors you should have at least 150 observations, in model with 7 independent regressors 210, in model with 10 independent regressors 300 and so on.


Bayesian Correlated Equilibrium in a one player case: relation with literature I am curious about the connection between one-player Bayesian Correlated Equilibrium (hereafter, BCE) introduced by Bergemann and Morris for a generic $n$-player setting with $n\geq 1$ (here)  and the Bayesian persuasion problem in Kamenica and Gentzkow (here) also discussed in Bergemann and Morris more recently (here).

I would like your help to summarise such  relation.

Preliminaries: DM denotes decision maker. $G$ is the basiline choice problem that consists of the DM's prior on the state of the world. $S$ is the information structure that contains the probability distribution of the signal used by the DM to update the prior. $(G,S)$ is the augmented choice problem.

$\underline{S}$ denotes the degenerate information structure, i.e., the information structure that does not convey additional information on the state of the world.

The set of one-player BCE of $G$ consists of the set of probability distributions over actions and states that are consistent with the prior and obedient.

Note that the set of one-player BCE of $G$ is equal to the set of one-player BCE of $(G,\underline{S})$.

This is my  attempt to link the two papers:

Suppose a mediator ("sender" in the Bayesian persuasion language)  could pick the information structure ("experiment" in the Bayesian persuasion language) that the DM ("receiver" in the Bayesian persuasion language) could process.

Kamenica and Gentzkow (here) characterize the set of distributions over actions and states
 that the sender could induce through picking the null experiment (i.e., $\underline{S}$) and having the DM choose
optimally. This set is equal to the set of one-player BCE of $(G,\underline{S})$.

Bergemann and Morris more recently (here) explains that such relation holds for any information structure. In other words, the set of distributions over actions and states
 that the sender could induce through picking ANY experiment $S$ and having the DM choose
optimally  is equal to the set of one-player BCE of $(G,S)$.

Is my connection correct?

There are a few imprecisions in the way you formalize things. For example saying " is the baseline choice problem" does not make a lot of sense, because a problem should include the DM's utility, the available actions, and the belief about the state of the world. You only included the latter.

Regardless of notation, I think that you are missing the key connection between these two papers. Let me summarize what each paper does first and then draw the connection for you.

The concept of BCE characterizes the answer to the following question: If the DM were to observe some signal (informative or not) what are all the actions that would be optimal?
Of course the DM can use mixed strategies, so we talk about distributions over actions. Also, it is clear that depending on what information is contained in the signal, the actions of the receiver can vary. So the set of BCE collects all possible actions for all possible signals. Note that the concept of BCE is agnostic about where this extra information is coming from.

So yes, the distributions of actions that are in the set of BCE are obedient (i.e. optimal given some belief), and the beliefs that rationalize these actions are consistent with the prior (I.e. they are the Bayesian posteriors derived from some signal given the DM's prior).

In contrast, Kamenica and Gentzkow (KG) set up a game where a sender chooses what signal to give a receiver and then the receiver takes an action that affects both players. Kamenica and Gentskow presented the simplest case, where the sender knows the prior of the DM and there is only one sender.

Their approach has some limitations because finding the optimal signal can be complicated; especially if the state space is not binary. In their paper, it is also not clear at all how to solve the problem if the receiver has more information than $\underline S$, or if there is more than one receiver. So yes KG assume that the receiver has some prior information $\underline S$, but in equilibrium the sender usually provides more information, so your statement "Kamenica and Gentzkow (here) characterize the set of distributions over actions and states that the sender could induce through picking the null experiment" is false.

Now, let me try to connect the two papers:

Bergeman and Morris (2019) found that we can drastically simplify the analysis of the game presented by KG if instead of maximizing over signals, we maximize the sender's utility choosing the distribution of actions that can be induced using some signal. They make the connection that if a distribution of actions can be chosen by the sender, it must be because it is optimal for the receiver to choose those action after observing some signal $S\geq\underline S$, i.e. if the distribution over actions is a BCE.

This is nice because the set of BCE's is relatively easy to find and to work with. So the game that KG setup can be dramatically simplified into a game where the sender chooses its favorite BCE.

Once you realize this connection, you can overcome many of the limitations in KG's approach. The concept of BCE can be easily extended to multiple receivers, and even receivers with private information. The authors showcase in their 2019 paper, the power of making this connection, and show how to think formally of receivers with more information than $\underline S$, among other things.


what is the Intuition behind Cholesky identification in VAR/SVAR In my understanding of Cholesky identification, $RF$ in the model below should be ordered last since it is contemporaneously affected by all variables in the model. So why does Leeper EM, Sims CA, Zha T, Hall RE, Bernanke BS (1996) put $RF$ before $MI$? Or maybe order does not matter as long as we can put zero restrictions however we want to ensure exact identification or overidentification? Does order only matter in Cholesky identification without zero restrictions?

The terms "ordered last" or "ordered first" do not necessarily relate to the place of the variable in the $y_t$ vector. Rather they describe the column (row) vector of the contemporaneous impact matrix pertaining to the variable. Once the restrictions have been set and the model is identified, where you exactly place the variables is an uninteresting computational issue that concerns only the implementation of the model in your software package. Here is what I mean in equations.
Let the structural model be: $y_t = c + Ay_{t-1} + Bu_t$
$y_t= \begin{bmatrix}
n_t\\
m_t\\
q_t\\
\end{bmatrix}$
and
$B = \begin{bmatrix}
b_{11} & b_{12} & b_{13}\\
b_{21} & b_{22} & b_{23}\\
b_{31} & b_{32} & b_{33}\\
\end{bmatrix}= \begin{bmatrix}
b_{11} & 0 & 0\\
b_{21} & b_{22} & 0\\
b_{31} & b_{32} & b_{33}\\
\end{bmatrix}$.
That is $B$ coincides with the lower triangular of a Choleski decomposition.
"Ordered first" means variables like $n_t$, that have only zeros in their row vectors where $i \neq j$. "Ordered last" are variables like $q_t$, that have only zeros in their column vectors where $i \neq j$ .
So "ordering a variable first" means assuming that it is not affected by the other variables contemporaneously and "ordering a variable last" means assuming that it does not affect the other variables contemporaneously.
It is not necessary that the model where we order some variable last actually has a lower triangular $B$. Perhaps we want to use partial identification (just like Cristiano, Eichenbaum, Evans (1999)) and we are not interested in the entire $B$.
In the specification you are showing, we wouldn't call any variable "ordered last" or "ordered first".
I once again encourage you to consult
Prof. Ramey's excellent exposition on identification
.
Consider especially Sections 2.3.1. and 2.3.2.
Presenting Blanchard Perotti (2002)  in section 2.3.2 on page 10 she writes:

Let ܻ$Y_1$ be net taxes, ܻ$Y_2$ be government spending, and ܻ$Y_3$ be GDP. They identify the shock  to  government  spending  using  a  Cholesky  decomposition  in  which  government  spending  is ordered first (i.e. ܾ$b_{21} = b_{23} = 0$). They identify exogenous shocks to net taxes by setting ܾ$b_{13}= 2.08$,  an  outside  estimate  of  the  cyclical  sensitivity  of  net  taxes.

The variable that is "ordered first" - government spending is actually the second component of $Y_t$:
$B= \begin{bmatrix}
b_{11} & b_{12} & 2.08\\
0 & b_{22} & 0\\
b_{31} & b_{32} & b_{33}\\
\end{bmatrix}$.


I agree with Herr, the payoff matrix looks right. Also, there are no strictly dominated strategies because a strictly dominated strategy cannot be a best response for any possible belief. However, If any player believes that the other player is choosing 19, then every strategy (both pure and mixed) is a best response.


Perfectly competitive constant MC Questions If I have a market in which I have constant MC, no fixed costs, and perfect competition- when would it make sense for a new firm to enter the market(granted they have the same technology)? Would I need more information about the market?

also would the cost curves for an individual firm be 1 line since $AC=MC=AVC$ and $MR=MC$ and $P=MC$ under perfect competition, leading to $P=MC=AVC=AC=MR$

and for the market

Supply would be perfectly elastic and demand being a downward sloping curve.

Theoretically, if all firms are identical and have the same cost schedule, then the supply curve for the market should be perfectly elastic, as you stated. The side-by-side market and firm graphs would appear as follows:

This is an odd situation. Typically, when there exists a surplus of a good, firms competitively lower their prices until enough firms go out of business for the surplus to no longer exist; and when there exists a shortage, firms enter the industry until the supply increases enough for the shortage to vanish.

However, in this case, since firms are not distinguished by the price that they can afford to charge, the natural tendency towards equilibrium cannot occur this way. Instead, when there is a surplus, firms cannot compete by price lowering and will either survive or perish based on the random purchase choices of  buyers (if prices are the same everywhere, consumers will probably choose where they buy their goods based on other factors, like geographic proximity, aesthetic preferences, etc, but “rational” buyers in the simplified model will be indifferent). For our purposes, which firms survive and which close down will be essentially random - whichever firms happen not to sell enough of their product for whatever reason will close.

During a shortage, it gets even weirder. Whether or not firms enter the industry depends on the location of the ATC curve (which is why I did not draw it in the above graphs). If $ATC < P_F$ at $Q_F$, firms would enter since profits are possible and people will buy the good they produce. If $ATC = P_F$ at $Q_F$, there is no telling whether firms will enter, since they will all be indifferent.

And if $ATC > P_F$ at $Q_F$, whether there is a surplus or shortage, firms will drop dead like flies until not a one is left. If the good being produced is of any real import, the government would probably offer subsidies to incentivise the production of the good.

So, to answer your question - it would make sense for you (a firm) to enter if $Q<Q_M$ and $ATC < P_F$ at $Q_F$. You could also enter when $Q\ge Q_M$, but then your success or failure would be left up to chance or other factors as consumers decide whether to buy your product or your competitor’s identically-priced product.


Is this a total derivative - if yes, why minus This is the beginning of the derivation of equation of motion from the Solow model (Romer, 2019):

My question is: is this the total derivative (w.r.t. ultimate source of change "t")? If yes, why there is a minus sign in front of the 2nd and 3rd term?
I assume because they are in the denominator. But I was not able find any rules for this on net. Everywhere are only "+" symbols. Thanks.
This is how I did it. Is it wrong? I did total derivative and got the same result as in the textbook:

This is just standard derivative. The minus sign there is because you are taking derivative of a quotient and the quotient rule for derivatives is:
$$ \frac{d}{dx} \left(\frac{f(x)}{g(x)}\right) = \frac{f'(x)g(x) - f(x)g'(x)}{g(x)^2}$$
In this case:
$$\dot{k} = \frac{d}{dt} \left(\frac{K(t)}{A(t)L(t)} \right)\\ = \frac{\dot{K}(t)A(t)L(t)-K(t)(\dot{A}L(t)+A(t)\dot{L}(t))}{(A(t)L(t))^2} \\= \frac{\dot{K}(t)A(t)L(t)}{(A(t)L(t))^2} - \frac{K(t)(\dot{A}(t)L(t)+A(t)\dot{L}(t))}{(A(t)L(t))^2}\\=  \frac{\dot{K}(t)}{(A(t)L(t))} - \frac{K(t)(\dot{A}(t)L(t)+A(t)\dot{L}(t))}{(A(t)L(t))^2}$$
So you just need to remember that $A$ and $L$ are both functions of $t$ so you need to take derivative of whole qutient and quotient rule has minus there (if you want explanation for why quotient rule includes minus the right place is mathematics.se)


How does tariff increase inflation? The Wall Street Journal claims that:

  Some are concerned over the likelihood of the U.S. adopting trade
  tariffs on imports from China. This policy option would risk
  retaliatory measures and hurt U.S. exports, a blow to growth momentum,
  while making imports more expensive in the U.S., fueling inflation
  pressure. (emphasis added)

An academic article also says that the relationship is universally agreed upon by economists (gated link):

  If there is one idea on which all orthodox economists concur, it is
  that tariffs raise prices, that protectionism, without exception, is
  inflationary. Professor Samuelson, for instance, argues that tariffs
  reduce labor productivity and enhance “the cost of living” (1976, p.
  694). In the words of Coughlin et al., “protectionist policies
  increase prices” (1991, p. 25). According to the 1992 Economic Report
  of the President, “Trade barriers not only raise the prices of
  imported goods to consumers but also the prices of domestically
  produced goods” (p. 196).

I understand that tariffs reduce labor productivity by disallowing countries to produce in accordance with their comparative advantage. However, how does this lead to inflation? Is it because a decrease in goods produced plus the amount of money kept the same leads to inflation?

Foreign produced goods will see price increases directly as a result of the tariff, which adds to the prices of these goods.  The full tariff may not be passed through, as these higher prices will reduce demand, changing the supply/demand balance

Domestically produced goods will usually see price increases indirectly as a result of the tariff, as demand for these domestically produced goods will increase as a result of the weaker competition from foreign produced goods, assuming an upward sloping supply curve

Your quotes translate these likely price effects from tariffs into "inflation pressure"


Why offer curves of a power plant are stepwise increasing? I was wondering why the supply curve of a power plant in the auction for the Day-Ahead Market is stepwise increasing and not a continuous function with first and second derivative strictly positive.
I am thinking of a gas plant (CCGT), the amount of fuel to be used can be adjusted continuously and not discretely, am I wrong?

One minor point- it could be that the factory schedules labor and other factors of production (coal deliveries, etc) in daily increments, and therefore pricing is fixed within each increment.


Assumptions of Ramsey Cass Model Field of Economics became mathematical and model based. I can grasp the appeal of the model but fail to understand why do we introduce certain assumptions.

(Actually I am trying to relax the assumptions of the model, Ramsey Cass Kooperman (RCK) model, just as an exercise but before I can relax them I need to know why they were significant in the first place)

So, in the context of RCK model
Why does the assumption of

1.Compactness,

2.twice continuously differentiable function, and

homogeneity (homothetic)  are taken.

Why are the relevant?

I know this that homogeneity produce constant returns to scale with Cobb Douglas production function and lt also implies homothetic. Why do we need homothetic functions?

In the presentation that the OP linked to, "compactness" is not assumed, but derived as a result from more primitive properties that are assumed, one of which is the "twice differentiability" of the functions involved.

The presentation deals with the vary basic deterministic growth model in discrete time. The per capita production function in each period is $g(k_t)$ for which it is assumed that it is continuous and differentiable $g'>0,\;\; g''<0$. The law of motion of capital is then

$$k_{t+1} = g(k_t) + (1-\delta)k_t -c_t$$

with $0<\delta<1$ being the depreciation rate. The sequence starts at some arbitrary, finite initial value.

The presentation wants to show the existence and uniqueness of the solution. To do that, in page 6 it first proves that the "choice set" is bounded -namely that the set from which the economic agents may choose the optimal levels of consumption and capital is not the whole $\mathbb R_+$.

This is proved by considering the maximal sequence of capital levels, irrespective of utility optimization considerations. If the maximal sequence is bounded, it means that the optimal sequence can only be chosen from a bounded set of values.

The maximum capital sequence obtains if we set consumption equal to zero: what happens when we consume nothing and we use all our capital stock and all the new output as capital only.
We have then the sequence

$$k^{max}_{t+1} = g(k^{max}_{t}) + (1-\delta)k^{max}_{t}$$

Now that consumption is set to zero, the sequence of capital is governed by a non-linear first-order difference equation. A sufficient (although not necessary) condition for the maximal sequence to be bounded is that this difference equation is asymptotically globally stable, namely, if starting from any initial point we converge to a fixed point (it is not necessary because we could have bounded oscillations also and obtain a bounded sequence).

The fixed point of the maximal capital sequence satisfies

$$k^{max}_*:  k^{max}_{t+1}=k^{max}_{t} \implies g(k^{max}_*) = \delta k^{max}_* $$

By standard theory, global stability of the fixed point will obtain if the derivative of the difference equation, evaluated at the fixed point, is less than unity in absolute value,

$$\left |\frac {\partial k^{max}_{t+1}(k^{max}_*)}{\partial k^{max}_{t}}\right| = g'(k^{max}_*)+1-\delta <1 \implies g'(k^{max}_*) < \delta$$

At the fixed point, it holds that

$$\frac {g(k^{max}_*)}{k^{max}_*} = \delta $$

For fixed point stability we want

$$g'(k^{max}_*) < \delta$$

So fixed point stability requires

$$g'(k^{max}_*)<\frac {g(k^{max}_*)}{k^{max}_*}$$

or that "the marginal product will be less than the average product". Under the assumption that $g''<0$ everywhere, this will also hold for the fixed point. Hence, we obtain fixed point stability, and so also convergence and so boundedness of the maximal capital sequence. This tells us why we assume 2nd-order differentiability: by having the 2nd derivative and making assumptions about it, we can easily determine whether the equilibrium points are unique and things like that. Note also that differentiability of any degree implies continuity.

If the maximal capital sequence is bounded, so will be any other capital sequence, and hence the choice set for capital is bounded. If it is for capital it is also for consumption. Then, the full capital equation expressed as an inequality

$$k_{t+1} \leq g(k_t) + (1-\delta)k_t -c_t$$

defines a set (a unidimensional set, an interval on the real line) that is a) bounded below at zero (by the assumption that capital cannot be negative  b) bounded above as proven c) it can attain its boundary points. So it is closed and bounded and therefore compact.

More over, we assume that there are no "holes" in it, that there are not "forbidden" values in this set. This makes the set convex.

Given these properties (incl. continuity of the production function), by standard theorems we are assured that a maximum, i.e. a solution exists, and it is unique, which is what the presentation wanted to prove at this point.


Why do prices of consumer products seem to rise independent of their supply? For example, in my country, the price of coconuts steadily rises, despite the fact that we still have plenty of coconuts. The same with vegetables.

Is this caused primarily by an increase in the cost of labor as a factor input, or are other forces at play?

To make it simple: let say your coconuts production is constant over time but the population is growing. It's a constant supply but an increasing demand, resulting in an increase of coconuts price.

If the prices were constant, the demand would be higher and thus not fully satisfied.


Wealth tax and share holdings Please help me to understand how the hypothetical introduction of wealth tax will affect the markets.
In my understanding, many of the super-rich own most of their wealth in shares of their own company (take heads of tech giants as an example).
Let's say that country X introduced an annual wealth tax of 3%. Let's also assume that a wealthy individual A owns 75% of their company B. The capitalization of B remains on about the same level. This would mean that after 37 years after the introduction of the tax, individual A will keep less than a quarter of company B shares ($0.75 * (1-0.03)^{37} ≈ 0.24$) and will hand more than a half over to the government. Would it mean that the government can take over the company by means of collecting a wealth tax? (unless the original owner has some kind of a super-voting stock)

No, this is not how wealth tax works. Wealth taxes do not transfer company ownership to the government.
In order to understand how wealth taxes work consider following example. Let us assume that there is individual owning 10 shares each worth \$10,000 dollars in company A. The individual has no debts or nothing else directly affecting the wealth of individual.
Given the numbers assumed above the wealth of that individual would be 10x\$10,000 = \$100,000.
Next let us assume no deductible so the wealth tax is applied to whole \$100,000. Lastly, lets set the wealth tax to 3% as in your question.
In the case above the wealth tax will be:
$$ (0.03) {\\\$} 100,000 = {\\\$}3000$$
per year. However, government does not get any of the shares in the company. The individual is free to get the \$3000 to pay the wealth tax from their labor income or from their dividend income, profits from some venture or rent they get etc (neither of which are wealth). So even with 3% wealth tax they get to keep their company and shares in their company forever.
The individual could pay for the wealth tax by selling some of their shares in the company, for example in year 1 they could sell 1 share for \$10,000 to someone else pay \$3000 tax to the government and consume rest or keep the rest on bank account for future. But the individual does not need to sell it to the government.
If government would want to buy the shares it could presumably do that on the same capital market where individual will sell their \$10000 share, but the government would have to compete with other buyers there or the individual could also just decide to sell it someone directly where government would have no access to actually buy the share (although I don't know why would government want to do that in the first place).
Consequently, even with 3% wealth tax it might take anything between 1 year (in case if the person just decides to directly sell all shares on market) or infinity number of years (in case that individual (and their descendants) will never decide to sell their shares, or never sell them to the government) for government to get more than 50% ownership in a firm owned by an individual that is being taxed.


Why do companies sit on cash while they have debt? Why don't they use cash to pay down their debts?

Debt is cheap. Flexibility is valuable.

They hold debt + cash up to the point where the value of flexibility is still greater than the net cost of servicing the debt minus any interest earnt on the cash.

It saves them the transaction costs of re-raising debt when they need it, had they paid it down early.

It's cashflow that typically kills businesses, rather than profitability. So holding extra cash, makes long-term business sense: it's the ultimate safety net.


What is the definition of "First Best", "Second Best", etc. in contract theory? What is the definition of "First Best", "Second Best", etc. in contract theory?

Especially, what is the difference between "First Best" in contract theory and "ex-post efficient" in mechanism design?

In contract theory

The first-best refers to the best you could do if you knew agents' preferences over labor an income (i.e., if you did not have to impose the incentive compatibility constraint), and the second-best is the best you can do if agents have to reveal their preferences themselves.

In mechanism design

A useful reference is Galichon, Alfred, Ex-Ante vs. Ex-Post Efficiency in Matching (May 21, 2011). Available at SSRN: http://ssrn.com/abstract=1837321 or http://dx.doi.org/10.2139/ssrn.1837321  :

  "an assignment is called ex-post efficient if no other deterministic assignment is improving on it in a Pareto sense; and ex-ante efficient if no lottery over deterministic assignments is." (my emphasis)

Difference between the two

There is not much connexion between the two notions as defined above. Every combination of the two notions is a priori possible. Both a mechanism and a contract can be

First-best ex-post efficient (i.e., efficient when incentive compatibility constraint is not imposed and the outcome of the mechanism/contract must be deterministic)
First-best ex-ante efficient (i.e., efficient when incentive compatibility constraint is not imposed and the outcome of the mechanism/contract can be random)
Second-best ex-post efficient (i.e., efficient when incentive compatibility constraint is imposed and the outcome of the mechanism/contract must be deterministic)
Second-best ex-ante efficient (i.e., efficient when incentive compatibility constraint is imposed and the outcome of the mechanism/contract can be random)

In the literature

Yet, in general, you are be more likely to find the first-best/second-best terminology in contract theory (random contracts are not that common in contract theory), and the ex-post/ex-ante efficiency in mechanism design (knowledge of the preferences is rarely assumed in a mechanism: the fact that we do not know agents preferences is the raison d'être of mechanism design).

Thus you can expect to see 3. and 4. being discussed in the mechanism design literature, and 1. and 3. being discussed in contract theory.

Beware

This being said, the notions of second-best and first-best are often used outside of contract theory in a rather permissive way, which may be confusing.

For some people, first-best simply means "if we do not impose some constraint $X$" and second-best means "if we do impose constraint $X$".

Thus you may hear people talk about (beware this is where it gets confusing)

an ex-post efficient mechanism as "second-best" efficient, because it is "efficient under the constraint that the assignment be deterministic".
an ex-ante efficient mechanism as "first-best" efficient, that is "efficient if we do not impose constraint $X$".

Hope that clarifies it (or at least does not confuse you more).


Do property values capture producer choice in agriculture? I am interested in conducting research into how climate change impacts the social welfare of a country, particularly how it affects producers of agricultural product. My immediate thought was that as the climate changes, certain crops will fare better under these new conditions and would generate a substitution effect towards these crops.

e.g. As temperatures rise, soybean becomes relatively more attractive than wheat in terms of yields and farmers would, over time, switch towards growing soybean so as to maximize rents.

After a discussion with a colleague, they suggested looking into property values of farms as these would encompass information about farmers' choices over time. I am not sure how to understand this connection formally. How would farmers switching crops be reflected in the property value of a farm?

Suppose that, initially, crop A is the most profitable crop that can be grown on a particular farm, yielding an average annual profit of \$X, profit being measured after deduction of all costs (including a normal return to the farmer) other than the cost of the property (ie the land).  In a competitive property market, the capital value of the property might be expected to approximate to the discounted present value of a stream of \$X per year.

Now suppose that, due to climate change, the relative profitability of different crops changes, and that crop B becomes the most profitable crop, yielding an average annual profit of \$Y. This could represent either an increase or a decrease in profitability. The former is possible for a farm in a cool climate, where perhaps crop B was previously too unreliable, but with a higher average temperature becomes more profitable than crop A.  The latter is possible for a farm in the tropics, where perhaps both crops used to be reliable but now crop A suffers from heat stress.  In either case the capital value of the property might be expected to change to the discounted present value of a stream of \$Y per year.

So in principle your colleague's suggestion is correct.  However, there are many reasons why it might be hard to identify such an effect in practice:

Some changes in crop in response to climate change might result in the new profitability being similar to the old.
Average annual profitability may be hard to estimate given random fluctuations in weather conditions.
Profitability depends on market prices for crops and for inputs such as seeds, labour, fuel and fertilisers which may change.
The relevant discount rate for converting annual profit to a capital sum may also vary with market conditions.


Price dispersion in online retail There are a number of online booksellers that are popular in India right now. The prices they charge for the same book often differ by as much as 10% (See this price comparison site to check http://www.indiabookstore.net/)

Since these are homogenous goods and anyone who can access one of the stores can as easily assess another I wonder how we might explain this price dispersion. I have not done a systematic study but it is my impression that it is not the case that there is an ordering of prices between stores which is the same for different books.

I was wondering whether there are any economic models which can explain this dispersion. In particular are there models which can be tested by using panels of price data.

[I confess I am fishing for a research topic.]

Yes, this has actually been quite an active area for research within the consumer search literature. As a starting point, I would recommend looking at the following:

BAYE, M. R., AND J. MORGAN (2001): “Information Gatekeepers on the Internet and the Competitiveness of Homogeneous Product Markets”, American Economic Review, 91(2), 454–474. These authors have a model that is interesting because it explains the persistence of price dispersion, even in environments like price comparison sites where one would ordinarily think that all consumers will buy from the lowest-priced merchant. The intuition is closely related to that of Varian's classic model of sales, if you know that. The idea is that some firms price low to sell to the consumers on the price comparison site, whilst others price high to sell to less-informed consumers who do not use the price comparison site and therefore do not compare as many prices.
BAYE, M. R., J. MORGAN AND P. SCHOLTEN (2004): “Price Dispersion in the Small and in the Large: Evidence From an Internet Price Comparison Site”, Journal of Industrial Economics, 52(4), 463–496. (older working paper link). This is interesting because they test various models (including the one mentioned above) against data from a price comparison site.
De Los Santos, B., A. Hortaçsu, and M. R. Wildenbeest (2012): "Testing Models of Consumer Search Using Data on Web Browsing and Purchasing Behavior." American Economic Review, 102(6), 2955-80. Not directly related to the question, but an interesting take on a similar issue. There are two classic models of consumer search: sequential and fixed-sample. In sequential search, consumers visit a merchant, evaluate its offer and decide whether to search again; repeating his process until they find an offer they are willing to accept. In fixed-sample search consumers first decide the number $n$ of merchants they will visit; they then visit precisely $n$ merchants and buy the best offer among them. Given dispersed prices, sequential search is optimal and the fixed-sample strategy is not. These authors test the two models against data from online retailers and find evidence to suggest that consumers use a strategy closer to the fixed-sample end of the spectrum.

A couple of extra references to finish up:

BAYE, M. R., J. MORGAN AND P. SCHOLTEN (2006): “Information, Search, and Price Dispersion”, in T. HENDERSHOTT (ed.) Handbook of Economics and Information Systems, Elsevier Science, 323–371 A nice survey of theories of search and price dispersion that can give you an idea of what work has been done on these general phenomena (and possibly some ideas of what can be empirically tested?).
ELLISON, G., AND S. F. ELLISON (2009): “Search, Obfuscation, and Price Elasticities on the Internet”, Econometrica, 77(2), 427–452 A study of how firms can obfuscate the search process to maintain market power in a frictionless context like a price comparison site. Ellison and Wolitzky also have a nice theoretical paper on this phenomenon in the RAND Journal of Economics.


Why are countries in the Gulf rich but lagging in technological innovation? Countries in the gulf are oil rich. But they are lagging in R&D sector. Governments do not spend much on R&D. Most countries employ foreign contractors or import technologies.

What is the reason?

Update

Resource Curse literature attempts to address the issues you are raising, take a look at here and here.

Here is an interesting example of a technology transfer case.

Original answer

They do, in fact, have increased the share of R&D spending by a huge margin in the past 5 years. Some of these countries see commerce, trade and tourism as more central to their development than other aspects of development.

The number of Arab students on government scholarship in the West has been on the rise and many western universities have opened branches in the Middle East, especially in the Gulf countries. In the past, only the rich kids of Arabs were able to go to universities in the West. By default, these kids, did not bother working as scientists or educators, they, probably, stayed in the west or became entrepreneurs.

Today, with the help of government scholarships, the ordinary folks can send their kids for education, and hopefully, these kids will bring the science to the other ordinary folks in their respective countries. Remember, technological shock is not so fast and abrupt as we assume in the models, it take decades to have a measurable effect in practice.

As younger 'kings' and 'princes' are involved in politics, there are signs of greater investment in education and science.

Here is the chart of R&D spending to GDP ratios in the Gulf countries.

In the countries, where younger generation have more say in politics, there the spending on R&D has been higher than in those where older 'kings' rule. See the chart, Qatar and UAE have had higher R&D shares, but the data is limited for these countries.


What's the difference between gross fixed capital formation and gross private domestic investment? Cited from Wikipedia, we know:

Gross private domestic investment is the measure of physical investment used in computing GDP in the measurement of nations' economic activity. This is an important component of GDP because it provides an indicator of the future productive capacity of the economy. It includes replacement purchases plus net additions to capital assets plus investments in inventories.

Gross fixed capital formation (GFCF) is a macroeconomic concept used in official national accounts. GFCF is a component of the expenditure on gross domestic product (GDP), and thus shows something about how much of the new value added in the economy is invested rather than consumed. GFCF is not a measure of total investment, because only the value of net additions to fixed assets is measured, and all kinds of financial assets are excluded, as well as stocks of inventories and other operating costs (the latter included in intermediate consumption).

If I wanna study the relationship between Effective federal funds rate and investment, in particular, whether there is a linear relationship between the annual percent change of these two quantities, which one should I choose to estimate the investment? Thanks.

Data source: https://fred.stlouisfed.org/series/USAGFCFQDSMEI

https://fred.stlouisfed.org/series/GPDI

The term gross private domestic investment (GPDI) seems to be used only by the US. The term gross fixed capital formation (GFCF) is used by the rest of the world (but not by the US). (This is thus simply the US being exceptional as usual by using its own terminology and methodology.)

Roughly, the difference is this: Ignoring inventories, GFCF includes government investment, while GPDI does. More precisely, the difference is this: $$\begin{alignat*}{1}
\text{GFCF} & =\text{Gross private domestic fixed investment}+\text{Gross government fixed investment}\\
 & =\text{GPDI}-\text{Change in private inventories}+\text{Gross government fixed investment}.
\end{alignat*}$$

To elaborate just a little, the rest of the world follows the UN System of National Accounts (SNA, 2008), while the US does not. In the usual identity $Y=C+I+G+NX$, we have the following differences between the UN SNA and the US:

If you are looking at countries other than the US, then you may not be able to find data for GPDI so easily. In which case, you may want to use GFCF.

Conversely, if you're looking at only the US, then you'll probably want to use GPDI.

Of course, in your analysis, you should be clear about what precisely your statistic, be it GFCF or GPDI, is supposed to measure.