Total differentiation in a IS curve context everyone. I'm having a hard time trying to figure out how the total differentiation occurs in this exercise.
In this excerpt, from Inflação e Crises", by Affonso Celso Pastore, the author develops an alternative form of the IS curve. First, he states some equations for its development.
The aggregate demand as the sum of household consumption (C), investment (I) and government spending (G):
$(1)$     $y = C + I + G$
Consumption as a function of disposable income ($y_d$) and non-human wealth (A):
$(2)$ $C = C(y_d, A)$      with $0 < C_y < 1$; $C_a > 0$
Investment as a function of the real interest rate:
$(3)$ $I = I(r)$ with $I_r < 0$
Non-human wealth (A) being equal to the sum of the money stock and the income originated by the stock of government bonds (B) divided by the real interest rate:
$(4)$ $A = M + \frac{B}{r}$
Disposable income (y_d ) being equal to the sum of the labor income (y) and the income originated by the stock of government bonds (B) minus the taxation, that applies both to the labor income and the income originated by the stock of government bonds:
$(5)$ $y_d = y + B - T (y + B)$
On (5), the author also states that
$T = T (y + B)$ with $T'> 0$
With this definitions, we finally arrive at this form of the IS curve:
$(6)$ $y = C\{[y + B - T(y + B)]; [M + \frac{B}{r}]\} + I(r) + G$
And we finally get where I'm having troubles in understanding it, when he uses the total differentiation:
$(7)$ $[1 - C_y(1 - T')]dy - (I_r - C_A \frac{B}{r^2})dr - [C_y (1 - T') + \frac{C_A}{r}]dB - C_AdM + dG = 0$
I've already tried so hard to understand it, but it always seems that I am missing some parts of the process. I explicitly have three doubts:
(i) I would like to know if there is a particular reason that, in this total differentiation, we use the derivatives dy, dr, dB, dM and dG, but we do not use dT, since T is a variable that appears in the original equation too.
(ii) Second doubt: although I can see how the "inner" derivation processes occur, I am not sure I can correctly interpret the signs (the "plusses" and the "minuses"). I mean, why C_a dM is a negative term while dG is a positive term? This doubt extend to the other terms as well.
(iii) The third one: I have a doubt in the derivation of the T variable in dy and dB. I don't know exactly how it got derived in dy and dB.
By the way, if necessary, I can provide some more informations of my book for contextualization purposes. Sorry if I'm sounding confused, I study economics by self-taught and this is my first time using Economics Stack Exchange.
Thanks for your attention!

Total differentiation means you are differentiating all variables in the expression. So if we start with
$$y = C\{[y + B - T(y + B)]; [M + \frac{B}{r}]\} + I(r) + G$$
we get:
$$ d y = C_y^{'} dy + C_y^{'} dB - C_y^{'} dTdy - C_y^{'} dTdB + C_A^{'} dM + C_A^{'} \left( \frac{dBr-Bdr}{r^2} \right) + I'dr + dG $$
Here you are using just basic calculus such as chain rule accordding to which $\frac{d}{dx}[y(u(x))] = \frac{dy}{du} \frac{du}{dy}$, plus you use the rule that with total differentiation  $dy(x_1,x_2) = y_1' dx_1 +y_2'dx_2$ and also quotient rule $\frac{d}{dx}[F(x)/G(x)]= \frac{F'G(x) - F(x)G'}{G(x)^2}$.
Next you just move everything to the LHS of the equation to get
$$dy - C_y^{'} dy - C_y^{'} dB + C_y^{'} T'dy + C_y^{'} T'dB - C_A^{'} dM - C_A^{'} \left( \frac{dBr-Bdr}{r^2} \right) - I'dr - dG = 0$$
Now just collect terms and clean up the mess above and you directly get:
$$(1 + C_y^{'}(1 -  T'))dy - (I_r - C_A \frac{B}{r^2})dr - [C_y (1 - T') + \frac{C_A}{r}]dB- C_A^{'} dM  - dG = 0$$
The expression looks difficult because it has a lot of terms but you should not get intimidated by its look.


Cross-sectional model vs panel model I have an unbalanced panel dataset of around 3000 firms for 5 years. My goal is to see if female-owned firm are less likely to survive, so I have a logit model with female-owned dummy as the key independent variable.

The cross-sectional models for year 2007 and 2009 (if year == 2007, if year == 2009) have significant female-owned variable. However, if I try to run a fixed effect logit across all 5 years then the female-owned coefficient is highly insignificant. I have included the i.year dummies in the panel model, and interact female-owned##year2007 but so far the coefficients are not significant.

So how do I interpret this sort of results? Thank you in advance for your help!

Note that the fixed effects estimates use only within-firms differences, essentially discarding any information about differences between firms. If predictor variables vary greatly across firms but have little variation over time for each firm, then fixed effects estimates will be imprecise and have large standard errors. So, if there is not enough variation or change in gender ownership, I may expect a non significant estimate in fixed effects compared to a cross-sectional model.


Why do there seem to be relatively few imports from India into the United States? In the United States I see significant quantities of manufactured good imports made in Taiwan, Japan, China and Korea. However, there seem to be relatively few imports from India. Why is this?

India has significantly worse physical/logistics infrastructure than China, Japan, Korea and Taiwan, so it is difficult to produce goods in India because it's difficult to move supplies and product around the country.  This, coupled with the comparatively higher complexity of dealing with government bureaucracy, makes it challenging to manufacture products in India for export.

Here is the World Bank's 2014 Logistics Performance Index for the countries, which illustrates the significant competitive disadvantage India has compared to China and others.

India still has a low-cost workforce, so they do export items where cost is very important (e.g. clothing, sneakers).  More importantly, India exports services (call centers, software offshoring) because it's much easier to lay down fiber optic cable than to build a railroad so certain cities (Hyderabad, Mumbai, Bangalore) have developed strong export services industries which do not need to depend on a lot of outside physical infrastructure to create viable exports.


Finding labor supply function from equation of labor market The supply side of the labour market is given by the following set of
equations:
Utility of worker is given by $$U = L^{\frac{1}{2}}C^{\frac{1}{2}}.$$
Real wage $w = 5$,
T-Max = 40 hours,
Investment Income (Fixed) = 100

Now assume that the real wage increase from 5 to 8; assuming labour
supply to liner line, find the equation of the labour supply function using
two discrete points?

Here is another way we could solve this problem with some simple calculus. We first start by maximizing the utility function subject to the budget constraint and the time constraint.
$$\underset{L,C}{max}\;\underset{s.t.\;C=100+w(40-L)}{L^{1/2}C^{1/2}}\qquad (1)$$
$$\underset{L}{max}\;L^{1/2}[100+w(40-L)]^{1/2}\qquad (2)$$
$\textbf{FOC:}$
$$\bigg(\frac{100+w(40-L)}{L}\bigg) ^{1/2}=w\bigg(\frac{L}{100+w(40-L)}\bigg) ^{1/2}\qquad (3) $$

With some math
$$L=\frac{50+20w}{w}\qquad (4)$$

Let $N$ be the number of hours worked. If you plug 5 and 8 in for $w$, you get 10 and 13.75 for $N$ respectively.

Now we have two points $(5,10),(8,13.75)$. Solving for slope we get $\frac{13.75-10}{8-5}=1.25$.

Now we must consider the intercept. Because $w=0$ is not defined, we must use the other intercept (where labor hours equal zero).
$$40-L=0\implies 40-\bigg(\frac{50+20w}{w}\bigg)=0\qquad (4)$$

With some math, we get $w=2.5$
$$\implies\qquad N=1.25(w-2.5)\qquad (5)$$

If we did not want to impose the restriction of linearity on the relationship between labor hours and real wage, we would simply use equation (4):

$$N=40-\bigg(\frac{50+20w}{w}\bigg)\qquad (6)$$

I know your question specified a linear relationship between labor hours and real wages, however this method of solving this question does not impose this restriction, which is nice because, as we can see, the relationship between labor hours and real wage is not actually linear.


Why could interest rates go up if Brexit happens? I was reading this article, George Osborne says Brexit would drive up mortgage rates:

  George Osborne has issued a stark warning that mortgage rates will
  rise if Britain leaves the European Union.

  The chancellor said he thought it was likely interest rates, and
  therefore the cost of home loans, would rise if Britons vote to leave
  the EU in the referendum on 23 June. But Brexit campaigners accused
  Osborne of panicking and resorting to intimidating voters.

  Asked if he thought the cost of mortgages would increase on a British
  exit from the 28-nation bloc, Osborne said: “The short answer is yes.
  I think that is likely, but I’m not in charge of interest rates.”

I was wondering what is the transmission mechanism for explaining why interest rates would have to go up if Brexit happens? Moreover, is there any historical example and precedent for this happening?

What would happen in the event of a "Leave" vote in the referendum? Well, the pound would quickly fall in value against its major trading partners - and some falls have already happened as the "Leave" vote appears to increase in probability. That makes imports more expensive, which is directly inflationary. Which pushes the Bank of England (the UK's Central Bank) to raise interest rates in response.

On top of that there are second-order effects which would pull in the other direction, but over a longer time period: there's the directly deflationary effect of the significant increase in unemployment. And the increased risk of further disintegration of the EU, with all the consequential risks to peace and prosperity that that would bring.

And as Alexis L. points out, the UK leaving the EU adds significant risk to the UK's currency; and that corresponds to a need for a higher return on the currency: that return is the interest rate. That's because if interest rates are too low, then people would keep selling the pound sterling, and it would keep dropping in value, pushing up inflation (requiring higher interest rates), and harming UK companies that rely on exports (creating political pressure to do something about the exchange rate - and that "something" is higher interest rates).


Deflation and positive real interest rate Economists say that deflation leads people to postpone their consumption because it increases the value of their money and gives them the ability to consume more in the future. But if a consumer saves his money in a bank with a positive interest rate, the value of the money also increases.
Let's assume we have two situations:

We have 5 % deflation. The consumer has 1000 dollars. If he postpones his consumption for a year, the real value of 1000 dollars will be $\frac{1000}{0,99}\doteq1010$.
Now we have a 5 % nominal interest rate. If I put 1000 dollars into a bank, I will have 1050 after one year. Let's assume that we have 3,9 % inflation. Then the future value of my money in today prices is again $\frac{1050}{1,039}\doteq1010$

So why is the deflation considered to be such a big danger for an economy?

Deflation means decreasing prices, but with the rigidity of wages (although this depends on the country in which you are), it means (i) higher unemployment rates or/and (ii) lower profits.

(i) higher unemployment means less consumption and thus more deflation which drives the economy into a vicious circle.

(ii) lower profits means lower investment in production capacity or R&D, etc... and also lower dividends, which to me is more desirable than (i). Since the majority of people are less exposed to variation in capital income than in wages, but this is political.

In this framework, if the central bank plays its counter-cyclical role, key rates should decrease to discourage savings, conditionally to the fact that those are not already too close from 0.

But I would say that in reality, many other determinants must be taken into account. Actually the trajectory of your economic system with its inertia, etc... e.g.: the fact that this deflation is imported or not;  the fact that the forecasted rentability of investments in alternative production capacities are conditional to high (or at least stable) prices so as to be competitive (example of renewable energies VS a decreasing fuel price); the shareholding structure of the economy under question, etc... Thus it may not be dangerous.

You cannot figure out why the deflation is considered to be such a big dangerous for the economy with the (partial equilibrium) numerical example you give.


Marginal rate of technical substitution I am a student in an intermediate microeconomics class and am having a little trouble understanding the marginal rate of technical substitution. I understand that it represents the amount that labor (capital) has to be decreased for capital (labor) to be increased and stay on the same isoquant, but I am having trouble understanding it in practice.

For instance when the MRTS = K/L and capital is 4 and labor is 1 than the MRTS is 4/1. Does that mean that mean if capital is increased by 4 units then labor has to be decreased by 1 unit to stay on the same isoquant? Or does it mean that mean if capital is decreased by 4 units then labor has to be increased by 1 unit to stay on the isoquant? Or am I way off in my understanding?

We start with a production function: $f(k,l)$, which tells us what quantity will be produced if we use $k$ units of capital and $l$ units of labour. Suppose that we cange that quantity of capital by $dk$ units and change the quantity of labour by $dl$ units. If this change is chosen so that we stay on the same isoquant then it must be that the total production doesn't change:

$$\frac{\partial f(k,l)}{\partial k}dk+\frac{\partial f(k,l)}{\partial l}dl=0.$$

Rearranging, we get

$$\frac{dk}{dl}=-\frac{\frac{\partial f(k,l)}{\partial l}}{\frac{\partial f(k,l)}{\partial k}}.$$

This is the marginal rate of technical substitution, the slope of the isoquant. It has the same interpretation as any other slope. It means that if I increase labour by one unit then I can decrease capital by $$\frac{\frac{\partial f(k,l)}{\partial l}}{\frac{\partial f(k,l)}{\partial k}}$$ units.

Example Suppose we have a Cobb-Doublas production function: $f(k,l)=k^a l^{1-a}$. We have

$$\frac{\partial f(k,l)}{\partial k}=ak^{a-1}l^{1-a}$$

$$\frac{\partial f(k,l)}{\partial l}=(1-a)k^{a}l^{-a}$$

$$MRTS=-\frac{(1-a)k^{a}l^{-a}}{ak^{a-1}l^{1-a}}=-\frac{1-a}{a}\frac{k}{l}.$$

Now we can plug some numbers in to this example to see how it works. Suppose $a=1/2$, and we currently have $k=4$ and $l=1$. Then, we have

$$MRTS=-\frac{1/2}{1/2}\frac{4}{1}=-4.$$

So, for each unit increase in the quantity of labour employed, we can decrease the quantity of capital employed by 4 units.

This works backwards too, so every unit decrease in $l$ would demand a 4 unit increase in $k$ to keep us on the same isoquant.


Supermarket selling seasonal items below cost? In a British supermarket, I saw the prices of Christmas chocolate gift boxes being cut dramatically (£1.50 to £0.15, and £7.50 to £0.22). I don't quite understand this behaviour, where the chocolate boxes are sold (presumably) below cost.
I've learned that this sort of strategy could be used to eliminate competitors and strengthen monopoly, but I don't think that's quite relevant for this case. It seems more of a clearance to me. What is the motivation behind such behaviour? Why don't the supermarkets just continue selling them at a low price, but not so low? Is it simply for saving warehouse costs?

Is it simply for saving warehouse costs?

Probably yes, holding onto inventory is very expensive. You have to pay for warehousing of the good, it takes the spot of some other inventory that might be in high demand. Food is also perishable so it cannot be stored indefinitely.
Stores have to always guess what demand for their products will be, sometimes they get it wrong and order excess inventory. It can often be more profitable to sell excess inventory below the production cost or many times even just to throw it away to make space for new products. Holding onto it would be a sunk-cost fallacy. The costs are already incurred in the past, even if they were a result of a mistake it does not make sense to try to double down on the mistake and hold onto them. It is more profitable to ignore the sunk-costs of getting them and make new decisions of what to do with the inventory based on new information.


Is conditional mean independence, $E(e_i | x_i)=0$, a different assumption from $E(x e) = 0$? (from Hansen) This question comes out of Hansen's Econometrics ((https://www.ssc.wisc.edu/~bhansen/econometrics/Econometrics.pdf))

In section 2.18, we only impose the assumptions of finite variance and $Q_{xx}$ being positive definite, and then derive the linear projection coefficient $\beta = E(\textbf{x} \textbf{x}^\prime)^{-1} E(\textbf{x} y)$ as the minimizer of the expected squared error of the linear projection model $y = \textbf{x}^\prime {\beta} + e$. This leads to the implication (NOT the assumption) that $E(\textbf{x} e) = \textbf{0}$.

Then in section 4.4, under assumption 4.2, we have: $E(e_i | \textbf{x}_i)=0$.

My question is: is $E(e_i | \textbf{x}_i)=0$ a newly-imposed assumption in chapter 4? Or is it equivalent to the condition $E(\textbf{x} e) = \textbf{0}$ which we reached in chapter 2, not by assumption but by implication?

I know that $E(\textbf{x} e) = E(E(\textbf{x} e|\textbf{x})) = E(\textbf{x} E(e|\textbf{x}))$
 (by law of iterated expectations and conditioning theorem, respectively), so imposing the assumption that $E(e|\textbf{x}) = \textbf{0}$ yields the implication that $E(\textbf{x} e) = \textbf{0}$. But is the reverse true? Does $E(e_i | \textbf{x}_i)=0$ follow from $E(\textbf{x} e) = \textbf{0}$, or is $E(e_i | \textbf{x}_i)=0$ a new assumption that we're imposing?

$E(\mathbf{x}e)=0$ does not imply $E(e|\mathbf{x})=0$, to see that, suppose that x is a variable that always takes the value of zero, but $e$ is independent of $\mathbf x$ and has a mean of, say, $3$. Then the expected value of the product is necessarily $0$, but the conditional expectation will be equal to 3 (given independence, the conditional mean is equal to the unconditional mean).


Solving Ag=b with non symmetric A Following is a question that did not receive attention at math.SE at all. I am aware that is would be better suited there, but given its Economic background, perhaps it will get more attention here. If not, I'm happy to call this a failed attempt and delete it.

I need to solve $Ag=b$ for $b$, where $A$ is not symmetric.

$$A g = b \\
A = \left(\begin{matrix} A_1 \\ E_{IJ} \otimes \mathbb 1  \end{matrix}\right)$$

For some positive integers $I, J$: $A$ has size $(IJ\cdot J)\times IJ$, $g$ has size $IJ \times 1$, and $b$ has size $IJ \times 1$. $A$ is vertically stacked $A_1, A_2$, where $A_1$ is $IJ\times IJ$.  $\mathbb 1$ is $J\times 1$ vector of ones, and $E$ is the identity matrix.

I need to solve this for $g$ on a computer for the case where $J$ small and $I$ large. I am fairly certain (through the way I get $A_1$ and $A_2$) that with $A_1$ being singular, my system of equations is exactly identifying $g$.

I'm used to the case where $A$ is symmetric and invertible. How do I proceed here?

Maybe this helps. One method to do this is to use least squares (as was mentioned by @cc7768).
Matlab does this by default when using the \ operator.
This is also useful because it's sensible even if the system is overidentified as in the following example:

A = [1 22; 2 100; 7 6]
b = [1 2 5]'
A\b

produces

ans =

    0.7108
    0.0061

. In Python, this can be done with

import numpy
from numpy import linalg
A = numpy.matrix("1 22; 2 100; 7 6")
b = numpy.matrix("1 2 5").T
linalg.lstsq(A,b)[0]

which gives

matrix([[ 0.71084144],
        [ 0.00611577]])

.


Free Disposal: the production set less the vector space of positive reals In Microeconomic Theory (3rd Edition), Mas-Collel, Whinston and Green state that the property of free disposal implies the following:

$Y - \mathbb{R}^L_+ \subset Y $

Y: Production set

y: Production vector

L: Amount of commodities considered

Why does this formula means that the extra amount of inputs or outputs can be disposed of or eliminated at no cost?

So the way that $Y$ is defined is such that negative values are  inputs and positive values are outputs. For example, if I used 3 units of labor, and 2 of capital to produce 10 pencils, that will be reflected as a single vector in $\mathbb{R}^3$ equal to $[-3;-2;10]\in Y$.

Notice that subtracting 1 unit to either the first or the second element of that vector will mean that I used more inputs to produce the same output, for example, $[-3;-3;-10]$. Similarly, if I subtract one unit to the third element, it would mean that I produced less output with the same inputs. For example $[-3;-2;9]$.

Both of these operations, respect the idea of free disposal (so long as you are subtracting units, not adding to them). Moreover, any notion of free disposal can be represented by one of these operations: i.e producing less with the same inputs, or using more inputs to produce the same.

Therefore you can conclude that a production set, $Y$, satisfies free disposal if and only if $Y-\mathbb{R}^L_+\subset Y$.


Fast way to write out the utility optimization problem for a Cobb-Douglas function? In my last problem set, I had to solve both the Utility Maximization Problem (UMP) and Expenditure Minimization Problem (EMP)  for a Cobb Douglas utility function. Recall, Cobb Douglas is defined as
$$U(x,y) = x^\alpha y^\beta$$

I can compute the EMP or UMP. I can then find the other by "duality". But writing the problem was very tedious and messy. I ended up with an indirect utility function like this

$$v(p_x,p_y,m) = \left(\frac{\alpha m}{p_x}\right)^\alpha \left( \frac{\beta m }{p_y}\right)^\beta$$

and doing the Lagrangian was kind of clunky with all this multiplication going on.

Is there a simpler way to write the problem that can save me time / effort?

Well all Cobb-Douglas have an structure, it is the utility that makes shares constants as budget shares independent of prices
$p_{l}x^{CD}_{l}(p,w)/w=\alpha_{l}$ with $u^{CD}(x)=\sum_{l}\alpha_{l}log(x_{l})$ and $\sum_{l}\alpha_{l}=1$.
then you can go back and compute $x_l(p,w)$, with this the indirect utility, then invert to obtain the expenditure and then derive to get the hicksian.
Not sure if this is what you want but some utility functions have a defining property, the same with the leontief or CES.


Meaning of Exchange rate Does exchange rate of local currency relative to US dollar mean LOC/USD or USD/LOC ?

LOC/USD and USD/LOC are currency pairs. Whatever currency comes first is known as the base currency. The currency that comes second is known as quote currency. For major currency pairs, the format of the currency pair is based on established priority. For example, EUR has the highest established priority and thus is almost always shown as the base currency.

Currency pairs quotes work such that one unit of the base currency can be exchanged for quoted amount of the quote currency (hence the name "quote currency"). For example, LOC/USD 6.25 means that one LOC can be exchanged for 6.25 USD. USD/LOC 0.16 means that one USD can be exchanged for 0.16 LOC.

Whenever people say "local currency relative to US dollar", that usually should be parsed as "[base currency] relative to [quote currency]", and thus it would be LOC/USD. A similar interpretation applies for "local currency quoted against the US dollar" (LOC/USD). Another hint is that most "minor currencies" are quoted against the US dollar.


Why is the Australian dollar, often viewed by traders as a proxy for the Chinese economy? The Australian dollar, often viewed by traders as a proxy for the
  Chinese economy, gained 0.3 per cent against its US counterpart.

From: S&P 500 hits one-month high on renewed trade hopes (September 5, 2019)

I couldn't read the FT article... but...

According to this article here, China imports a lot of raw material from Australia. This means that if Chinese economy is doing well, they import a lot of stuff from Australia... hence AUD will appreciate.

This news piece, for example, says that as China is hit with new tariffs, AUD falls. This is because the Chinese won't be able to export as much, which means they won't demand as much raw material from Australia anymore.

Or this more recent article says that Chinese CPI comes out higher than expected. This means that it's more likely that the PBOC (China's central bank) will need to do something to reign in inflation, slowing down the Chinese economy and Australian exports. This depreciates AUD.


Production function and isoquant slope Given the company's production function $f(L,K)=L^{1/3}K^{3/4}$, find slope of the isoquant passing through $(L,K)=(20,40)$ is equal to $-4/5$ (K is on the vertical axis).

I need to state whether the statement above is true or false. In my opinion that is true because i need to calculate $MRTS_{LK}$ which is obviously equal to $-4/5$, but the answer in my textbook is: $-8/9$. Thus my question is am i doing something wrong or just the answer in my textbook is wrong?

The book is right. The proper way to go about this is of course to work out the theory and the math before plugging in any specific numbers. Fixing the quantity produced, we have
$$ \bar Q = L^bK^a \implies K = (\bar Q)^{1/a}L^{-b/a}$$

Then, since capital is on the vertical axis

$$\frac {dK}{dL} = -\frac{b}{a}(\bar Q)^{1/a}L^{(-b/a)-1} $$

Note that we do not differentiate $\bar Q$ since we want it to be fixed, for different combinations of inputs.

Inserting the production function expression

$$\frac {dK}{dL}= -\frac{b}{a}[L^bK^a]^{1/a}L^{(-b/a)-1}$$

$$\implies \frac {dK}{dL}= -\frac{b}{a}\frac{K}{L}$$

Then, plug in the specific numbers: $b=1/3, a=3/4, K = 40, L = 20$ so

$$\frac {dK}{dL} = -\frac{1/3}{3/4}\frac{40}{20} = -\frac{4}{9}\cdot 2 = -\frac{8}{9}$$


Marginal product of capital net of depreciation I am trying to understand how marginal product of capital net of depreciation is the following:

Given that the production function is quite standard

I understand the first term of the marginal product, but I am asking about the depreciation part.

This is a misuse of terms.

The marginal product of capital net of depreciation is indeed $MP_k - \delta$, there is no doubt about it.

What the authors mean  is that

$$R = 1 + (MP_k - \delta)  $$

is the "gross return on capital" factor. In fact a few lines below the equation they call it exactly that, which is the correct term. Here "gross" reflects the inclusion of $1$.


What is the percentage of announced Merger & Acquistion deals actaully completed? I am assuming that not all M&A deals announced are completed. There are factors such as anti trust laws and consumer protection agencies that legally prohibit the two companies from completing the M&A. Statistically, what is the percentage of completed M&A deals to announced M&A deals .

Please provide reference if possible

If I'm reading it correctly, Table X (page 2633) of Schwert (2000) (Journal of Finance, Hostility in Takeovers: In the Eyes of the Beholder?) says that about 78 percent of deals in 1975-1996 were successful.

However, this measure is constructed based on the acquisition of the firm, not the bid of the acquirer, so that if there are multiple bidders this is coded as a 1 if any succeed and a 0 only if all of them fail. So it isn't what percentage of bids succeed but rather what percentage of targets are ultimately acquired. I couldn't find any measure of the probability of a bid succeeding but it must be significantly lower.

One tricky issue is that while successful bids must be revealed unsuccessful one need not be, so there is selection bias in the sample of bids. Therefore, a narrower way of characterizing this result is to say that of the potential deals where at least one bid was made public 78 percent were ultimately acquired by some firm.


Textbook covering calculus and probability theory Is anyone able to recommend a textbook that covers the following topics at a level suitable for econ undergraduates?

Differential calculus, including the various rules of differentiation and partial derivatives.
At least some integral calculus.
Probability theory, expected values, Bayes' rule.
(optional) basic set theory.

I can find books with a nice treatment of calculus, but am struggling to find a book that also includes coverage of topics in probability.

Failing one book that covers all of these topics, I also welcome suggestions of books that might work well together to give such coverage.

In a course similiar to yours at the Radboud University Nijmegen, the Netherlands, they use two different lecture notes (in Dutch) and each set of notes recommends a book.

For probability theory, they recommend the following book:

Murray R. Spiegel, John J. Schiller, R. A. Srinivasan: (Schaum’s Outline of Theory and Problems of) Probability and Statistics. McGraw-Hill
Companies, 2000, 408 p., ISBN: 0071350047.


Prove the sample variance is an unbiased estimator I have to prove that the sample variance is an unbiased estimator. What is is asked exactly is to show that following estimator of the sample variance is unbiased:

$s^2=\frac{1}{n-1}\sum\limits_{i=1}^n(x_i-\bar x)^2$

I already tried to find the answer myself, however I did not manage to find a complete proof.

For a shorter proof, here are a few things we need to know before we start:

$X_1, X_2 , ..., X_n$ are independent observations from a population with mean $\mu$ and variance $\sigma^{2}$

$\mathbb E(X_i) = \mu$ , $\mathbb{Var}(X_i)= \sigma^{2}$

$\mathbb E(X^2) = \sigma^{2} + \mu^{2}$

$\mathbb{Var}(X)=\mathbb E(X^2)-\mathbb [E(X)]^2$

$\mathbb E(\bar{X}^2) = \frac{\sigma^2}{n} + \mu^2$

Let's try to show that $\mathbb E(s^2)= \mathbb E\left(\frac{\sum_{i=1}^n (X_i - \bar X)^2}{n-1}\right) = \sigma^{2}$

To make my life easier, I will omit the limits of summation from now onwards, but let it be known that we are always summing from $1$ to $n$.

$\mathbb E\left(\sum (X_i - \bar X)^2 \right) = \mathbb E\left(\sum X_{i}^2 - 2 \bar X \sum X_i + n \bar X^2 \right) = \sum \mathbb E(X_{i}^2) - \mathbb E\left(n \bar X^2 \right)$

$\sum \mathbb E(X_{i}^2) - \mathbb E\left(n \bar X^2 \right) = \sum \mathbb E(X_{i}^2) - n \mathbb E\left(\bar X^2\right) = n \sigma^2 + n \mu^2 - \sigma^2 -n \mu^2$

This simplifies to $(n-1) \sigma^2$

So far, we have shown that $\mathbb E\left(\sum (X_i - \bar X)^2 \right) = (n-1)\sigma^2$

$\mathbb E(s^2)= \mathbb E\left(\frac{\sum (X_i - \bar X)^2}{n-1}\right) = \frac{1}{n-1} \mathbb E\left(\sum (X_i - \bar X)^2 \right)$

$\mathbb E(s^2) = \frac {(n-1)\sigma^2}{n-1} = \sigma^2$

We have now shown that the sample variance is an unbiased estimator of the population variance.


The problem of transformation: what is it all about? I've just learned Marxist concepts that

Value= cost + wages + owner profit

But I do not understand what the transformation problem is and what problems exists because of this. Would someone mind to explain it with examples? Also can someone tell me the Marxist and non Marxist solutions?
P.S.Can someone clarify for me whether or not

Value is fixed as in after the job is done (e.g., worker did $6 of work)

and

Value is equal to price

According to Samuelson (1971) the transformation problem is to find some general formula by which transform the value of labor into market prices. This is not strictly speaking marxian problem as it already features in the classical works, especially Ricardo wrestled with this problem a lot, since labor theory of value is a classical theory but became associated with marxians later on because they derive profit from the ‘surplus value’, however empirically even industries with various different capital to labor ratios tend to have equal return on capital.
Samuelson argues there is no general solution to the problem. Since the labor theory of value fell out of favor in economics I am not sure if there are any more recent successful attempts, if there are any scholars that specialize in that here they might give additional comments on that.
The labor theory of value is not used by contemporary mainstream economists so the non-marxian solution is simply not to use the labor theory of value but rather the subjective theory of value which does not have this problem and has proven to provide better explanations than the labor theory of value.
Regarding the questions in PS:

Value is not fixed after the job is done. For example, a fashionable purse might have high value in a current year because it is in fashion but as soon as fashion changes its value might became very low. Or another example is given by 'diamond paradox'. In a normal situation diamond is more valuable than water because people already have access to high quantities of water so their marginal utility of consuming another glass of water is low, but they do not have access to many diamonds so their value is high. In a desert however the value of water would suddenly jump above that of diamonds.

No value is not generally equal to price. Assuming that the exchange is voluntary we can say that the price is either equal or greater than the value of money that buyer gives for it and the value for seller is either equal or lower. For buyers who refuse to partake in the transaction the value will be lower than price and for sellers that refuse to sell the value will be higher than price. Only in special cases is the price exactly equal to value.


Sources on competition policy Are there any good books or blogs on Economics in Competition Policy?

I am primarily interested in US and EU.

I know of the Motta and Bishop-Walker books but I would like something with more details on the economic methods.

E.g.:

more details on the econometric methods
more details on acquiring or cleaning data
more details on the industrial organization (or other) models used

I was recently recommended 'Quantitative Techniques for Competition and Antitrust Analysis' by Peter Davis and Eliana Garcés. While it does not contain all the necessary info, it does refer to more specified books.


Calculating 3m annualised rates Calculating 3m annualised rates is a concept I've been struggling with for some time, but I think the below example illustrates what I am looking at trying to understand.

The past 6 months of monthly YoY inflation data for Hungary has been as follows:

From which is has been calculated that the 3m annualised rate is as follows:

How is this number calculated on a rolling basis?

Let’s assume that the price index is denoted $p_t$, with $p_1$ the first month, and $p_4$ the fourth. To calculate the 3-month annualised rate between the 1st and 4th month, we note that :
$p_4 = (1 + r)^{\frac{1}{4}} p_1,$ where $r$ is the annualised inflation rate.

Or: $(1+r) = (\frac{p_4}{p_1})^4$.

We cannot calculate the price index level from the 12-month change data; you need either index levels or 1-month percentage changes.


Why is the supply curve in the foreign-currency exchange market vertical? In the book 'Economics' by Mankiw and Taylor the demand and supply curves on the foreign-currency exchange market are shown as follows:

The supply equals the Net Capital Outflow (NCO). I would have assumed that the exchange rate influences NCO in the same way it influences imports and exports, for example a higher exchange rate makes it more profitable to invest abroad than domestically, leading to an increased NCO. However, the supply isn't influenced at all by the exchange rate according to Mankiw and Taylor and that's what I don't understand.

Because the supply of pounds in the model is controlled and fixed by the central bank. The central bank does not have to change (increase) the supply of pounds when the exchange rate changes. So the supply of pounds will be just a flat vertical line because no matter what the exchange rate is the supply of pounds will not respond to exchange rate as it is given by the central bank's monetary policy.


National debt vs having national assets What hypothetical benefits and problems would a country have if it decided to have positive balance? That is, to have its debt much smaller than its assets. Similar to what Norway does.
And reverse, what would happen if Norway would decide to go full-USA and take loans untill the balance will reach 100% yearly gdp in debt, and then spend all this money on its industries, social programs.
Im mostly interested in comparing this two extremes, long term effects, over decades. I realise that any such massive change will cause short term disturbance. Mostly interested in cases where a country goes from 100% yearly gdp debt to 100% yearly gdp in assets, and the reverse, in a few decades, to be able to compare similar magnitude of change.
And in the very long term, would assets having country, outcompete the debt having countries? Would Norway as is slowly gain more and more capital and grow faster than USA, or would USA having money earlier invest it wisely and grow so fast that it would outpace the debt management? What conditions would change the outcome? What path is more stable against catastrophes? Does any path change how likely that a country would participate in a war?

Build a balance sheet:

Assets = Liabilities + Equity

Assume a simplified government budget constraint:

Deficit Spending = New Money + New Debt - Taxes

Assume that spending is to accumulate assets on the balance sheet. So to accumulate assets without spending new money or new debt into an economy over a period the government must run a tax surplus. The government would accumulate equity claims instead of matching debt to assets with no change of equity.
Taxes that transfer money from non-government to government savings accounts kept on the books of the aggregate bank amount to a zero-sum transfer of savings from non-government to government. What public purpose is served if the government accumulates significant financial savings in the aggregate bank sector? The benefit from taxes or borrowing or money issue is the government spending and using assets wisely for public purposes. There is no benefit from government financial saving because society discounts nature at the interest rate and creates financial relations as we go along from past to present to future.
One famous case study for debt financed purchase of asset is the Louisiana purchase where USA bought large territory claimed by France:
https://www.monticello.org/thomas-jefferson/louisiana-lewis-clark/the-louisiana-purchase/
Then the public benefit of debt or tax financed purchase could be debated in the political process whether one is a voter, citizen, or economist because no one had a definitive answer to the ethical question what is the public good and how should the government use finance to cause the public good?
However if the United States government issues debt just to accumulate a financial savings account, that is, a debt claim against some other non-government sector, then there could be adverse consequences which are associated with government corruption and bad public policies.
Currently in the United States the American families owe over $1 trillion in student loans which are financed by the issue of Treasury securities held as assets by some other non-government units. So the federal government acts like a bank or financial intermediary when it subsidizes the university system via direct federal loan policy in this way and the working class families with student debt may or may not be able to service and pay down debt via income flows in aggregate.
In terms of the financial float in a banking region the bankruptcy rate and net repayment of debt destroys financial assets (and liabilities) while the credit dealer systems generate new financial assets and matching liabilities in some other sector or unit. Funding government via taxes either enables the private credit systems to function better or may impair the function of the private systems depending on your theory for how financial systems operate in a case study. When the United States ran the so-called Clinton surplus there is a Congressional report studying the problems caused in the financial sectors if the persistent surplus retires the Treasury securities. The Treasury securities are the backbone of credit dealer markets in the global economy.


Bayes Correlated Equilibrium with complete information Model

Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world.

The state of the world has support $\mathcal{V}$.

When DM chooses action $y\in \mathcal{Y}$ and the state of the world is $v\in \mathcal{V}$, she receives the payoff $u(y,v)$.

Let $P_V\in \Delta(\mathcal{V})$ be the DM's prior.

The DM also processes some signal $T$ with support $\mathcal{T}$ distribution $P_{T|V}$  to refine his prior and get a posterior on $V$, denoted by $P_{V|T}$, via the Bayes rule.

Let $S\equiv \{\mathcal{T}, P_{T|V}\}$ be called "information structure".

A strategy for the DM is $P_{Y|T}$. Such a strategy is optimal if it maximises his expected payoff, where the expectation is computed using the posterior.

Let us now define the concept of 1-player Bayesian Correlated Equilibrium provided in Bergemann and Morris (2013,2016,etc.).

$P_{Y,V}\in  \Delta(\mathcal{Y}\times \mathcal{V})$ is a 1 player Bayesian Correlated Equilibrium if

1) $\sum_{y\in \mathcal{Y}}P_{Y,V}(y,v)=P_V(v)$ for each $v\in \mathcal{V}$

2) $\sum_{v\in \mathcal{V}}u(y,v) P_{Y,V}(y,v)\geq \sum_{v\in \mathcal{V}}u(k,v) P_{Y,V}(y,v)$ for each $y$ and $k\neq y$.

Theorem 1 in Bergemann and Morris (2016) claims  that $P_{Y,V}$ is a 1-player Bayesian Correlated Equilibrium if and only if there exists an information structure $S\equiv \{\mathcal{T}, P_{T|V}\}$ and an optimal strategy $P_{Y|T}$ for the DM such that $P_{Y,V}$ is induced by $P_{Y|T}$, i.e., for each $(y,v)\in \mathcal{Y}\times \mathcal{V}$
$$
(\star) \hspace{1cm}P_{Y,V}(y,v)=\sum_{t\in \mathcal{T}}P_{Y|T}(y|t)P_{T|V}(t|v)P_V(v)
$$
[for simplicity, I have assumed that $\mathcal{T}$ is finite]

Question 1:

How does the 1-player Bayesian Correlated Equilibrium induced by the complete information structure look like?

This is my attempt to answer.

The way in which I represent the complete information structure is
$$
S^{c}\equiv \{\mathcal{T}\equiv \mathcal{V}, P_{T|V}(t|v)=1\text{ if $t=v$ and $0$ otherwise}\}
$$
Under $S^c$, $P_{Y|T}$ is an optimal strategy if for each $t\in \mathcal{T}$ and for each $y\in \mathcal{Y}$ such that $P_{Y|T}(y|t)>0$ we have that
$$
u(y,t)\geq u(k,t) \text{ }\forall k\neq y
$$
[Note that, even under the complete information structure, the optimal strategy may be mixed, if two actions lead to the same payoff $u$.]

Hence, from ($\star$) and for each $(y,v)$
$$
P^{c}_{Y,V}(y,v)=\sum_{t\in \mathcal{T}}P_{Y|T}(y|t)P_{T|V}(t|v)P_V(v)=
\sum_{t\in \mathcal{V}}P_{Y|T}(y|t)P_{T|V}(t|v)P_V(v)=
P_{Y|T}(y|v)P_V(v)
$$

For example, suppose $\mathcal{Y}\equiv \{1,2,3\}$, $\mathcal{V}\equiv \{1,2,3\}$, $P_V(1)=P_V(2)=P_V(3)=1/3$, and
and
$$
u(1,1)=2, u(1,2)=4, u(1,3)=3\\
u(2,1)=2, u(2,2)=3, u(2,3)=3\\
u(3,1)=1, u(3,2)=3, u(3,3)=3\\
$$
Then, a possible optimal $P_{Y|T}$ under $S^c$ is
$$
P_{Y|T}(1|1)=1/2, P_{Y|T}(1|2)=0, P_{Y|T}(1|3)=1/3\\
P_{Y|T}(2|1)=1/2, P_{Y|T}(2|2)=1/3, P_{Y|T}(2|3)=1/3\\
P_{Y|T}(3|1)=0, P_{Y|T}(3|2)=1/3, P_{Y|T}(3|3)=1/3\\
$$
and the corresponding 1-player Bays Correlated Equilibrium is
$$
P^c_{Y,V}(1,1)=1/6, P^c_{Y,V}(1,2)=0, P^c_{Y,V}(1,3)=1/9\\
P^c_{Y,V}(2,1)=1/6, P^c_{Y,V}(2,2)=1/9, P^c_{Y,V}(2,3)=1/9\\
P^c_{Y,V}(3,1)=0, P^c_{Y,V}(3,2)=2/9, P^c_{Y,V}(3,3)=1/9\\
$$

Question 2:

Is it true that, for each $v\in \mathcal{V}$, $P^{c}_{Y|V}(y|v)\equiv \frac{P^{c}_{Y,V}(y,v)}{P_V(v)}$ should be equal to $1$ for a $y\in \mathcal{Y}$ and zero otherwise?

Is it true that, for each $y\in \mathcal{Y}$,  $P^{c}_{V|Y}(v|y)\equiv \frac{P^{c}_{Y,V}(y,v)}{\sum_{v\in \mathcal{V}}P^c_{Y,V}(y,v)}$ should be equal to $1$ for a $v\in \mathcal{V}$ and zero otherwise?

Question 3:
Is it true that by adding the constraint $P_{Y,V}(y,v)>0$  (strictly) for all $(y,v)\in \mathcal{Y}\times \mathcal{V}$ in the definition of 1-player Bayes Correlated Equilibrium above  we exclude $P^c_{Y,V}$? Why?

Question 1

Yes, the BCE induced by a completely informative information structure will look like this.

This is true even though there are other ways to represent fully informative information structures. Think of $T$ as labels. A fully informative information structure should use each element of $T$ to label only one state of the world. That way, when the DM observes the realized label, $t$, they know which is the state. By assuming that $T=V$, a natural way to label each state with a different label is to assign each state their own label, i.e. $P_{T|V}(t|v)=1$ if and only if $t=v$. However, reshuffling the labels is as informative. For example if the label "low" is sent with probability 1 when the state is "high" and the label "high" is sent with probability 1 when the state is "low" the information structure is not in $S^c$, but is also perfectly informative because after receiving the signal (or label) "low" the DM learns that the state is "high" for sure. (There are ways to represent this formally using permutations, or other ways, but I thought it will be more clear with words).

Question 2

the answer is "Not necessarily" for both questions.

1) If the DM is choosing a mixed strategy (as you correctly point out this is possible even with complete information) then $1>P^c_{Y|V}(y|v)>0$ for the actions that the DM is mixing when they learn that the state is $v$.

2) If there is an action that is optimal for more than one state of the world  then $1>P^c_{V|Y}(v|y)>0$ for the states for which $y$ is optimal.

In many papers, people assume that each action is strictly better for one and only one state of the world. In that case, your two statements are true.

Question 3

Yes it is true:

Claim: a BCE that satisfies that $P_{Y,V}(y,v)>0$ for all $(y,v)\in Y\times V$ cannot be induced by a completely informative signal.

Proof: Proceed by contradiction. Suppose a BCE, $P_{Y,V}^*$, satisfies the restriction and is induced by a completely informative information structure.

Consider some state, $v_0$, for which action $y_0$ is not optimal. Note that if there is no such a state, then the decision problem would be trivial since all actions would be optimal for all states of the world. I assume that such a pair exists.

Now, without loss of generality, we can assume that the completely informative structure is the signal defined as $S^c$.

By assumption $P_{Y,V}^*(y_0,v_0)=\sum_{t\in T}P_{Y|T}(y_0|t)P_{T|V}^c(t|v_0)P_V(v_0)>0$, therefore at least one of the summands must be strictly positive. However, $P_{T|V}^c(t|v)=0$ for all $t\neq v_0$. Further, for $t=v_0$, it must be that $P_{Y|T}(y|v_0)=0$ since $y_0$ is not optimal given $v_0$.

We conclude that $P_{Y,V}^*(y_0,v_0)=0$, i.e. a contradiction!


Why is there negative sign for income effect in slutsky equation? Slutsky identity is given by: ∆x/∆p = (∆x/∆p)|substitution effect + (∆x/∆p)|income effect
Now we know ∆m= x*∆p => ∆p=∆m/x
Therefore, ∆x/∆p = (∆x/∆p)|substitution effect + (x*(∆x/∆m))|income effect
But in HAL Varian's book there's minus sign in front of income effect. I am not being able to figure out how the minus sign came there.
I think of income effect as total effect minus substitution effect.

Intuitively, if the price of a particular good in a basket rises, then the individual can no longer afford to buy the same overall basket of goods

If there were no substitution effect, then this would be likely to result in amounts of each of the goods being bought being reduced, even those whose price had not changed, since the overall effect would be similar to a real reduction in income. Since the impact is negative, the equation needs a negative sign for this income effect

In general there will be a negative income effect on all goods and a positive substitution effect on all goods apart from the one whose price has increased.  Which is dominant for a particular good may depend on the particular situation


Utility function types - request for review I am working on a Wikipedia page that compares several common utility functions. Although I found some information about these topics on the web, I didn't find it all in one place, and often got confused by the different terms. I will be happy for any comments or reviews. Most importantly: are the facts in this page correct?

EDIT: to make the question self-contained, I copy its current contents below. Because StackExchange markdown does not support tables, I used Senseful Solutions to create the text table.

This page compares the properties of several typical utility functions of divisible goods. These functions are commonly used as examples in consumer theory.

The utility functions are exemplified for two commodity types, $x$ and $y$. $p_x$ and $p_y$ are their prices. $w_x$ and $w_y$ are constant parameters.

+---------------+-------------------------------------+-----------------------+-----------------------------------------------------------------------------------+----------------+-------------+-----------------------------------------+----------------------------------+
|     Name      |              Function               |  Indifference curves  |                                   Demand curve                                    |  Monotonicity  |  Convexity  |                Good type                |              Example             |
+---------------+-------------------------------------+-----------------------+-----------------------------------------------------------------------------------+----------------+-------------+-----------------------------------------+----------------------------------+
| Linear        |  ${{x\over w_x}+{y\over w_y}}$      |  Straight lines       |  Step function: only goods with minimum ${w_i p_i}$ are demanded                  |  Strong        |  Weak       |  Substitute good|perfect substitutes    |  Potatoes of two different farms |
| Leontief      |  $\min({x\over w_x},{y\over w_y})$  |  L-shapes             |  hyperbolic: ${\text{Income} \over w_x p_x+w_y p_y}$                              |  Weak          |  Weak       |  Complementary good|perfect complements |  Left and right shoes            |
| Cobb–Douglas  |  $x^{w_x} y^{w_y}$                  |  hyperbolic           |  hyperbolic: $\frac{w_x}{w_x+w_y} {\text{Income} \over p_x}$                      |  Strong        |  Strong     |  Independent good|independent           |  Apples and socks                |
| Maximum       |  $\max({x\over w_x},{y\over w_y})$  |  ר-shapes             |  Discontinuous step function: only one good with minimum ${w_i p_i}$ is demanded  |  Weak          |  Concave    |  Substitute good|substitutes            |  ?                               |
+---------------+-------------------------------------+-----------------------+-----------------------------------------------------------------------------------+----------------+-------------+-----------------------------------------+----------------------------------+

Are the details in the table correct?

EDIT: Many thanks to all commenters and answerers. I revised the page accordingly.

Currently (Dec-1-2015) I see listed Linear, Leontief, Cobb-Douglas, and Maximum.

To incorporate here a comment by @denesp the C.E.S utility function (that nests the Leontief and Cobb-Douglas) should certainly be included

$$u(x,y) = B\big(ax^{-\rho}+(1-a)y^{-\rho}\big)^{-1/\rho}$$,

(which also is a functional form that has non-zero cross partial derivatives),

as should the quasi-linear form

$$u(x,m) = h(x) + m$$

which is very often used, with $m$ standing for residual money income (what's left after purchasing $x$).

I would also include the Translog utility function.

Finally, I think you should increase the scope of the page and also include in a separate section univariate utility functions that are used in environments with uncertainty and in macroeconomics (say, the HARA class of functions). We may keep in our minds these subfields of economics clearly distinct and also from basic consumer theory, but what you build is a wiki page that is likely to be visited by outsiders (e.g. mathematicians or engineers interested in the subject) or just-arrived students, so a broader scope appears useful.


Can tariffs be said to subsidise domestic industry? If a state places a tariff on a good, domestic manufacturers of that good become more price-competitive in the domestic market at the expense of overseas suppliers.

Could this be said to be a policy choice that subsidises that industry?

This is how I read your question:

If a state places a tariff on a good,             <- added a comma here
domestic manufacturers of that good become
more price-competitive in the domestic market
at the expense of overseas suppliers.

Could this be said to be a policy choice that subsidies that industry?

Assuming the country is a small and could not affect world price, then the answer is yes. To be more precise, an import tariff is equivalent to product-specific subsidy PLUS a consumption tax of that product.

Subsidy + consumption tax: Domestic producers gain the subsidized amount for each unit sold. Buyers pay for that extra amount the producers gain.

Tariff: The price of import goods (world price) rises, so domestic producers can sell at a higher price. The buyers are the ones who pay for that price difference.

"Credible" sources:

http://internationalecon.com/Trade/Tch95/T95-3.php
https://www.cairn.info/revue-reflets-et-perspectives-de-la-vie-economique-2004-1-page-25.htm, Section 4


Informed traders do know the cross section of the privately known signal between each other I am having the following setup of privately known signals and I am trying to understand an assumption. Here, I quote the setup.
Consider two agents idexed by $i=\{1,2\}$ and each one observes some privately noisy signal, that is
\begin{align}s_i=\tilde{v}+\tilde{u_{i}}\end{align}
where $(\tilde{v},\tilde{u_{i}})$ are identically distributed, with $\tilde{v}\sim N(v,\sigma_{v}^2)$ stand for the payoff of the risky asset and $\tilde{u_{i}}\sim N(0,\sigma_{u_{i}}^2)$ denotes the error term of each of the privately known signals. Also, it holds that $\sigma_{(u_1,u_2)}\neq 0$ and $\sigma_{(v,u_1)}=0=\sigma_{(v,u_2)}$.
The assumption that I am trying to understand following the aforementioned setup is the following:
``Every informed agent does know the cross sectional distribution of the privately knonw noisy signal that the other agent observes." Also in the market, there are uninformed traders etc. Does this mean, that in fact they know exactly the signal that each other observes or do I catch it wrong?

Yes, that assumption just means that every informed agent knows the true distributions where signals come from (i.e. roughly speaking, they know the parameters that define them).
The terminology "cross-sectional distribution" comes from the usual interpretation that instead of having literally 2 agents, in reality, you have a continuum of agents that come in 2 types. If that is the case, due to the law of large numbers, the empirical distribution of signals at any point in time will be equal to the theoretical distribution of signals. Therefore, knowing the cross-sectional distribution is the same as knowing the theoretical distribution. Since these distributions are normal, the latter corresponds exactly with knowing the mean and variance of signals of the other (type of) agent.


Why do we use tax brackets? Majority of countries (if not all) use tax brackets to define how much tax should the earning workforce pay. So we could have something like this.

Pay | Tax
0 - 10,000 | 10%
10,001 - 20,000 | 20%
20,001 - 30,000 | 30%
etc.

The breakpoints are what I am going to ask about. It has been proven in other schemes, such as the UK's Stamp Duty Land Tax that separating tax into categories like this leads to clusters on the lower bound of the breakpoints. My understanding is that this is not a desired effect and the distribution on the scale should be more fluid.

I come more from the software engineering side as opposed to the economic side, so I assume that in the past it was easier to calculate tax using this system and that's why it was chosen. Humans would not be able or willing to do complex tax calculations had we used rules that can be charted for example as S curves.

However, I wonder if we could have a better system today? (Assuming the current system is not sufficient.) Are there any proposals or significant movements that are not satisfied with the current tax system?

Note: I am not making assumptions about how the collected money is being spent, or how much is being collected. This is purely about the curves behind the tax brackets and clustering.

I think you've misunderstood how the (UK) income tax brackets work. They work differently to how stamp duty used to work.

Stamp duty brackets used to be absolute rates: so when the purchase price crossed over the bracket threshold by £1, the marginal rate would be huge, as the whole purchase price was taxed in the higher rate. Hence the clustering.

That's not what happens with income tax. (and it's no longer what happens with stamp duty, either)

With income tax, only the amount of income that's above the threshold, gets taxed at the higher rate. So, the marginal rate is always equal to the band rate. i.e. if the rates are as in your example, and your income rises from 10,000 to 10,001 then you would pay 10% on the first 10,000 and 20% on the extra 1. You would not pay 20% on all 10,001.


A maximization problem with multiple goods and integrated markets Update:
I will try to clarify the question: Let us say that the total harvest of the fish population at time t is $H_t$. Every harvest produce three types of fish: salmon ($f_1$), which is valuable and sold as a filee in salmon markets S; Pike ($f_2$), which is less valuable and sold to the fish soup markets P; and roach ($f_3$), which is solely used for fishsticks and sold at the markets R. The prices are endogenous and derived from the utility functions S,P,R, which are strictly concave and have a decreasing marginal utility.

If all the fish could be sold in any possible market, the constraints for the maximisation problem would be:

Total harvests at time t: $H_t=\sum_{i=1}^n v_{it}-\sum_{i=1}^n v_{i,t+1} $ ,             (1)

fish to markets at time t $H_t=\sum_{i=1}^n f_{it}$ , (2)

Where $v_{it} $ is the amount of fish $i$ in the lake at time $t$.

Now, if optimal, it should be possible to sell salmon to soup markets and salmon & pike to the fishstick markets: $S(f_1)$, $P(f_1, f_2)$ and $R(f_1,f_2,f_3)$. You cannot sell other fish but salmon in the filee markets, and roach cannot be sold at the soup markets.

Now the issue is: constraint (2) is pretty and you can easily see that the maximization problem is concave. However, it would allow any fish to enter any markets. If I use  $S(f_1)$, $P(f_1, f_2)$ and $R(f_1,f_2,f_3)$ and (2), it would be optimal to sell all $f_1$ in $S$, all $f_1, f_2$ in $P$ and nothing in $R$, hence the double-counting. I struggling to come up with a constraint that would clearly satisfy the argument that fish that have been sold in some market cannot enter any other market. Thanks for your help!

I think there is an approach problem in the constraint. (1) implies that:
\begin{align}
v_{n,t} - v_{n,t+1}=H_t - (\sum_{i=1}^{n-1} v_{it}-\sum_{i=1}^{n-1} v_{i,t+1})
\end{align}
As the number of fish caught that are not the $ n $ species increases, the number of fish that belong to the $ n $ species decreases. This, i understand, may arise from a production decision: company 1 decides to produce more fish of species not $ n $ and reduces its production of type fish $ n $. But what exogenous force can create this phenomenon? it would make sense if they are species that compete for the same resources in a limited space, but this would affect future non-current populations, and it would be necessary to see if it is reasonable that the effect has a linear form, it is more likely that it affects according to a logistics function. The other option is for one species to be the predator of another, but in this case it appears that it is not.
I suggest either directly assuming that there is no inter-species resource struggle or choosing a different function that determines the resource struggle among fish. If you decide that there is no fight between species, you can separate the population dynamics of each species and you could choose a function like this:
\begin{align}
P_{i,t} = P(v_{i,t} - v_{i,t+1},K) \\
\frac{\partial P_{t}}{\delta t}=\delta P_{ t}[1-\frac{P_{t,i}}{K}]  - (v_{i,t} - v_{i,t+1})
\end{align}
The differential equation $ \delta P_ {t} [1- \frac {P_ {t}}{K}] $ is based on studies in biology on the dynamics of fish population, you can see a simple model in this link https://scholar.harvard.edu/stavins/publications/problem-commons-still-unsettled-after-100-years. $ P_{i, t} $ is the population of the species $ i $ in the period $ t $, and $ K $ is the "Carrying Capacity", this is the maximum level of fish population that can exist. You would only have to adapt that differential equation to the discrete case.
As for the second constraint, why make the quantity produced of one species of fish decrease with increasing another? This is something that arises endogenously as the producer's decision: it is optimal for company 1 to produce more of the type 1 fish and less of the type 2. This second restriction is not necessary, I think. You can use a production function like this:
\begin{align}
f_{m}=f(v_{i}-v_{i,t+1},v_{-i}-v_{-i,t+1} ) \ \forall \ m \in M
\end{align}
Each company endogenously chooses which fish to produce. It is clear that with this objective function, companies that cannot sell some type of fish will simply not sell that fish. In addition, you can analyze interesting phenomena such as the presence of economies of scope or simply choose a simpler function to find equilibrium in the long term. I think these observations would solve the problem you are having.


Is economic growth measured in real GDP or in real GDP per capita? As an example, take a country where real GDP (measured in base year dollars) increases every year, but where the real GDP per capita (also measured in base year dollars) fluctuates, increasing and decreasing in equal measure. In this example, does the country experience economic growth every year? That is, does economic growth reflect the consistent increasing of RGDP or does it reflect the sometimes increasing, sometimes decreasing RGDP per capita?

Usually GDP growth rates are publicly talked about in real terms but not per capita, see for example World Bank where, above the relevant table we read

  Annual percentage growth rate of GDP at market prices based on constant local currency. Aggregates are based on constant 2005 U.S.
  dollars. GDP is the sum of gross value added by all resident producers
  in the economy plus any product taxes and minus any subsidies not
  included in the value of the products. It is calculated without making
  deductions for depreciation of fabricated assets or for depletion and
  degradation of natural resources.

Real GDP levels are also used in empirical research papers and books -for example, in Blanchard & Fischer, the first figure in the book is real GNP (not per capita).

A technical issue regarding per capita magnitudes is that population is not measured quarterly, or yearly (in fact it is usually measured per decade). So any attempt to provide quarterly or yearly "GDP per capita" figures would require extrapolating the population from sparser data. While this is not necessarily catastrophic as regards accuracy, it requires more resources to be devoted to its calculation.

Per capita concepts certainly appear more often in theoretical research papers. The main reason is that theoretical models look also for possible "steady-states" (as attractors of the economy's evolution). Since GDP in levels exhibits a long-run upward trend, the next step is to consider "GDP per capita" (to "take out" the effect of population growth), and then the next step is to consider efficiency-indexed growth, like "GDP per labor efficiency unit", in order to look for the model's steady-state.


Too much of a good thing - examples of production (or utility) functions that are initially increase in a factor and then decrease I'm attempting to build a spatial model that estimates labour distributions after climate change impacts agricultural production. The key point to note is that some rainfall is good, and some temperature is good, but only up to a point - too much rain will drown the plants, and too hot a temperature will cause them and the soil to lose moisture too quickly.

In the model, I use the data I have to calibrate and get values for productivity in the context of the model, and I would like to use those estimates to estimate the parameters of some production function, so that to run the counterfactual, I can apply projections of climate data to estimate productivities in each country. Does anyone know of production functions with the required property?

$$F(R,T)=100000-(R-200)^2-(T-25)^2,$$

where $F$ is production (in kg), $R$ is rainfall in a year (in mm), and $T$ is average temperature over the course of a year (in °C).

This says that under the optimal growing conditions of $R=200$ and $T=25$, production will be 100,000 kg.

If rainfall $R$ or temperature $T$ is higher or lower than these optimal levels, then production will be lower than 100,000 kg.

(Concepts you may be looking for include satiation and bliss point.)


Are there any surveys of economists on the determinants of healthcare price increases in the US, particularly over several decades? It was asked recently on politics SE what drove healthcare (actually healthcare insurance) prices in the US to rise faster than the CPI.
Neither of the top two answers resorted any actual econometric analysis, but both illustrate some popular ideas/answers to this question namely:

demand for healthcare is inelastic; healthcare/insurance providers basically extract economic rent (most upvoted)
the market is not free due to licensing and other forms of regulatory capture (2nd most upvoted & accepted answer)

In a comment below the 2nd answer from this short list, it was pointed out that other confounding factors may exist, e.g. price increases due to technological innovations (e.g. MRI) that suddenly everybody wants once they become available.
Looking at Wikipedia's article on this [which none of the P.SE answers actually bothered with], it does say for example that:

The Congressional Budget Office analyzed the reasons for healthcare cost inflation over time, reporting in 2008 that: "Although many factors contributed to the growth, most analysts have concluded that the bulk of the long-term rise resulted from the health care system's use of new medical services that were made possible by technological advances..." In summarizing several studies, CBO reported the following drove the indicated share (shown as a range across three studies) of the increase from 1940 to 1990:

Technology changes: 38-65%. CBO defined this as "any changes in clinical practice that enhance the ability of providers to diagnose, treat, or prevent health problems."
Personal income growth: 5-23%. Persons with more income tend to spend a greater share of it on healthcare.
Administrative costs: 3-13%.
Aging of the population: 2%. As the country ages, more persons require more expensive treatments, as the aged tend to be sicker.

According to Federal Reserve data, healthcare annual inflation rates have declined in recent decades:

1970-1979: 7.8%
1980-1989: 8.3%
1990-1999: 5.3%
2000-2009: 4.1%
2010-2016: 3.0%

While this inflation rate has declined, it has generally remained above the rate of economic growth, resulting in a steady increase of health expenditures relative to GDP from 6% in 1970 to nearly 18% in 2015. [CDC cited for this last sentence].

What I want to ask here: are there any (IGM-like) surveys what economists think were the main factors for the faster-than-CPI US healthcare cost inflation, particularly over longer time frames? Does a survey of economists find agreement for example with the CBO's conclusion that technological changes were the main factor over longer time frames?
If there are no such surveys, are there highly-cited economics papers that substantially disagree with the CBO on the determinants?

This was actually already indirectly answered by the IGM forum.
In this question the forum asks economists the following:

The US spends roughly 17% of GDP on healthcare, according to the OECD; most European countries spend less than 12% of GDP.
Higher quality-adjusted US healthcare prices contribute relatively more to the extra US spending than does the combination of higher quantity and quality of US care (interpreting quantity and quality to reflect both greater American healthcare needs due to underlying population health and the delivery of more or better healthcare services to Americans).

With the following answers:
From European economists:

From US economists:

This answer (albeit only indirectly) suggests most top policy economists think there is some factor other than technology or quantity demanded that is leading to the increased cost of American healthcare. If you skim the survey some of the alternative reasons presented include increased barriers to entry for American physicians, a dysfunctional insurance system, and market power in the American hospital system.


Is egyptology a pyramid scheme: Self-perpetuating university programs My friend got a degree in egyptology, but can’t get a job, So he’s paying more money to get a Phd, so he can work teaching other people egyptology.  In his case college is literally a pyramid scheme.

Copied from here, but I have seen the joke elsewhere as well.
My personal experience is that neither the university nor most university professors care to evaluate whether their curriculum has a lot of applicability/use. (Some professors claim this is not a goal or cannot be measured in any way; while many universities claim their programs are also very practical, but if you read the actual claim it is very much PR with little scientific measurement.)
Has there been any academic research into which fields satisfy the following criteria:

Most of the people who complete the university program do not find placement in the field.
There is some (perhaps not conclusive) statistical evidence that the program gives no benefits in the actual field (not the field the program was in) where these people eventually start to work in. E.g. it can be useful to study theoretical math even if you end up programming, as your logic may improve. Perhaps this could be measured with a control group of people who had similar backrounds to those who got into the math program but did not apply to get in; how different is their success in the same field?

P.s.: Does egyptology really fulfill these criteria?

Edit: Added the word perhaps.

Partial and tangential answer, but no other answers so far, so here goes:
For the first part of the definition (people who complete the university program do not find placement in the field), data from the Survey of Earned Doctorates may be useful, particularly "Postgraduation plans (e.g., work, postdoc, other study or training) - Type and location of employer". Papers that use this dataset may compare by field.
The "no benefit" part could be studied by regression discontinuity around the admission cutoff, but the small sample size of fields like egyptology makes it low-powered.


Average employment length From Macroeconomics 7th edition by Gregory Mankiw, p166.

  Here’s a numerical example. Suppose that 1 percent of the employed lose their jobs each month ($s$ = 0.01). This means that on average jobs last 100 months, or about 8 years. Suppose further that 20 percent of the unemployed find a job each month ( $f$ = 0.20), so that spells of unemployment last 5 months on average. Then the steady-state rate of unemployment is

  $\frac U L = \frac {0.01} {0.01 + 0.20}
= 0.0476.$

  The rate of unemployment in this example is about 5 percent.

Well, here I don't get this part.

  This means that on average jobs last 100 months

To me, the fact that 0.01 times 100 months comes to be 1, looks very plausible in a sense. But I don't get the process in it.
My guess was like as follows. If anyone among 100 people loses their job monthly,

(suppose they can never be reemployed, which is the opposite in the text book; I'm not sure that this matters on the issue here)

then the first guy loses after 1 month, second guy 2 months, ...
So we can add up all their work period 1+2+3+...+100 which is 5050, and divide it with 100 people, then we get 50.50 months per person. What am I missing?

This is simply the geometric distribution.

A job lasts 1 month with probability $s$.

A job lasts 2 months with probability $(1-s)s$.

A job lasts 3 months with probability $(1-s)^2s$.

$\vdots$

A job lasts $n$ months with probability $(1-s)^{n-1}s$.

Hence, the average length of a job is: $$\begin{align*}
 & 1\cdot s+2\left(1-s\right)s+3\left(1-s\right)^{2}s+\dots+n\left(1-s\right){}^{n-1}s+\dots\\
= & \left[s+\left(1-s\right)s+\left(1-s\right)^{2}s+\dots\right]+\left[\left(1-s\right)s+\left(1-s\right)^{2}s+\dots\right]+\dots\\
= & \frac{s}{1-\left(1-s\right)}+\frac{1-s}{1-\left(1-s\right)}+\frac{\left(1-s\right)^{2}}{1-\left(1-s\right)}+\dots=\frac{s}{s}+\frac{1-s}{s}+\frac{\left(1-s\right)^{2}}{s}+\dots\\
= & \frac{1}{s}\left(s+s\left(1-s\right)+s\left(1-s\right)^{2}+\dots\right)=\frac{1}{s}\frac{s}{1-\left(1-s\right)}=\frac{1}{s}.
\end{align*}$$

In the specific numerical example given by Mankiw, we have $s=0.01$ and hence the average length of a job is $1/s=100$.


Exact definition of one-player Bayesian Correlated Equilibrium Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world $V$. The state of the world has support $\mathcal{V}$. The DM receives the payoff $u(y,v)$ depending on the chosen action $y$ the realisation $v$ of $V$. Let $P_V\in \Delta(\mathcal{V})$ be the DM's prior.

Is the following the correct definition of 1 player Bayesian Correlated Equilibrium provided in Bergemann and Morris (2013,2016,etc.)?

$P_{Y,V}\in  \Delta(\mathcal{Y}\times \mathcal{V})$ is a 1 player Bayesian Correlated Equilibrium if

1) $\sum_{y\in \mathcal{Y}}P_{Y,V}(y,v)=P_V(v)$ for each $v\in \mathcal{V}$

2) $\sum_{v\in \mathcal{V}}u(y,v)P_{Y,V}(y,v)\geq \sum_{v\in \mathcal{V}}u(\tilde{y},v)P_{Y,V}(y,v)$ for each $y$ and $\tilde{y}\neq y$.

In particular, I have doubts about $2)$: what if there is a $y$ such that $P_{Y,V}(y,v)=0$ for each $v\in \mathcal{V}$? Am I missing something?

The concept of the BCE from their 2016 paper is similar to what you have. I think Bergemann and Morris' intuitive explanation is valuable so I'll paraphrase it here.

Each player in the game has a decision rule that chooses an action, $y$, dependent on the state of the world $V$, and the player's information set, which we'll call $S$. This information set includes both a finite set of signals for each player, $T_i$, and a signal distribution, $\pi: \mathcal{V} \rightarrow \Delta T$. As you wrote your example, you assume the set of signals is a singleton, leaving us with only a player's prior. This is a possible information structure, but is not necessary.

We can thus write the the decision rule as a mapping, $\sigma$,

\begin{align*}
\sigma : S \times V \rightarrow \Delta Y
\end{align*}

The lone criteria for a CBE in this setting is that each players' decision rule is ``obedient''. By obedient we simply mean that the action, $y$, chosen by the decision rule must be the optimal action for the player. Thus, a player will always follow the action chosen by their decision rule.

I believe you are confusing the information structure and the decision rule. My information set is not a function of the action I choose in this setting, so $P_{V,Y}(y,v)$ does not have any meaning. Thus, you don't need to be concerned about the existence of a $y$ such that $P_{V,Y}(y,v)=0$ for all $v$.

It is possible to be in this setting that there exists an action $y$ such that $\sigma(y_i|t_i)=0$ for all signals, $t$. But this would simply mean the player never chooses that action in equilibrium.

Is it possible that there exists a signal $t$ such that $\sigma(y_i|t_i)=0$ for all actions, $y$? No, and it would follow for the basic Nash existence proof, given certain constraints on $u(\cdot),$ $\mathcal{Y}$ and $\mathcal{V}$.


What are the consequences of deflation in Japan? Most of the literature I can find about deflation in Japan takes for granted that deflation is bad for the country. I can also find a lot of literature on why deflation is bad in theory. Is there any analysis of the 20 years of deflation in Japan and its specific consequences?

I guess it is a wonderful recent study case of deflation, to be compared with the established view on the subject, so someone must certainly have done it. Can you point to such literature?

Here is some evidence from third-party colleagues who have been to Japan in the 90s and recently visited again last year. He informed me that prices were the same as in the 90s or lower.

This is definitely the result of deflation working in Japan.

Another example of deflation in action is a report you can read here:
https://www.ozy.com/fast-forward/back-to-the-future-japanese-youth-flee-cities-for-the-countryside/87547

While here in the United States, most people don't get why someone like myself who works in the tech/economics field would want to own a small farming business, the youth of Japan do get it and they are moving back to rural villages and renting large traditional farm houses and adjoining land for $200/month, which is a fraction of what they were paying in cramped up studios in the city. This is an example of deflation in action where young Japanese citizens are abandoning costly housing, transportation, etcetera and adopting lifestyles that generate far less income and far lower expenses, both are deflationary.

So what are the consequences for these young people in Japan? Less stress, better health, higher quality of life overall? You would have to read the article and make your own conclusion.

You were not specific on consequences for whom.

The Bank of Japan has tripled its asset purchases:

This has had little apparent effect on conventional measures of inflation. The purpose is to offset deflationary declines but it has not worked and its starting to burden the State. So those are consequences the State of Japan will have to deal with. They may try to pass that off to its citizens the way our government does here, but as you have seen above, more and more Japanese are fleeing to a simpler life in the countryside.

All this new spending on the part of the BOJ may lead to mal-investment and systemic asymmetries that will eventually destabilize the entire financial system.


Calculating Price Elasticity of Demand Hi I was given the following price vs quantity values.

Price   Quantity Demanded
4   221
5   210
6   185
7   162
8   144
9   122
10  102
11  81
12  61
13  46
14  25

The graph was plotted as shown below.

The equation was, $Y = -0.0496 X + 15.133$. What I need to know is, I was asked to find the PED when price is $\$7.5$.

Then what I did was, I found the quantity at price $7.5$ substituting to the price quantity equation. And then found the PED using the equation

The quantity derived for price $7.5$ was $153.89$. Then I calculated the PED as below. Is it correct?

$$\frac{(153.89-144)/144}{(7.5-8)/8} = 1.099$$

May I know whether this calculation is correct?

The answer will vary slightly depending on which notion of elasticity you're using.

Arc elasticity (or midpoint elasticity) uses the formula
\begin{equation}
\epsilon^\text{arc}=\frac{Q_1-Q_0}{P_1-P_0}\cdot\frac{\frac12(Q_0+Q_1)}{\frac12(P_0+P_1)},
\end{equation}
where $\frac12(Q_0+Q_1)$ is the midpoint between $Q_0$ and $Q_1$. Note that in your case, $7.5$ is the midpoint between $7$ and $8$.

Point elasticity uses the formula
\begin{equation}
\epsilon^\text{point}=\frac{\mathrm dQ}{\mathrm dP}\cdot\frac{P}{Q}.
\end{equation}
Here, $\frac{\mathrm dQ}{\mathrm dP}$ is the derivative of the demand function (evaluated at the point you want to calculate the elasticity, but it will be constant if demand is linear), and in your case, $P=7.5$ and $Q$ is the quantity demanded corresponding to that price.


Simple model to predict oil prices Back when Hugo Chavez was still alive (former leader of Venezuela), he said they made "simulations" to predict how much oil prices will increase if they retire the supply of oil they were giving to the world, and that in that time that would cause trouble to US. That made me wonder how oil price could be predicted, since I had classes of computer simulation of different type of systems in the University and I can't even imagine how could it be done to predict oil prices. If I recall correctly, I was also told by a neuronal network professor that a researcher worked in predicting oil prices for years with neuronal networks, and the work became useless when a war triggered oil prices in a completely unexpected way. Knowing how hard making accurate predictions of oil prices could be, is there still an oversimplificated equation or something to predict oil prices in the market?

The most comprehensive survey of estimating oil prices is here. There you fund from very complicated models to very simple ones. As the article shows, the ultimate answer depends on whether you are estimating nominal or real price, and short-term or long-term prices.

Some simple models to estimate price of oil might be:

no-change forecast: if changes in the spot price are unpredictable, the best forecast of the spot price of crude oil is simply the current spot
price ($S_t$):

$$ \hat{S}_{t+h|t} = S_t \quad h>0$$

futures-based forecast: simply take the market's average expected oil price forecast as your forecast:

$$ \hat{S}_{t+h|t} = F^h_t \quad h>0$$

where $F^h_t$ is the future forecast in the market. There are plenty of sources available online (e.g. here or here).

Double-difference forecasting: proposed by Hendry (2006), it assumes past growth rates for future price changes:

$$ \hat{S}_{t+h|t} = S_t \left(1+ \Delta s_t \right)^h \quad h>0 $$

where $\Delta s_t$ is the percent growth rate of $S_t$ between $t-1$ and $t$

inflation-based forecast: use forecasts for inflation to predict oil prices (which according to Anderson et. al. 2011, this is how households predict gasoline prices):

$$ \hat{S}_{t+h|t} = S_t \left(1+ \pi^e_{t,h} \right)^h \quad h>0 $$

where $\pi^e_{t,h}$ is the forecast of inflation, for example, from the Survey of Professional Forecasters.

AR, ARMA, ARIMA regression models: last but not least, the famous AR-based models are very common. Simply regress the price of oil on its past values, using as many lags as you want (or the information criterion tells you), accounting for MA errors (ARMA) and possible cointegration (ARIMA). For example, the AR model with $p$ lags is:

$$ S_{t} = \beta_0 + \beta_1 S_{t-1} + \cdots + \beta_p S_{t-p} + \mu_t $$

After you have estimated the model and obtained values for $\beta_i$, you can forecast oil prices by simply lagging the last $p$ observations one period and put into the model, from where you get $\hat{S}_{t+1|t}$ (assuming $\mu_{t+1} =0$). Then, iterate forward to get forecast for any other future period.


Taxes and GDP, where do these come in in the formula? We all know that the formula for GDP I'd given by

GDP = C + I + G + NX

I would like to know, whether I am right in deducing that when consumers and industry pay taxes, or when there are import and export taxes I suppose, these do not increase the value of C and I in the equation. Instead, these increase the value of G, provided that the money supplied in taxes to the government is spent.

Is this correct?

Thanks.

In this equation:

GDP = C + I + G + NX

Taxes come from a combination of C+I but are offset by an increase in G.

Any government taxation which is not spent is an investment, so remains part of I.


Book for Bretton Woods conferences and gold standard I am looking for a good book to explain to me why the gold standard existed and why in the Bretton Woods conferences, some countries choose to abandon it. An explanation of the general scenario in a historical setting would also be greatly appreciated.

Covering the historical part, you may want to look at:

1) The Battle of Bretton Woods: John Maynard Keynes, Harry Dexter White, and the Making of a New World Order

which appears to be written in a "non-fiction thriller" style, revolving around the argument that

  "(Bretton Woods) was in reality part of a much more ambitious geopolitical agenda hatched within President Franklin D. Roosevelt's
  Treasury and aimed at eliminating Britain as an economic and political
  rival. At the heart of the drama were the antipodal characters of John
  Maynard Keynes, the renowned and revolutionary British economist, and
  Harry Dexter White, the dogged, self-made American technocrat."

while the raw-data option would be

2) The Bretton Woods Transcripts

that

  "...offer the reader a front row seat at the conference that has shaped the international monetary system for nearly 70 years. The
  Bretton Woods Transcripts were never intended for publication, and
  give an inside perspective of what participants at this major
  international gathering said behind closed doors."


Can Direct Taxes on the consumers have a impact on the Demand (rather than supply)? I'm a 12th-grade student doing a school research paper evaluating the effectiveness of the recent increase in Additional Buyers Stamp Duty in the Singapore Housing market. This tax is directly imposed by the government on the consumer after the purchase of housing has been made. So will this have a demand-side effect (I know this isn't really applicable because it's macroeconomics, but contractionary fiscal policy like increasing income tax decreases Consumption and is responsible for a leftward shift in Aggregate Demand) like income taxes? Or will it have the conventional leftward shift in Supply curve (but I'm not sure how this is the case as there is no tax incidence on the producer)? Any help would be great, Thanks!

In microeconomics you can analyze tax incidence on supply demand graph. If you levy tax on consumers this will shift demand curve to the right.

However, this does not mean that whole tax burden rests with consumers. The tax drives a wedge between the price that consumers pays and the price that consumers receive. The whole tax burden is the triangle ABC and you can see that this triangle is split in half by original price. The upper half that cuts into consumer surplus is the tax incidence on consumers and lower half tax incidence on producers.

The tax incidence depends on elasticity of supply and demand. The more inelastic demand relative to supply the more tax burden is shifted to consumer and the more inelastic supply the more tax burden is shifted to producers.

I am not familiar with Singapore’s real estate market but usually the housing market is thought to have elastic demand and relatively inelastic supply so the tax incidence should fall more on suppliers.

Now to your macro question. First of all tax on a single market should not even had any macroeconomic impact in general. When we talk about increasing taxes in macroeconomic classes we usually mean that across whole economy for example increasing VAT that affects all markets.

But let’s for now suppose in Singapore housing market is such a great share of GDP that taxes there have macroeconomic impact. Well this would first in short run shift aggregate demand to the left to new equilibrium with lower prices and GDP but in a long run the equilibrium GDP will be determined by long run supply curve of the economy. As firms adjust to the new prices GDP will go eventually back to the same level but at lower overall price level.

Here is the example of macroeconomic effects of aggregate demand shifts. In the picture demand shifts due to decrease in investment but taxes would work the same way.


How to solve for the potential of a cournot duopoly problem? So i have this question

And i have no clue on how to get to verifying that that function on the answer sheet is a potential Cournot game.

I started answering the question like this, but then i got lost when calculating the MC since i only have c as a unit cost and not total cost.

But probably i was answering the question in a wrong way.

Please tell me if i am.

Could you show me the steps on how to get to the function which is a potential for the Cournot game ?

I have learning disabilities and I have difficulties grasping on to hard concepts like these. If you could show me clear and simple steps to get to the answer it would be greatly appreciated ! Thanks!

A function $P(q_1,q_2)$ is said to be the potential function of a game if its derivatives, coincide with the marginal payoff of each player.

So for example, in your case, if you have that the  payoff of a firm is its profit. Let me call it $\pi_1(q_1,q_2)=TR-TC=p\cdot q_1-c\cdot q_1$ for firm 1 and $\pi_2(q_1,q_2)=TR-TC=p\cdot q_2-c\cdot q_2$ for firm 2, then to check that P is the potential of this game you want to check that $\frac{\partial P(q_1,q_2)}{\partial q_1}=\frac{\partial \pi_1(q_1,q_2)}{\partial q_1}$ and that $\frac{\partial P(q_1,q_2)}{\partial q_2}=\frac{\partial \pi_2(q_1,q_2)}{\partial q_2}$.

The problem is not asking you to solve for the optimal quantity just yet, so $MR=MC$ will not quite help you (at least not in that specific question).

To see more aboutthe definition of a "potential function" and a "potential game" see here.


Why does immigration boost the economy? (or does it not...?) I'm a novice at macroeconomics, and trying to understand the effect of immigration (from developing nations) on the economy of a developed nation. Specifically, I am considering the effect when the nation itself does not have full employment.

So, from what I have read, immigration is a positive thing for the economy in general. The increase in workforce capacity means that production can increase, therefore exports increase, and therefore the economy grows.

However, what if the nation does not have full employment? In this case, there is already a section of society (let's say 5%) which is available to work. This would suggest that there are actually not enough jobs around, and so any immigrants arriving will also not have any jobs. If there had been any jobs for the immigrants to take, then employment wouldn't be at the 5% level. Despite this however, all developed nations have at least some level of unemployment, yet immigration is still beneficial. Why is this?

My suggestions are the following:

Immigrants from developing nations tend to be happier to take on unattractive jobs, which citizens of the developed country may refuse to do. Therefore, whilst the citizens remain unemployed and live off benefits, the immigrants will take on "newly created" jobs which would otherwise not have existed, boosting the economy.
The 5% unemployment rate is actually due to people who are sick / disabled / otherwise unable to work. Therefore, assuming the immigrants are able to work, again there will be new jobs created which would otherwise not have existed.
Higher immigration creates more competition for jobs, causing wages to decrease and allowing companies to pay their employees less. Therefore, the nation's companies make more money, and this causes the economy to grow.

Are any of these correct, or reasonable suggestions? Or are there any other thoughts? Thanks!

Alternatively, is my hypothesis that immigration typically boosts the economy not, in fact, correct?!

You’re right, the migration of workers boost the economy. It’s a stylized fact. It may have political consequences, though, but it is not the part of the analysis of economics. Let’s consider $A$ the set of active labour force of an economy before, and $A'$ after the migration. Then $A$ is the subset of $A'$:
$$A \subseteq A'$$
This notation means that the social planner of the economy is able to optimize on a greater number of workers. We can assume that opening the door for migrant workers is at least as good as it was before migration:
$$A \preceq A'$$
If this condition is not true (e.g. the migrants doesn't want to work), the authorities of the economy won't open borders for migrant workers.

You're considering the effect when the nation itself does not have full employment. This condition is not important. The nation could have 0% unemployment, however, the migrant workers would still get jobs.

  Immigrants from developing nations tend to be happier to take on unattractive jobs, which citizens of the developed country may refuse
  to do.

Absolutely, these people have got different preferences. Here're the utility functions of residents ($r$) and immigrants (i):
$$u_r=C-\alpha_r L$$
$$u_i=C-\alpha_i L$$
where C and L denotes consumption and work. We can conclude that $\alpha_r$ must be higher than $\alpha_i$. The disutility of work is higher in the case of the residents.

  That means migrant workers are more cost-efficient for firms. Higher immigration creates more competition for jobs, causing wages to
  decrease and allowing companies to pay their employees less.

Therefore, the nation's companies make more money, and this causes the economy to grow. Growth and R&D may also improve by means of brain-drain effect, because there are migrant scientists and white-collar workers, too.

  The 5% unemployment rate is actually due to people who are sick /
  disabled / otherwise unable to work.

By definition it is not correct. In Economics, active workers and job-searchers are on the labour market only.

The main concept of migration being good is the increase of the horizon of labour optimization. See also: Krugman & Obstfeld: International Economics Theory and Policy


Fill out Normal-Form Game to obtain exactly one mixed equilibrium I'm given the following incomplete Normal-Form Game:

 | L | R
+--------
O|1,?|7,?
U|?,2|?,1

First I was asked to fill out the missing pieces to obtain a game with exactly two Nash-Equilibria in pure strategies. I came up with:

 | L | R
+--------
O|1,0|7,7
U|2,2|0,1

The next question is to fill out the table to obtain a game with exactly one mixed strategy and I'm stuck at this point on how to approach this.

To ensure that the game has a single, completely-mixed, Nash equilibrium there needs to be "cyclic unique best responses", i.e., either

BR(L) = O, BR(O) = R, BR(R) = U, BR(U) = L,

or

BR(L) = U,  BR(U) = R, BR(R) = O, BR(O) = L.

The strict cyclic preferences both rule out pure equilibria and allow a (unique) completely mixed equilibrium.

There are infinitely many ways to achieve either of the two cases above. Aiming for the first case with BR(L) = O, given that the payoff to the row player for (O,L) is 1, to ensure that BR(L) = O, i.e., the unique best response against L is O, one can set the payoff to the row player for (U,L) as any number strictly less than 1, i.e. so that against L, the row player strictly prefers O with payoff 1 to U with payoff strictly less than 1. The rest of the payoffs can be filled in similarly.


How to track costs and calculate price? I run a large Massively Multiplayer Online (MMO) gaming community and one of the services we’ve try to provide to our members is crafting. One of the challenges of this has been determining the price of crafted items when we sell to our membership.

While a lot of the time the materials that we use to craft items is donated to us; there a plenty of occasions were we run short or need rare materials that make up a bulk of the cost of an item. When this happens, we have to buy them from other players at the market rate in-game.

In a lot of MMOs, the price of the crafting materials can be higher than the crafted item on the market. This happens for several different reasons. Crafting material is necessary to “level” a character’s crafting ability meaning the materials are more valuable than the end result.  Crafting is chance based and some outcomes are less desirable so the non-desirable results are sold to recoup as much cost as possible to fund another chance.

On top of all this, we want to offer our crafted items at a discounted rate than what our membership can get on the open market. Determining a price that keeps our profit margins at least breaking even with our losses have been difficult. In the past, we’ve tried basing the price on the material price with a base discount, but a lot of times this doesn’t adequately cover our costs or beat the prices on the market.

How can we determine a price for an item that takes into account our supply of donated materials and materials we have to purchase? Is there a standard method of tracking costs in this situation?

I'm a gamer and a web developer, not a economist so some help here would be appreciated. Thanks!

The concept which you should be looking it is called prime costs. Businesses use prime cost as a way of measuring the total cost of the production inputs needed to create a given output. Usually this would be e.g. material, working hours, machine time and so on; since in your case there are only materials they are the only components you should consider when calculating the price.

So in your example the prime costs would be cost of purchased material + cost of donated material at market price. After this you would have to add a profit margin which you feel comfortable offering to your members.

As you mentioned their might be cases when the prime costs are higher then prices on the open market. In this case the only thing you can do is sell your material and buy the product directly on the market this is classical make or buy decision. If you still want to offer these product at a discount to the market price your only option is to take a loss on every sold item.