Econometrics: why the i.i.d assumption and weak exogeneity assumption imply strict exogeneity? The proposition is from lecture notes of advanced econometrics of Yongmiao Hong:

A1: $\{Y_t,X_t'\}_{t=1}^n$ is an i.i.d. random sample.

A2: $E(\varepsilon_t|X_t)=0$ almost surely with $E(\varepsilon_t^2)=\sigma^2<\infty$.

Then A1 and A2 imply the strict exogeneity holds:
\begin{equation}
E(\varepsilon_t|X)=E(\varepsilon_t|X_1,...,X_t,...,X_n)
=E(\varepsilon_t|X_t)=0
\end{equation}
My question is about the second equality: why we have $E(\varepsilon_t|X_1,...,X_t,...,X_n)
=E(\varepsilon_t|X_t)$ under assumptions given above?

\begin{align*}
\mathbb{E}\left[ \epsilon_t \vert X \right] &= \mathbb{E}\left[\epsilon_t \vert X_1, \dots, X_t, \dots, X_n \right]\\
&= \mathbb{E} [Y_t - X_t'\beta^0 \, \vert X_1, \dots, X_t, \dots, X_n] \\
&= \mathbb{E} [Y_t - X_t'\beta^0 \, \vert X_t] \quad \text{since $\{Y_t,X_t\}$ is iid.} \\
&=\mathbb{E}\left[ \epsilon_t \vert X_t \right] \\
&= 0 \quad \text{by Assumption A2.}
\end{align*}


Question about an ergodicity in economics paper Disclaimer: I'm not well read in economics but am mathematically literate (PhD in Mech Eng)

Recently I was sent a paper from Nature Physics, "The ergodicity problem in economics" by Ole Peters.

I was discussing this with a friend who also isn't an economist but has more than just a passing interest.

He made the claim that in figure 2 of the paper the graph is wrong i.e. that the expectation values (the blue line) are wrong in that they should be plotting a plot of 0.9^(number of rounds/2), which would have a negative slope. He then goes on to say that this renders the paper garbage.

Now obvioulsy this paper was published in Nature Physics which currently has an impact factor of 22.8 so I find it hard to believe that this would have slipped past peer review.

So my question, is the paper wrong or is my friend?

EDIT #1:

One of the comments was where did the expectaion equation derive from. I'm not sure of my friends derivation but if you run the model proposed in equation 2 of the paper then you do indeed get an ever decreasng return. I used the following Python code to run the model...

from matplotlib import pyplot as plt
import numpy as np

wealth     = 1000
num_tosses = 1000
h_t        = np.random.randint(1, high=1000, size=num_tosses)
x          = []
acc_wealth = []

for idx, toss in enumerate(h_t):

    if toss % 2 == 0:
        wealth = wealth + (0.5*wealth)
    else:
        wealth = wealth - (0.4*wealth)

    x.append(idx)
    acc_wealth.append(wealth)

fig = plt.figure()
plt.plot(x, acc_wealth, "o-", lw = 2)

A typical plot of accumulated wealth v toss number....

This is clearly not what we're seeing in figure 2 of the paper...

Here the blue line is the accumulated wealth (log scale on the y axis) v toss number. It is increasing!!!

EDIT #2

I'm going to post an amended version this on the Statistics Exchange page too.

EDIT #3

Answer from Cross Validation Stack

OP's Python code is computing one path in time and is not averaging over the paths. So it is not the value shown in the plot. In fact what the OP's Python code computes is $(1+\Delta x_H)^h(1-\Delta x_T)^t$ where $h$ denotes the number of heads and $t$ the number of tails tosses. It is closer to the red line which is the most likely path where $h=t$.
$$\mathbf E[x_{t+1}|x_t] = \big[(1+\Delta x_H)p_H+(1-\Delta x_T)p_L\big]x_t=(1+p_H\Delta x_H-p_L\Delta x_T)x_t=:ex_t,$$
and
$$\mathbf E[x_{t+1}|x_{t-1}]=\mathbf E[\mathbf E[x_{t+1}|x_t]|x_{t-1}]=e^2x_{t-1}.$$
So $\mathbf E[x_t|x_t]=e^tx_0$ exactly as shown in the paper plot. This can also be derived directly through the generating function of the expected $\frac{x_t}{x_0}$ which is, due to the independence of each toss, simply the product of all the dot product of payoff and its associated probability, i.e., $e^t$.


Does a negative interest decrease the money supply? If there is less money, its value increases.
There is less liquidity when there is less money.
Does a negative interest decrease the money supply?

Especially when people don't need money: they saved it up but nobody needs it -- nobody needs to borrow it from them so they saved up for their pensions and now they want to buy a pension but nobody really needs their money. So a negative interest rate is established to entice them to spend it: a little late because they are buying pensions but OK. They are too old to spend it well. They think the washer will outlive them. So they leave the money in the incinerator of negative interest bank accounts. Then there is less and less money. Now somebody wants to sell something (liquidate it) but there isn't that much money there at the moment. It was burnt. The money becomes a kind of commodity that people are willing to pay more assets for. The asset price in currency is lower. People think, hey cool: Let as much people as possible have their money burnt so that my cash becomes more valuable. Run on the bank. But then it turns out that the CB really can print money...

Here's a story. I guess it can be what happened in the repo market recently.

Definition of Money Supply:
The money supply is the entire stock of currency and other liquid instruments circulating in a country's economy as of a particular time. Because of it's definition, the money supply can only be affected if a central bank prints or burns currency. Thus, technically, rates don't affect it per-se.

Velocity of money and money in circulation:
What you may be thinking of is related more with how much money is in circulation and how fast it changes hands.

Effect of negative rates:
In theory, when rates go up, money flows into bonds and "leaves" circulation. By the same logic when rates go down, money flows out of bonds and "enters" circulation.


Would GDP for a pure endowment economy be equal to zero? (Am I correct?)

As far as I understand, a pure endowment economy means that good just appears in the country without any labor involved in producing them. Like maybe given country lives entirely from aid/gifts/tribute sent from abroad, literally producing nothing of its own (including services).

There are three ways that show that GDP=0

1.GDP stands for Gross Domestic Production. In a pure endowment economy there is no domestic production as such, thus GDP should be equal to zero.

2.We can try to calculate GDP using the income approach. This can result in negative GDP.

GDP=TNI+Sales taxes + Deprecation + NFFI

TNI=Wages + Rent + Interest + Profit

Wages=0 because nobody produces goods (including services!) inside the country.

Profit>=0. There is no profits domestically because nothing is produced domestically, but it's possible for local corporations to get profits aborad.

Interest>=0. Lending money is a service, but there are no local services in our economy, thus no lending to by local lenders to the citizens/firms of the country. But it's possible that local lenders lend their their money abroad.

Rent=0 because renting land is a local service and there are no local services (renting a building isn't an option because nobody builds anything in the country and it's not possible to sent a built building from abroad). So either nobody lends their land OR all lands are common property of all people living inside the country OR property rights over land don't exist as such

Thus TNI>=0. If TNI>0, then TNI+NFFI=0.

Sales Tax=0 because there is no State to collect taxes. And there is no State because any State provices services like the police, the army, the public healthcare, etc. The only way to not have all of these services, is to have NO entity with monopoly on violence, consequently making it impossible to collect taxes.

Deprecation=0 because businesses would have no capital to deprecate

NFFI=Income of foreigners earned here - Income our citizens earned abroad.

Income of foreigners earned here=0 because Wages,Rent,Interests,Profits=0 domestically (i.e. they can be >0 only if they get money from abroad)

Now it's possible that our citizens earned something abroad, in this case NFFI will become negative, but it will be compensated by equaly-sized positive TNI, consequently making the whole GDP equal to zero.

3.We can caclulate GDP using the expenditures approach.

GDP=Consumption+Investements+Government expenditures+Export-Import

Government expenditures=0 because there is no State.

Consumption=positive number because although there is nothing to buy on the national market it's possible to spend money on imported goods.

Investments=0 because there are no businesses and no new homes to be bought by households.

Export=0 because these are supposed to be goods produced in the country but sold aborad.

Import>0 if our citizens earn money abroad. In this case they can buy goods abroad too and then consume said goods inside the country. This coupled with positive "Consumption" will result in in GDP=0

P.S. From what I read I concluded that the number 1 is incorrect because production of endowment, although happens somehow magically, without any labor of our workers (for an example, it's produced out of the thin air by a magic lamp) is still DOMESTIC production.

The number 2 is incorrect because it's possible to sell endowments to other citizens and get positive profit as the result  (i.e. domestic profit>0).

The number 3 is incorrect because other citizens would buy (domestically!) endowments owned by other citizens/firms. Thus at the least Consumption would be >0 for domestic goods.

GDP would not be zero in endowment economy in general. There are still prices and also interest rates, savings and investment in endowment economy. First, lets ignore other countries because foreign aid complicates GDP calculations (as Art pointed out if the endowment is foreign aid GDP would be zero). So lets suppose there is only one country, lets call it Arstotzka, which has an endowment economy (i.e. production is fully exogenously given).

A simple macro endowment model of economy would be the following.

There is one representative individual with following utility

$$u = \sum^T_{t=1} u(C_t)$$

where $U$ is the utility, and $C_t$ is a consumption at time $t$. Standard assumptions apply $U'(C_t)> 0, U''(C_t)< 0 $, that is utility is increasing but at decreasing rate.

Now this will be an endowment economy so lets assume initial endowment of $A_0$ and additional per period endowment $Y_t$.

Logically consumption must be equal or less the endowment, but rational consumers will always use up their whole resources (in this model there is no inheritance) so I can set it as an equality (this just simplifies the math):

$$\sum^T_{t=1} C_t= A_0 + \sum^T_{t=1} Y_t$$

This problem gives us the following lagrangian:

$$\mathcal{L} =  \sum^T_{t=1} u(C_t) + \lambda \left( A_0 + \sum^T_{t=1} Y_t - \sum^T_{t=1} C_t\right) $$

First order conditions are given by:

$$u'(C_t) = \lambda \implies C_1 = C_2 = C_3 =... =C_T $$

This means that the consumption will be same in each period because marginal utility of consumption is constant.

Hence we know consumption will be $C_t = \frac{1}{T}\left( A_0 + \sum^T_{t=1} Y_t \right) $

Furthermore, assuming no government and hence no public saving the saving is by definition just difference between endowment income and consumption at time $t$ $S_t = Y_t- C_t$

Now lets parametrize our model.

Lets suppose we only have two years $t=1,2$. Next the initial endowment is set to 0\$ (to simplify calculations) and the per period endowments are $Y_1 = 60\$ $ and $Y_2= 40\$ $

Hence consumption based on the above solution will be $C_1 = 50\$, C_2=50\$$ so in period 1 there is 10 dollars of savings and in period 2 10 dollars of dis-saving $S_1=10\$ $  $S_2=-10\$ $.

Now GDP using consumption approach would be in period 1 $Y = C + I + G = 50 + 10 + 0 = 60 $ (since $I=S$  which is the same which you would get through the income approach as by our set up the endowment in $Y_t = 60\$ $.

To sum it up GDP wont be zero because endowmends are income. In real life on a tax return it would be some windfall profit but regardless thats just semantics. In real life pure endowments dont exist so we dont really have a name for them in accounting formulas but the point of income approach is to add whole income of a nation regardless of how you call the source of income as long as it was produced withing borders of a country for GDP. For expenditure, approach you again just add all spending in an economy again regardless of the fact that spending was based on purchasing some some endowment output $Y_t$ or actually produced through some inputs.


What does a stock market index stand for? I know that a stock market index (like S&P, NIKKEI, etc.) is computed from the prices of selected stocks, but I was wondering why the name of the currency is almost never expressed. For example, if the S&P price is 2927 points I assume those are dollars, but how about NIKKEI? Is its price is expressed in yen? Is DAX expressed in euro? Is there a standard in financial community?

Indexes don't have units. They're indexes.

An index is a ratio of two numbers. The two numbers have the same dimension. So their ratio is unit-less.

The compilers of each stock market index set a denominator which represents a base set of conditions, and they then may adjust that denominator to ensure that events that change market cap, but which should not change the index, do not change the index. The sum of the market capitalisations of all of the index members forms the numerator. These are both expressed in the domestic currency (so for the FTSE 100, the currency is GBP; for the S&P 500, the currency is USD)

For more, see https://www.investopedia.com/ask/answers/040215/what-does-sp-500-index-measure-and-how-it-calculated.asp

Stock market indices are still exposed to currency variations, because the denominator is not adjusted for currency variations, and the numerator is exposed to them: the index members' market caps are all in the same currency, and their profitability will almost always have some exposure to the currency too.

For a multi-currency index, a standard currency is chosen, and then each company's market cap is converted to that currency. Again, the numerator and denominator are expressed in the same currency, so the index has no unit.

The one freak in all this is the Dow Jones Industrial Average, which doesn't behave like other indexes (it's an index, but it's a straight price average, not weighted by market cap), and should, broadly speaking, just be ignored.


Existing metric for personal productivity hours needed per life hour? With about 50 hours of productivity a week, including work, cooking, etc. I can complete the tasks and pay the expenses necessary to live about a week. Subtract maybe 5 hours of labor that goes into personal savings, and 45 hours of weekly work affords me 168 hours (1 week) of life.

Thus the number of hours of "life" that a single productivity hour buys me is about 3.7. I'd imagine in parts of the developing world, this can get as low as 2 or even 1.5, while for the best earners in the cheapest markets, this may exceed 1000, though obviously with very high earners, the meaning of "life expenses" is very much up to interpretation. But I just made this metric up.

Is there a formalized, existing metric for how many hours one gains from a single hour of "work"?

It seems to me this seminal paper has looked at the question

Gary Becker - A Theory of the Allocation of Time

You can use economic intuition to establish the value of one hour of work in terms of one hour of life. Suppose you have a consumer/worker that has to choose how much time to devote to work or leisure. His total daily hours allotment is

$24=h+\ell$

where $h$ is the number of hours worked and $\ell$ is the number of hours of leisure. He values leisure according to some utility function $u(\cdot)$ and his total utility also depends on the amount of goods $x$ consumed

$U(x,\ell)=x+u(\ell)$

he earns a hourly wage $w$. He spends all of his income in this single consumption good, which we assume has a nominal price of 1$. Therefore he has the following budget constraint

$x=wh$

Then, if the consumer/worker is choosing optimally how much to work the margin, it must be true that, on the margin, one hour of leisure has the same value as one hour of work

$\dfrac{\partial u}{\partial\ell}=w$

In other words, he must be indifferent on the margin between working
1 more minute or using it for leisure.

To know the value of every hour of leisure we need to know of course the function $u(\cdot)$. But at least on the margin, if you want to know what's the value of one unit of time not spent on work - there you have it: it's the hourly wage rate.

Becker suggested you could use that intuition to include leisure and household production in GDP. You should weight all hours not spent on work by their respective wage rate.

With regards to your initial question: how many hours of "life" do you gain for every hour of work? It should be 1, otherwise you're not choosing your leisure time optimally.

R.I.P. Gary Becker, Nobel Prize in Economics. I had the privilege of attending his last Price Theory course at UChicago before he died. He lectured on this.


The 'Economic Man' (Reference Request) We are writing a paper about the 'economic man.' By this, we mean that the choices he makes epitomize a rational economic thinker. However, we also acknowledge the fact that there are other, non-economic reasons that people make decisions such as religion. What (if any) literature addresses the idea that even with other considerations, a person will still act rationally in the economic sense. Preferably we would like to have a theoretical model that encases these other choice considerations. Also, we would love to hear whether there are any case studies on this idea.

I would point you firstly to work pioneered by the late Gary Becker on applying the principles of economic optimisation to non-market behaviour.

Becker's insight was that the kinds of trade-offs people face when trading goods and services also affect many other kinds of decisions, including things such as criminal behaviour or marriage and family life. For example, Becker modelled criminals as deciding what crimes to commit based on an evaluation of the costs (if caught) against the benefits flowing from the crime's proceeds (whether material or psychological). A list of Becker's papers can be found on Repec.

Becker's style of applying economics to such topics has been influential and there are now huge literatures applying economics to social behaviour of every variety—to the extent that it is hard to even know where to begin summarising such literatures.

At the time of Becker's death, many leading economists wrote articles summarising his impact on the field of economics.

Becker's contribution was recognised with the award of the 1992 Nobel Prize. The citation read

  for having extended the domain of microeconomic analysis to a wide range of human behavior and interaction, including nonmarket behavior.

The Nobel press release is here and his Nobel lecture "The Economic Way of Looking at Behavior" was published in the Journal of Political Economy.


In classical macroeconomics, why Labor supply responds to real wages and not money wages? real wages =  money wages/price(P).
what are the assumptions here?
why labor doesn't respond to money wages ?

To begin with, economics is all about assumptions. Because of classical dichotomy, money level doesn't impact the growth of an economy in the long run. Money has no effect on GDP in classical macroeconomics. If you want to model the effect of money, you have to introduce nominal rigidities in your model. That means, at least the goods market or the labour market is NOT perfect. If labour responds to money wages, the result would be a prefect market situation.

According to Keynes (General Theory, 1936),  the nominal wage (money wages) is completely unresponsive to current-period developments (at least over some range):$$W=\bar{W}$$
As you can see, because nominal wages are sticky, the result is an imperfect labour market. Because the labour market is imperfect, there is unemployment.  The
labor market has some non-Walrasian feature that causes the equilibrium
real wage to be above the market-clearing level.
In Keynes's model, aggregated labour supply is given. Firms are competitive and their prices are
flexible, and so they hire labor up to the point where the marginal product
of labor equals the real wage: $$F'(L)=\frac{\bar{W}}{P}$$

The main conclusion of Keynes' model is that GDP and real wages are countercyclical. Later, it was turned out to be moderately procyclical by empirical research.

Other more sophisticated models:
 - sticky prices, flexible wages, perfect labour market
 - sticky prices, flexible wages, imperfect labour market
 - flexible prices, sticky wages, imperfect labour market

If you want to model nominal effect, you should take note of nominal wages. If you are modelling fiscal shocks without the effect of the money, then considering real wages are maybe enough. It depends on one's research philosophy.


Intellectual property as a retarder of innovation I am aware of some work such as

  O'Donoghue (1998): "A Patentability Requirement for Sequential
  Innovation", RAND Journal of Economics

and

  Hunt (1999): "Nonobviousness and the incentive to innovate: an
  economics analysis of intellectual property reform"

that discuss cases in which offering better protection for intellectual property (in these cases, by lowering patentability requirements) might reduce the incentive for firms to innovate.

Very roughly, the basic mechanism in these papers is that lowering the threshold for patentability means that an incumbent with a patent expects to be superseded by someone else with a better patent very quickly. Since the advantage to a patent does not last long, the incentives to invest in innovation to acquire such a patent are reduced.

I am curious whether people can suggest other mechanisms by which strengthening intellectual property protection (including moving from no protection to a positive degree of protection) can reduce innovation, and provide relevant references.

The cuisine and fashion industries both largely exist without intellectual property protection other than trademarks (n.b., they can use copyright on certain aspects of their work but this is generally thought to give little protection) yet they seem to flourish. How is this possible?

In fashion, it is thought that copying the work of other designers can be good for everyone, allowing the industry to have a color of the year and products like bags and dresses at various quality, fit, and price levels.

There may be related forces at play in cuisine. It is difficult to imagine the Cronut fad lasting as long as it did without other bakeries making very similar efforts to keep customers interested and the product in the news.

This is only one mechanism. Another mechanism giving rise to negative outcomes is barriers to entry. Think of patents as raising the returns and costs both to entry into an industry. They raise returns because conditional on getting greater IP protection you have more economic rents from your IP based monopoly. But because others already have these heavy protections the cost to a new entrant of innovating and litigating in a way that permits entry to the industry will be much higher. The consensus seems to be that at some point the marginal benefits of greater protection fall faster than the marginal costs of entry increase, leading to something like the Tabarrok Curve for patent protection:

Source: Marginal Revolution


If the Number of Workers in an Economy Doubled, Would Productivity Fall to Half its Former Value? I am assuming that the production function for the economy has constant returns to scale, and all other inputs stay the same.

These are the steps I have made to try to answer this question:

1) Y/L = Productivity

2) Therefore, if Y=3 and L=2 (There were 2 workers in the economy), so Productivity = 3/2

3) L doubled, so now L=4

4) Now Productivity is equal to 3/4.

5) Productivity has therefore fallen by half of its former value.

Am I right in stating this? If not, can you please explain to me where I am going wrong?

Since you say holding other variables as they were and double $L(t)$ I assume you have a production function that may include capital $(K(t))$, including this and assuming a Cobb-Douglas production function:

$$ Y(K(t), L(t)) = K(t)^{\alpha} L(t)^{1-\alpha} \; \; 0< \alpha < 1 $$

Doubling $L(t)$ gives, (and omitting $t$ from the writing for clarity):

$$ Y(K, 2L) = K^{\alpha} (2 L)^{1-\alpha} $$

$$ = 2^{1-\alpha} Y(K,L) $$

$$ \Rightarrow \frac{Y(K, 2L)}{2L} = \frac{2^{1-\alpha} Y(K,L)}{2L} $$

$$ \frac{Y(K,L)}{2^{\alpha} L} < Y/L $$

So yes in this sense as you described doubling labour decreased productivity.

You mention $Y$ having constant returns to scale, this implies if you double both $K$ and $L$ then $Y$ will double as well, then productivity will stay the same


Ordinal utility and monotonic transformations If u(x) is an ordinal utility function that represents the (weak) preference relation R, then
(a) any strictly monotonic transformation of u(x) also represents $R$, or
(b) any monotonic transformation of u(x) also represents $R$.
Which is the right proposition, (a) or (b)?

I thought that (b) is the right answer, but when I looked up various online sources I found both definitions, so I'm no longer sure.
I thought (a) cannot be right, because the condition for a monotonic transformation is usually formulated as a conditional: F is a strictly monotonic transformation of u if the following holds: (1) if $u(x)>u(y)$, then $F(u(x))>F(u(y))$. But that doesn't deal with the case (2) $u(x)=u(y)$, which represents xIy. Wouldn't $F(u(x))>F(u(y))$ be compatible with (1) and (2), but represent xPy? Thinking about it, however, it seems that the same as (1) with "greater than or equal" wouldn't do it either. Are the monotonicity conditions formulated as biconditionals? I'm confused.

You need to be clear about the definitions. Lets take:

(1) $u: X \to \mathbb{R}$ represents $\succsim$ if $u(x) \geq u(y) \iff x \succsim y$.

(2) A function $h: \mathbb{R} \to \mathbb{R}$ is monotone if $z \geq w \implies h(z) \geq h(w)$. $h$ is strictly monotone if $z > w \implies h(z) > h(w)$.

First, note that every strictly monotone function is monotone. Why? Well let $z \geq w$, and there are two cases to check: (i) $z > w$: apply the definition; (ii) $z = w$: then $h(z) = h(w)$ by the definition of equality (this is because $\mathbb{R}$ is a totally ordered set).

So immediately, we see that your condition (b) implies your condition (a). However, (b) is false (I do not understand Kanak's line of reasoning, but it is certainly wrong, although perhaps can be rationalized by non-standard definitions). To show that it is wrong, we need a counter example. Lets let $X = \{x,y\}$ and let $x \succ y$. Then $u(x) = 1$ and $u(y) = 0$ represents $\succsim$. Moreover, $h: z \mapsto 0$ is a monotone transformation. But, $h(u(x)) = h(u(y)) = 0$ does not.

Indeed, this example shows that it is weakly monotone transformations that destroy information (they need not be invertible), which in terms of the representation, indicates that strict preference gets collapsed into weak inequality.

Showing that (a) holds is a straightforward application of the definitions. (Hint: show that strict monotonicity can be defined via a bi-conditional statement).


How to properly interpret logged interaction variables I have the following regression to interpret elasticity of demand:
$$\ln(demand) = const - 0.6*\ln(fare)$$
I understand that a 1% increase in fare results in a 0.6% decrease in demand
I want to add dummy variables for days of week (excluding one of course) and want to add day-of-week $* \ln(fare)$ interactions so that I can determine the elasticity of demand by day of week (which I already know differs)
For simplicity in writing this out let’s pretend there are 3 days: mon, tue, wed and I will leave Wednesday out as my base
So now my regression is:
$$\ln(demand) = const - 0.45*\ln(fare) + 10*(mon) + 15*(tue) + 0.05*\ln(fare)*(mon) - 0.15*\ln(fare)*(tue)$$
Here, my elasticity of demand for Wednesday is interpreted as a 1% increase in fare results in a 0.45% decrease in demand
But my question is how to interpret elasticity of demand for Tuesday. I know that the interaction and even the dummies are relative to the base.
So the question is for Tuesday should The coefficients be added? Or multiplied since it’s logged?

You have to add them even though they are in $\ln$ the model is still linear in the parameters. To see this more clearly you can rewrite your equation as (I use $D$ for demand, $c$ for constant, $F$ for fare and $M$ and $T$ for Monday and Tuesday):
$$\ln(D) = c  + \left(- 0.45  - 0.15(T)  + 0.05(M) \right)\ln(F) + 10(M) + 15(T)$$
Hence when both $T=0$ and $M=0$ the elasticity for Wednesday is -0.45, when $T=1$ and $M=0$ (i.e. its Tuesday) the elasticity is $-0.6$, and finally when $T=0$ and $M=1$ (i.e. its Monday) the elasticity is $-0.4$.
If you want to learn more Wooldridge discusses this in his introduction to econometrics in chapter 7.


Commercial bank balance sheet after Fed purchases $10 million in Treasury Bonds Suppose the Fed conducts an open market purchase by buying $10 million in Treasury bonds from Acme Bank. Sketch out the balance sheet changes that will occur as Acme converts the bond sale proceeds to new loans. The initial Acme bank balance sheet contains the following information: Assets – reserves 30, bonds 50, and loans 50; Liabilities – deposits 300 and equity 30.

The sale of the bonds (assets) will only affect the assets-side of the balance sheet.

If Acme bank did not lend out the money, your “bonds” would go 50-10 = 40. And your cash would go 0+10 = 10.

If they lend out the money, bonds still go to 40 and lending goes up by 10, so 50+10 = 60.


Which measures are there to evaluate a country economical development? I'm familiar with the measures of Gross domestic product (GDP PPP) total, per capita and GDP nominal total and per capita. But I'm not sure if these measures evaluate the economical development of a country since they don't take into account what a country owes, and external debts sometimes get countries into economical crisis when they become unable to pay them.
Then I found about net international investment position (NIIP) that is defined as a country's external financial assets and liabilities.

My question is, can this measure be used to evaluate the economical development of a country and if not, are there specific measures which are used to evaluate economical development?

Your question brakes down into:
- Alternatives to measure "economic development": there are several ways to interpret what development is, it can be social, intensity of money flows, or volume of "money flows".

If you look for social development and well-being, the HDI (Human Development Index) is a good start, but there are several others like the Genuine Progress Indicator (GPI)

If you look more to assess the level of financial risk that a government or country is exposed to (debt wise) in combination to the wealth generated in that country, you can take as an example what the European union measures for economical stability: a combination of Budget deficit to GDP and debt-to-GDP ratio.


What's wrong with have a 'one second tick' on stock market trades, to prevent high frequency trading? Part of how high frequency trading works, is by taking advantage of millisecond advantages over other traders in communicating with the stock exchange.

To gain these advantages, high frequency traders have moved their servers closer to the stock exchange's server, or have rebuilt a a Chicago - New York IP cable to be straighter and thus reduce latency by milliseconds.

To create a 'fair playing field', traders can put all their servers in the same building, and each be given the same length of cabling.

HFT has been criticised essential for giving the high frequency traders an unfair advantage.

My question is - why not just make the stock exchange work on a one second 'tick'. ie. during that second trades are queued up, and on the tick, they are all executed simultaniously.

This would prevent any - 'see other people's trades and buy them before they do' type trades.

There is nothing wrong with your idea. Some people may say that it would reduce liquidity - but there is way more than enough liquidity in the system already. HFT is just parasitical - it serves no useful purpose.

A small transaction tax would have a similar effect.


Do rich people on average have the vast majority of their wealth invested or they have lots of liquid cash/no productive properties? I often read about really rich people with billions of dollars, and I'd like to   know if they have, for example, just a big part of their wealth in shares of their company or they have lots of wealth in not productive activities?

The Federal Reserve has two statistical programs that I believe might address your question. The first is the Survey of Consumer Finances (SCF) and the second is the Flow of Funds (FoF). You should be able to find the data on the Fed's website.


Open market purchase of securities and it's effect on balancesheet An open market purchase of securities lead to increase in bank reserves ( Liability side) and increase in assets(asset side) of central bank balance sheet.
My doubt is why it leads to increase in Reserves?

When the central bank buys anything, it transfers a deposit (reserves) to the reserves account of the bank of the seller. (The seller could be the bank itself, or a customer of the bank.) This keeps everyone’s balance sheet in balance.

Until the central bank does something to destroy reserves (e.g. sell something), all the bank can do is transfer the reserves to other banks. That is, the reserve increase is “permanent,” even if the initial bank gets rid of them.


Why doesn't land value go to 0 when tax rate goes to 100%? I'm looking at this equation here:

$$y = \frac{ra}{r+x}$$

Where:

$y$ = market value of land
$r$ = real interest rate, set at 0.01
$a$ = land value, set at 1
$x$ = tax rate

I don't really understand this equation conceptually.

The correct answer is that it does not. It goes to zero as tax rate increases to infinity.

The reason for that is that the rent derived from land (assuming away any necessary land maintenance) can be thought of as a windfall gain. As a result all incidence of burden from such tax must fall on the holder of the land. Already If the tax is equal or above 100% the whole rent is confiscated and hence the holder of land would be willing to sell it away for nothing, although in the model you shown 100% tax rate would not reduce the property value to zero but to:

$$y=\frac{ra}{r+1}=\frac{0.01}{1.01}\approx0.0099>0$$


Question about the "No Dictator" Criterion in Arrow's Impossibility Theorem I have a question about Arrow's impossibility theorem. I'm not sure I understand exactly what is meant by the "no dictator" criterion. Does the presence of a "dictator" mean that across all possible combinations of individual preference orderings for N individuals, the same person's preferences will always match the group preference ordering exactly? Or does it simply mean that across all possible combinations of individual preference orderings for N individuals, there will be some individual for each one of those combinations whose preferences match the group preferences exactly, but that individual doesn't necessarily have to be the same for each combination?

If the former, I can clearly construct a counter-example that (I think) satisfies the other two criteria (unanimity and independence of irrelevant alternatives). For example:

Combination 1:

Person 1: A > B > C

Person 2: B > A > C

Person 3: C > A > B

Group preference: A > B > C

Combination 2:

Person 1: A > B > C

Person 2: B > A > C

Person 3: B > A > C

Group preference: B > A > C

In this example, Person 1 is the "dictator" in combination 1, but not in combination 2. Therefore, by the first definition above of "dictator" there is no dictator in this system (I'm also assuming I haven't violated the other two criteria: someone please point out if I have). If we're going by the second definition of "dictator" above, sure, this system has a "dictator" under each combination, but this doesn't seem like an appropriate definition to me. If the ballot changed with new issues to rank (e.g. A*, B*, and C*) these "dictators" might not hold sway anymore, so are they really "dictators" in the sense we normally think? Or is it just happenstance that their preferences happened to align with the group preferences one time? Obviously, there's something about the theorem that I'm not understanding, so if someone could please clarify that for me I'd be very appreciative. Thanks!

Arrow's Theorem concerns a social preference function ---that is, a function that produces a group preference order for every possible profile of individual preferences.  The axioms "Nondictatorship", "Independence of Irrelevant Alternatives", etc. must then be satisfied by the function at every profile.  (To be more precise, an axiom like IIA involves a comparison between the behaviour of the function at two different profiles.  So it must be satisfied by the function for every pair of profiles.)   Your counterexample only shows me the outcome at two particular profiles;  it does not specify the function itself.  Until you specify a function, we can't know whether the axioms are satisfied.  Arrow's Theorem says that, when you try to extend your example to completely specify the outcome at every profile, sooner or later you will run into a situation where you must violate one of the axioms.


What is the best way to compare the price of a GB of internet across countries I have the average price of a GB of data / internet across 45 different countries. I want to be able to compare the price of using data on the people in that country.
Let's say 1 GB of data costs 1.37 USD in the USA and the equivalent of 1.1 USD  (regular conversion rate) in China. I cannot state the the internet is "cheaper" in China than it is in the US, as 1.1 USD in China could buy so much more for a family living there and therefore is more taxing on their income than 1.37 USD would be on an American family.
How can I compare the effect that spending these 2 values could have on a family in these 2 countries? Would the purchasing power parity be the right way to go here? If so, can someone explain to me how to use it? I looked up the PPP in China, and it's 4.15.
I read online that to compare the price of the good across both countries we would calculate: 1.1 / 1.37 / 4.15 = 0.19. So the price of a GB of data is about a fifth of that in the US? And not almost the same? But that's not what I'm looking for, I'm looking for a number that would tell me that since life is so much cheaper in China, and spending a dollar is so much more taxing.
Wouldn't (1.1 / 1.37) * 4.15 = 3.33 make more sense? So spending 1 USD in the USA on internet would be equivalent to spending 3.33 USD in China for the same amount of internet?

Purchasing Power Parity (PPP) is probably the most convenient way of doing such comparisons so you are on right track. As mentioned in the comments there are other ways how to do international price comparisons but PPP is probably one of the few ways that do not require much auxiliary estimation/research as it is already readily avaiable to public.
PPP works in a very similar way to an exchange rate. In fact PPP is sort of an exchange rate built under the assumption that the law of one price holds (Krugman et al (2012). International Economics: Theory and Policy). Consequently PPP is an alternative to market exchange not another factor you use on top of it (so the calculations in question are not appropriate).
For example, if in China 1 GB of data costs $¥10$ and PPP is $4.15 \frac{¥}{\\\$}$, the adjustment would be made as: $¥10/(4.15 \frac{¥}{\\\$})\approx {\\\$}2.41$. Afterwards, the prices can be compared as apples to apples so in this case 1GB of data in China would be more expensive than 1GB of data in US (which according to your data costs ${\\\$}1.37$ ), once adjusted for PPP (although I just made the $¥10$ price up you should use your prices).
Note, even tough it is not always stated PPP is implicitely expressed in $\frac{\text{local currency}}{USD}$ since it is based on comparison of price levels of two countries and by convention US is always in denominator. In fact most datasets will even warn you about this. For example, OECD dataset reports its PPP as:

Purchasing power parities (PPP)Total, National currency units/US dollar,
[emphasis is mine]

You can read more about PPP in Krugman et al. International Economics: Theory and Policy 9th ed. Chapter 16. It is an undergraduate textbook so it contains some worked simple examples.


robinson economy with production Facing a little bit of a problem with this questions, did a similar one BUT the utility function was not linear and got MRS dependent on goods (was not just a number) - here I am at a loss.

The question: There are two individuals A and B, each having one unit of time which can be used either for leisure or labor (to produce a good to consume). Their utility functions are respectively:

  uA(lA,cA) = 6(1-lA) + cA and uB(lB,cB) = 10(1-lB) + cB

Where 1-lA/B is the leisure time for A/B. Furthermore, we know that A can produce 4 units of the consumption good per 1 unit of labor time, and B can produce 24 units of the consumption good per 1 unit of labor time.

The last information I transformed into:

  cA = f(lA) = 4lA and cB = g(lB) = 24lB

(where f and g are some production functions)

I am being asked to find the set of Pareto-optimal allocations of consumption and labor.

I assume I need to start with MRSA = -6 (or 6? never know when to use negative/positive?) and MRSB = -10. However, I am not sure what piece of information I can get from that? I assume that indifference curves are lines, right? And that they will always cross, which then would imply that the set of Pareto-optimal points is on the boundary of Edgeworth box?

On the other hand, these guys maximize their utilities so that:

  max 6(1-lA) + cA = max 6(1-lA) + 4lA = max 6 - 2lA

and

  max 10(1-lB) + cB = max 10(1-lB) + 24lB = max 10 + 14lB

meaning that lA = 0 and lB = 1. That is, A will spend his 1 unit of time for leisure: 1-lA = 1-0 = 1 and B will spend his 1 unit of time for labor.

Two other questions are:

Find Pareto-optimal allocations that are also envy-free.
How would the analysis go when A could produce 7 units of good per 1 unit of labor time.

But I think I should be able to answer them, after some hints for the first part of the question. ;)

Hint 1: So I think you are making a mistake by substituting their production technology into their utility: when you went from $\max 6(1-l_A)+c_A$ to $\max 6(1-l_A)+4l_A$, by doing this, you are assuming that $A$ only consumes what she produces.

Hint 2: Let me give you a Pareto optimal allocation: $B$ spends his $1$ hour working to produce 24 units of consumption and gives them to $A$ who spends her 1 hour in leisure. This allocation is feasible (there are enough resources to do it, given the technology), and it is Pareto optimal because $A$ is the happiest, so there is no way to improve $A$, and in order to improve $B$, you would have to decrease $A$'s utility. Of course, this is allocation is not envy-free, but it is a Pareto optimal allocation.

Hint 3: I would first find all the possible allocations in order to then see which ones are Pareto, and then which ones are envy-free.


Can we compare risks of lotteries? I understand the concepts of risk-aversion, risk neutrality and risk-attraction. I wonder if it possible to compare risks between two lotteries without giving the utility function. For instance,  Let X = (10, 20, 30) and consider two lotteries L1 = (1/3, 1/3, 1/3) and L2 = (5/12,1/6,5/12). Can we say that one lottery is riskier than the other?

You might be looking for the concept of stochastic dominance:

Roughly speaking, first order stochastic dominance of distribution A over distribution B, means that for every possible outcome gamble A pays out weakly more and in at least one state it pays out strictly more. Roughly speaking, second order stochastic dominance means that distribution A has the same risk as distribution B but a higher mean (but not necessarily weakly-higher in every state of the world. Alternatively, you preserve the mean of distribution B and you "scrunch" the probability mass to create distribution A. "All risk-averse expected-utility maximizers (that is, those with increasing and concave utility functions) prefer a second-order stochastically dominant gamble to a dominated one."

The seminal paper is Rules for Ordering Uncertain Prospects (Hadar and Russell (1969))


how is new money actually introduced in the United States? I'm aware that the fed controls the supply of money by contracting and expanding through permanent and temporary open market operations. Consisting of purchasing Treasury securities or through repos. These are sold primarily to primary dealers I  derstand but also to other organizations.

Can someone explain how the interest that is paid is set during auctions? Additionally it seems that the securities alone can not introduce money but through the interest paid on them?

The Treasury auction process is described here: Treasury Direct

Bidders can either enter competitive or non-competitive bids. Non-competitive bids are limited in size; the price is set by the competitive bids, which generally come from Primary Dealers (that are obliged to bid).

As a simplified example of the bidding process, assume that the government announces an auction for $2 million in 30-year bonds. (Note that this example ignores bidding size limits.)

There are three bids:

a bid for \$1 million at 4% from A
a bid for \$1 million at 4.25% from B
a bid for \$1 million at 4.50% from C.

The government looks at the bids (starting with the lowest yields) until the amounts cover the amount to be issued. The highest winning bid yield is used for all. In this case, that means that A and B get filled with a $1 million in bonds at 4.25%, and C gets nothing.

The connection to money is somewhat complicated. The issuance of the bonds reduces the money supply - the bidders have to pay for the bond. The coupon and principal payments will increase the money supply.


Why can't a country print its own money to spend it only abroad? If a country prints money and distributes it between the people, it causes inflation. But what if a country prints its own money to spend ONLY abroad, which would allow a country to buy whatever it wants. What's wrong with this logic?

This wouldn't work - for the money to have any value abroad, it has to find its way back to the source country.

Consider an example; the President of Ruritania wants a Swiss watch. He prints a thousand Ruritanian dingbats and sends them to his ambassador in Bern with the instruction to buy him a watch. However, the Swiss watch-maker doesn't want to be paid in dingbats - he wants Swiss Francs. So the ambassador goes to a Foreign Exchange (Forex) broker and asks to buy Swiss Francs using Ruritanian dingbats. What rate does the Forex broker give him? The broker has to consider what he could do with the dingbats - all he can do is sell them to some Swiss guy who needs dingbats for some reason. So it's the demand for dingbats in Switzerland that determines the rate.

Let's assume the Forex broker gives the ambassador some Swiss Francs and off he goes and gets the watch. What happens next? The broker sells the dingbats to a Swiss importer who is buying Ruritanian apples. The Swiss guy uses the dingbats to pay his supplier in Ruritania and now, the dingbats have ended up back in Ruritania!

So the Ruritanian money supply has increased and, despite the best efforts of the President, inflation is stoked.


How should the government react to 50% of the population being wiped out? In Avengers Infinity Wars the villain snaps his fingers and wipes out 50% of all living creatures.

His rationale is that it will save people from starvation and collapse due to resource exhaustion in a finite universe.

Presumably the impact of the loss of half the workforce and half the consumers would threaten to implode the economy as many markets would effectively lose half their consumers.

Assuming governments and industry were able to in some way function after the snap, would  they reach for the tools they're used to deploying in economic downturns and try to stablise the economy through a massive stimulus package to fill the gap left by the missing consumers?

Would the intent of such a stimulus be to permanently negate the snap by enabling the remaining population to consume double the resources they previously did? Would it be successful?

Let's break the problem into two parts.

Part one is the negative shocks to supply and demand from half the consumers and half the producers never coming back. This is a permanent negative real shock, and it isn't clear that the government can do much about those with fiscal or monetary policy. The Avengers Endgame movie also suggests widespread and long lasting mental health issues that the government might have a helpful role in mitigating. One could also imagine changes in immigration policy now that a substantial number of homes are now vacant. With an infrastructure base built for twice as many people resources could be redirected to other purposes. However, in the long run things should be largely neutral. The US had half as many people in 1950 and the economy functioned.

Part two is the transitory shocks from disruption from some companies or teams losing members and being unable to produce. It is possible that the government could mitigate the disruption by lowering interest rates, cutting taxes, and resorting to other forms of emergency transfers (like perhaps opening the strategic petroleum reserves or changing federal law enforcement priorities to allow federal police to assist with local matters). They might also try to stabilize a banking system where almost half of consumer loans were never to be repaid. Some resources might also be redirected to handle the abandoned housing, cars, and other infrastructure and millions of abandoned pets and livestock would need assistance.


Which area of Economics involves heavy mathematics and also appears to be directly helping the people? The thing is that I am writing a scholarship essay and one of the questions asks me to list my career goals and suggests as to how would the college where I am applying for the scholarship to would help me achieve these career goals. So my career goal is that I want to pursue research in Economics and publish papers. But I want to connect with the fact that I am very much interested in Mathematics and also participate in a lot of community service projects. I, therefore, want to write about an area of Economics something like Econometrics or Quantitative Finance which bears a strong relation to above-mentioned themes because then I will be able to elaborate on how the college offers a strong program in these areas and that this would, in turn, would help me succeed in my career.

PS. (1) I don't want to hint that I intend to make lots of money. So may be Quant is out.

PS. (2) A list of courses can be viewed on this link (http://www.lse.ac.uk/resources/calendar/programmeRegulations/undergraduate/BScEconomics.htm).

Some ideas based on the course list:

Environmental economics is doing work to try to understand and mitigate the effects of climate change. Key concepts in this debate, such as common action problems and externalities will feature in EC325 Public Economics.
Game theory is used as a basis for auction theory, which plays a major role in the design of important auctions. Auctions are used, for example, to sell licenses to companies wishing to use the radio spectrum. You can read more about spectrum auctions here.
The market design/matching markets idea is a good one with some real practical applications. For a basic intro, take a look at section 20.5 of this free book. In particular, there is a neat video by Alvin Roth, who won the Nobel prize for work in this area.
Development economics studies the process by which countries do (or don't) escape from poverty and can help us to understand what sorts of policy interventions are likely to be helpful.
Industrial economics (also known as industrial organisation) helps us to understand how competition in markets works (and when it doesn't work). The insights from this field underpin the work of organisations such as the Competition and Markets Authority (the UK's competition regulator) in ensuring that markets deliver good outcomes for consumers. You can read more about competition policy here.


is surplus just an approximation? let's say we have a consumer with a demand curve $q^d(p)=10-p$ and the good its price is $5$. So the consumer will consume 5 units. The surplus of the consumer would then be equal to $(10-5)+(9-5)+(8-5)+(7-5)+(6-5) = 5+4+3+2+1 = 15$. However, when solving this in the conventional manner it gives me $(10-5)\times 5/2 = 12.5$
What am I doing wrong? Or is surplus just an approximation?

Your second answer is correct. The problem your first approach has, is that you assume that you may only buy a discrete amount of goods. However, your demand curve is continuous and the usual assumption in microeconomics is that you can consume any amount of this good, for instance $1.478926574$ units. Thus, your first calculation for the surplus is not correct, the correct way to do it is

$$CS = \int_{5}^{10} (10-p) \mathcal{d}p = 10p-\dfrac{p^{2}}{2}|^{10}_{5} = 100-50-50+12.5=12.5$$

This result is equal to the second calculation of yours simply by the fact that it is a triangle. If demand wouldn't be linear, you'd have to use the integral form to calculate CS.


How prevalent is the use of machine learning among economists? I wonder how machine learning, particularly deep neural net which is considered the state-of-the-art among many data scientists, is used among economists, or other experts who is in in the similar field to predict economic situations, such as bank analysts, etc...

I know in econometrics people heavily use statistics. But it is focused on  statistics, not on machine learning, let alone deep learning.

How prevalent is it? What kind of methods/algorithms/models, if any, are frequently used for what kind of purposes among what kind of economists? Where can I see their work (e.g. blog, paper, etc...)

I will attempt to answer the first (How prevalent is it?) and last question (Where can I see their work?).

There was a recent post in The Economist about the emergence of machine learning into standard economic papers. They produced a nice graph, reproduced below:

Albeit machine learning is confounded with big data, it shows a rise in their use since 2014. Surely, this is a very narrow selection of the literature (NBER working papers, and only abstracts), but is a start.

Regarding where you can find papers using machine learning, you can use "keyword" search here (26,665 documents are found), or here (337 documents are found). The latter allows you to select dates, which you could use to build your own indicator of machine learning related publications per year.

Finally, related to blogs, I am not aware of a dedicated ML/DL economist's blog. However, here there is a very useful blog aggregator, which has indexed most of the "serious" blogs available. The full list of blog posts indexed is here. A search for "machine" or "deep" does not yield a result. However, there are some hits for "econometric" and "statistics" which might help you.


Does price affect quantity or vice versa? On nearly all graphs found within economics textbooks, quantity is label on the x-axis and price on the y-axis, implying that the quantity supplied affects the price. Is this really so? Intuition would tell you (or me at least!) that the quantity someone wishes to buy is dictated by the price, which in turn is decided by whoever is selling the item.

This is a common problem among students first learning economics. The way these graphs are displayed are not meant to tell you anything about causality, let along the direction of causality. The reason that price is on the y-axis is partly because of tradition and partly because that's what makes the most sense from the perspective of developing economic theory.

One of the central questions of economics is the determination of prices. What causes prices to be what they are? So, it maybe seems natural to write relationships that give a price as the dependent variable. However, the layout is not meant to convey any information about causality.


How is inheritance classified in Adam Smiths profit/wage/rent classification? It seems to me that inheritance can't be classified as profit or wage. So does it fulfill the definition of rent, or are there some economic activities that don't fit into this classification?

Profit, wage and rent are rewards for inputs used in production, they constitute a decomposition of Income (or the Income-decomposition of output produced)

Inheritance is a transfer, it does not involve production. So it is invalid to try to fit it into the mentioned classification.

Consider now any gift: say I work, earn a wage in the form of consumer goods, and give them to you. The consumer goods I got as a wage is a reward for my labor. Giving them to you is a transfer of already produced output.

In inheritance, this output has already taken the form of assets rather than consumer goods.


How to get this budget constraint? I have an Euler equation $ (\frac{ c_ {t+1} }{c_t})^\sigma = \beta (1+r)$,where $c_t$ is the t period consumption,r is interest rate and $\beta$ is discount rate, and a budget constraint $\sum _{t=0}^\infty \frac{c_t}{(1+r)^t}=\sum _{t=0}^\infty \frac{y_t}{(1+r)^t}$, where $y_t$ is income.

My question is how to substitute Euler equation into budget constraint to get the following equation?

$c_t\sum_{j=0}^\infty\frac{[\beta(1+r)]^\frac{j}{\sigma}}{(1+r)^j}=\sum _{t=0}^\infty \frac{y_t}{(1+r)^t}$

The hint is to use the recursive Euler equation to express all future consumptions $c_{t+j}$ as a function of current consumption $c_t$, and to play with the indexes in the sum of the left.


Why would higher expected inflation increase corporate earnings and dividends' rate of increase? A Random Walk Down Wall Street (2015 11 ed). p. 125.

Determinant 4: The level of market interest rates. The stock market does not exist as a world unto itself. Investors should consider how much profit they can obtain elsewhere. Interest rates, if they are high enough, can offer a stable, profitable alternative to the stock market. Consider periods such as the early 1980s when yields on prime-quality corporate bonds soared to close to 15 percent. The expected returns from stock prices had trouble matching these bond rates; money flowed into bonds while stock prices fell sharply. Finally, stock prices reached such a low level that a sufficient number of investors were attracted to stem the decline. Again in 1987, interest rates rose substantially, preceding the great stock-market crash of October 19. To put it another way, to attract investors from high-yielding bonds, stock must offer bargain-basement prices.*
  *The point can be made another way by noting that because higher interest rates enable us to earn more now, any deferred income should be “discounted” more heavily. Thus, the present value of any flow of future dividend returns will be lower when current interest rates are relatively high. The relationship between interest rates and stock prices is somewhat more complicated, however, than this discussion may suggest. Suppose investors expect that the rate of inflation will increase from 5 percent to 10 percent. Such an expectation is likely to drive interest rates up by about 5 percentage points to compensate investors for holding fixed-dollar-obligation bonds whose purchasing power will be adversely affected by greater inflation. Other things being the same, this should make stock prices fall. $\color{red}{\text{But with higher expected inflation, investors may reasonably project that corporate earnings and dividends will also increase at a faster rate}}$, causing stock prices to rise. A fuller discussion of inflation, interest rates, and stock prices is contained in Chapter 13.

Please expound the sentence that I reddened overhead?

I don’t have the book, but the passage hints that it will be covered in Chapter 13.

The passage has “reasonably project” as a disclaimer, which does imply that it would not hold in all cases. It is not that hard to find counter-examples. If we define inflation as a change in the CPI, oil price spike will normally raise CPI. The higher energy costs are bad for firms with energy input costs, while the oil producers that benefit may be foreigners.

However, if we stick to an idealised scenario, where all prices are rising at roughly the same rate, we can get the result that profits rise in line with inflation. If we make two assumptions:

real activity is not affected by the change in inflation rates;
profit margins are stable.

We then are in a situation where we are just projecting current variables forward with the same real growth rate, while nominal variables are growing by the sum of real growth and inflation.

If profit margins are stable, then that implies that nominal profits are proportional to nominal revenues, and so would scale with inflation.

The passage implies that the author thinks those two assumptions are reasonable, and presumably detailed in Chapter 13. (I don’t have any references handy, but I’ve certainly seen similar arguments many times. The main difficulty is whether higher inflation is associated with higher or lower profit margin.)


Linearity in Pricing and Duality, UMP EMP I have read the statement below and don't quite understand what it means. This is probably because I don't have full understanding of duality with support function in math, but just to foster understanding... The statement is:

  "The utility maximization problem(UMP) has a non-linear utility objective and a linear price constraint. The expenditure minimization problem is exactly the other way around: a linear price objective and a non-linear utility constraint. This is at the heart of the idea of the meaning of dual - to recast the problem with the objective as a constraint and the constraint as the objective. An important observation to make is linearity in pricing in them. This linearity, either in objective or constraint, is the cornerstone in enabling us to use the duality theorem."

Denote a bundle of goods $\mathbf{x}=(x_1,...,x_n)$ and a price vector $\mathbf{p}=(p_1,...,p_n)$. The cost of any bundle is the scalar product $\mathbf{p}\cdot\mathbf{x}$.

Consider first the UMP, which consists in finding the bundle $\mathbf{x}$ that maximizes utility $u(\mathbf{x})$ subject to the budget constraint that the bundle of good costs less than an income $R$:
$$\underset{\mathbf{x}}{\max}u(\mathbf{x}) \text{   s.t.   } \mathbf{p}\cdot\mathbf{x}\leq R.$$

Consider now the EMP, which consists in finding the bundle $\mathbf{x}$ that minimizes expenditures $\mathbf{p}\cdot\mathbf{x}$ subject to achieving a minimal level of utility $\underline{u}$:
$$\underset{\mathbf{x}}{\min}\mathbf{p}\cdot\mathbf{x} \text{   s.t.   } u(\mathbf{x})\geq \underline{u}.$$

These problems are dual in the sense that you can relate the solution of the first one to the solution of the second one. The solution of the UMP gives you the Marshallian demands, $\mathbf{x}^M(\mathbf{p},R)$, as the function of the prices and the income. The solution of the EMP gives you the Hicksian demands, $\mathbf{x}^H(\mathbf{p},\underline{u})$, as the function of the prices and the minimal level of utility.
The link between these two functions is heavily studied in microeconomics, it is rich in many economic intuitions and useful mathematical relationships.

Duality enables you to find one solution once you know the other. For instance suppose we know the function $\mathbf{x}^M(\mathbf{p},R)$ but we do not know the function $\mathbf{x}^H(\mathbf{p},\underline{u})$, how can we find $\mathbf{x}^H(\mathbf{p},\underline{u})$?
First, denote the indirect utility of the first problem by $v(\mathbf{p},R)=u(\mathbf{x}^M(\mathbf{p},R))$. Second define the income $\underline{R}$ as the solution of $v(\mathbf{p},\underline{R})=\underline{u}$ (the existence of $\underline{R}$ comes from the linearity property that is emphasized in the last sention of the citation). $\underline{R}$ is the minimum amount that is required to achieve utility $\underline{u}$. I will not show, but you can understand intuitively that we have:
$$\mathbf{x}^H(\mathbf{p},\underline{u})=\mathbf{x}^M(\mathbf{p},\underline{R})$$

Lastly, note that we should write $\underline{R}$ as a function of $\mathbf{p}$ and $\underline{u}$ to be rigorous.


What is the difference between gross, operating, net profit and EBIT(DA)? What is the difference between the following accounting measures, if any?

Gross profit
Operating profit
Net profit/income
EBIT
EBITDA

So, here goes:
Gross Profit = Revenue - COGS (Cost of Goods Sold)
If you bought an orange for a dollar and sold it for two, you have one dollar of Gross Profit
Operating Profit = Gross Profit - Labor - SG&A
If you're business paid someone \$100 to sell 200 oranges (like above), you would have \$200 in Gross profit, and \$100 in Operating Profit (assuming no other overhead like licenses, etc) for that business line. Operating Profit can be for a firm, business line, or whole company. Depreciation and Amortization can be included here for assets and debts in service to the entity or business line in question.
Typically Operating Profit tells whether a business line, unit, or company is profitable (independent of interest and taxes as explained below in the EBIT section).
Operating Profit and EBIT are not completely interchangeable in common parlance, though, as EBIT is typically used only for a company and Operating Income is often used both for Companies, and individual product lines within the company.
EBITDA is Earnings Before Interest, Tax, Depreciation, and Amortization
If the same business paid \$10 to incorporate, that would come out here, so your company's EBITDA would be \$90.
EBIT includes Depreciation and Amortization
If you'd also used your \$100 office (independent of the orange selling operation or it would have also been in the orange selling Operating Profit line) for 1/100 of it's operating life, you would have \$1 in depreciation. Bringing your EBIT down to \$89. EBIT is almost always a company level statistic, and rolls up all Depreciation, Amortization, and costs other than Interest and Taxes.
The reason people analyze EBIT, is that it gives you a feeling for if the company could be profitable if moved to a different tax jurisdiction, or if its WACC (weighted average cost of capital) were changed through recapitalization.
Net Profit = EBIT - Interest - Taxes
So if you'd paid \$1 in interest on a \$100 loan to buy the oranges in the first place, you're pre-tax income would be \$88, which you would report to the appropriate tax agency, assuming a 35% corporate tax rate, you'd pay \$30.80 in taxes, leaving you a Net profit of \$57.20.
This is usually the "bottom line" of an income statement.


Discrete returns versus log-returns I read this link and it is very helpful.

However, if log-returns are easier for time-aggregation, then why do economists work with discrete returns e.g. in GDP growth?

I would say people usually use log-returns for continuous data (although no data is really continuous, not even tick data). And discrete returns when your data is discrete. In the case of GDP, you only get the data every 3 months, so that is as discrete as it gets.


Which econometric test applied here? I have been reading an article about the Phillips Curve. But I got stuck in a part of econometric analysis. I am not good at econometric. Therefore I need help here. In this link you can read the article. If you search 0.97 with Ctrl+F, you can see the first finding that I want to ask about it. She says in there "By applying Equations 5–7 to the data, one need not assume any specific form of nonrationality in expectations. Since the task here is to compare the different models on their own terms, the theoretical restrictions are imposed in the estimated specifications of the New Keynesian models. Thus, in the New Keynesian Phillips curve, the imposed value of β is 0.97 and as seen in Equation 7, the sum of forward- and backward-looking components is restricted to unity for the Hybrid Phillips curve." I confused about if she applied any specific econometric test or not. If she applied, which test did she applied? Please help me.

As they clearly say on pp 2267:

Alternative specifications were compared using the
specification test by Davidson and MacKinnon and
the Wald test of coefficient restrictions.

So they two tests Davidson and MacKinnon specification test and Wald test.
Wald test is a classic test for coefficient restrictions you can learn can learn more about it in any econometrics textbook, for example Verbeek (2008). Guide to modern econometrics. 4ed.
For Davidson and MacKinnon specification test you can have a look at the original Davidson and MacKinnon (1990) paper.


How do central banks earn profit? I thought of Central banks as the regulators of financial markets. But surplus reserves of some Central banks surpass giant corporate companies.

Please explain me how do they manage to make profit in just regulating activity and printing currency.

Central Banks are not made to make profit. They are there to stabilize the price (inflation) and avoid crisis.

But to do that, they sell and buy assets. If they do a good job, they must purchase assets when they are undervalued and sell when they are overvalued. By doing that they are making profit.

This is good because Central Bank's infrastructure does have a cost. If they were not making profit, they would have to be financed by the taxpayer. When a central bank is making profit, they typically give this money back to the state, lowering the amount of needed taxes.


Help understanding Lagrangian multipliers? I am trying to understand Lagrangian multipliers and using an example problem I found online.

Problem Set Up:

Consider a consumer with utility function $u(x,y) = x^{\alpha} y^{1-\alpha}$, where $\alpha \in (0,1)$. Suppose this consumer has wealth $w$ and the prices $p =(p_x,p_y)$. That's all we were given.

Work I Did:

I then defined a budget constraint equation: $w = xp_x + yp_y$. I also then defined an associated Lagrangian for the consumer's maximization problem:
$\Lambda(x,y,\lambda) = x^{\alpha} y^{1-\alpha} + \lambda ((xp_x+yp_y)-w)$.

My question:

What does this equation allow me to do? Although I set it up given the formula on Wikipedia's page on Lagrangian multipliers, I really have no idea what the purpose of this equation is. Like I don't understand how the equation as given allows me to determine how to maximize my utility function.

Note: I am familiar with multivariable calculus and Lagrangians ($L = T -V$) in physics, but this method is new to me.

A constrained optimization function maximizes or minimizes an objective subject to one or more constraints. As I understand it, the Lagrangian multiplier approach transforms a constrained optimization problem (I) into an unconstrained optimization problem (II) where the optimal control values to problem II are also the optimal control values to problem I. Additionally, the the objective functions in problems I and II take the same optimal values. The trick is a clever way of putting the constraints into the objective function directly rather than using them separately.

I agree with your presentation of the consumer's maximization problem:
$\Lambda(x,y,\lambda) = x^{\alpha} y^{1-\alpha} + \lambda ((xp_x+yp_y)-w)$.

Now we take the partial derivatives with respect to x an y, set them equal to zero, and then solve for x* and y*.

$0=\partial\Lambda / \partial x  = \alpha x^{\alpha -1 } y^{1-\alpha} + \lambda p_x = (\alpha / x ) x^{\alpha  } y^{1-\alpha} + \lambda p_x$

$\Rightarrow -\lambda = (\alpha / (x p_x)) x^{\alpha  } y^{1-\alpha}$

$0 =\partial\Lambda / \partial y  = (1 - \alpha) x^{\alpha} y^{-\alpha} + \lambda p_y = ((1 - \alpha) / y ) x^{\alpha  } y^{1-\alpha} + \lambda p_y$

$\Rightarrow -\lambda = ((1- \alpha) / (y p_y)) x^{\alpha  } y^{1-\alpha}$

$\Rightarrow (\alpha / (x p_x)) x^{\alpha  } y^{1-\alpha} = -\lambda = ((1- \alpha) / (y p_y)) x^{\alpha  } y^{1-\alpha}$

$\Rightarrow (\alpha / (x p_x)) = ((1- \alpha) / (y p_y))$

$\Rightarrow ( y p_y ) / (1- \alpha) = (x p_x) / \alpha$ (eqn 1)

Recover the budget constraint equation by taking the partial derivative $\partial\Lambda / \partial \lambda = 0$.

$0 = \partial\Lambda / \partial \lambda = xp_x + yp_y - w \Rightarrow xp_x /  w + yp_y /w = 1$ (eqn 2)

We now have two equations and two unknowns (x,y) and can solve for x* and y*.

$\Rightarrow yp_y / w  = xp_x/w \cdot (1 / \alpha - 1) = xp_x/w / \alpha - xp_x/w$

$\Rightarrow 1 = yp_y / w + xp_x/w = xp_x/w / \alpha$

$\rightarrow \alpha = xp_x/w$ (result 1)

$\Rightarrow \alpha = xp_x/w = 1 - yp_y /w$

$\rightarrow 1-\alpha =yp_y/w$ (result 2)

Results 1 and 2 form the famous constant expenditure shares result for the Cobb-Douglas utility and production functions. Which can also be explicitly solved for x* and y*: $x^* = \alpha w /p_x$ and $y^* = (1-\alpha) w /p_y$ which are the optimal values for both the Lagrangian and the original problems.


What are directional derivatives used for in economics? In a basic mathematics for economists course one is exposed to the concept of directional derviative. Recall that a directional derivative is defined as:

$$\nabla f \frac{\mathbb{v}}{\|\mathbb{v}\|}$$

I know that it mathematically tells you the direction the function is increasing on a two or three dimensional graph, however I am yet to see an application of such a formula in any economics problems.

What are some applications of the directional derivative in Economics?

Recall, that the directional derivative of a function is defined as the the rate at which the function $f(x,y,z)$ at a given point $(x_0, y_0, z_0)$ changes in  direction of the vector $v$, where $||v||$ is the norm of $v$1.
What comes to mind
Applications of the directional derivative can be used in determining the rate of switching inputs in production functions, which can be very helpful in determining/forecasting switching costs for a given bundle of inputs. Though it does not tell you where the optimum points are it does tell you the rate of change (i.e. the switching costs) of  moving to a different bundle.
Hope this is helpful
1 http://mathworld.wolfram.com/DirectionalDerivative.html


What are the different patterns/quantity of employment according to demands of different income ranges? I don't really have that much knowledge on economics or anything, so perhaps that's something I'd find an answer if I just knew the adequate terminology.

Rephrasing/explaining my question: different income ranges have different propensities to expend ("versus" save), and somewhat different consumption patterns (quality of products and services).

And industries working on different quality levels also probably have different numbers of employees working on it, for the same absolute amount of money. In other words, "ten dollars" may employ less people in the cheaper food industry, than in luxury organics, and, perhaps, conversely "ten dollars" may employ more people in a "cheap towels" factory than in a "luxury towels" factory.

So, in the end, we'd have something like in general, poor people employ the less number of people per dollar invested, middle-class the most, and the richer, somewhere in between. But perhaps it would be more interesting to see that actually separated in different industries as well.

So, is that something about which there is hard data/cool graphs somewhere,  or that isn't generally a matter of concern, or yet, perhaps the answer is so obvious and easily empirically verifiable that no one really cares to elaborate on that?

So the phenomena you've identified is linked to a goods being labor intensive or not. Often ``craft'' goods required high-quality labor (think watches) to be built, while lower quality goods can be made using machinery. Now farming of all kinds used to be very labor intensive, but technology has replaced most of those workers.

So the substitutability of a worker matters a lot here and the skills that luxury goods need may be less substitutable.

Another factor is that when the good is more expensive, cutting costs (such as labor) at the potential expensive of quality is not always a goods idea - think how often you see ``handcrafted'' or pictures of the people working on the farm on organic products.


Shall we anticipate regression results？ Shall we anticipate the regression result? Saying the coefficient sign .

If not, why?
If so, what should we do when it fails to achieve anticipated results?

Saying what the theory predicts is a good idea as then we can make a testable hypothesis of the theory. Much of empirical economics is to test the validity of the theory.

If your result conflicts with the theory, then you can try to rectify the conflict or propose a better alternative.


Oliver Hart said that financing deficits by printing money can lead to hyperinflation "once the economy is close to full capacity". What does he mean? In response to a poll on Modern Monetary Theory, Nobel Laureate Oliver Hart said that Governments financing deficits by printing more money "can quickly lead to inflation or even hyperinflation once the economy is close to full capacity".
What does he mean by the economy being close to full capacity?

Full capacity means utilization of all resources in economy. That is all labor, capital and other resources are already used at their best uses.   Economy will not always work at its full potential for various reasons. For example, due to fall in aggregate demand during recession, which can cause unemployment to be above natural rate.
Monetary policy or fiscal policy can stimulate economy but only to the point economy reaches full capacity (i.e. all resources are put to their best uses). After that point as Hart mentions monetary stimulus will likely lead just to inflation or potentially hyperinflation.


Rational expectations econometrics: a theory or an excuse? I've been reading up on the topic of Rational expectations  econometrics, and have really been wondering if it is a theory useful for prediction or just used to "fit" a model.

Your standard rational expectations model (otherwise referred to as efficent markets model):
$$y_t=\tilde{y}+\sum_{i=1}^n\beta_i(X_{t-i}-X^e_{t-i})+\epsilon$$

$y_t=$ Economic variable of interest at time $t$ like unemployment or real output.
$\tilde{y}_t=$Natural rate or equilibrium of economic variable at time $t$
$\beta_i=$ coefficents.
$X_{t-i}=$ an aggreagte demand variable like money growth, Inflation or Nominal GDP growth.
$X^e_{t-i}=$ Anticipated aggregate demand conditional on knowing all  information at point $t-i$
$\epsilon_t=$ an error term

Where the property of "rational expectations" is defined as the true expected value of $X_t$ is equal to the markets expected value of $X_t$. Mathematically written as:
$$\mathbb{E}(X_{t}|\phi_{t-1})=\mathbb{E}_m(X_t|\phi_{t-1})$$
$$\mathbb{E}(X_{t}-\mathbb{E}_m(X_t)|\phi_{t-1})=0$$

If rational expectations hold, we should observe when expectations are taken:

$$y_t=\tilde{y}_t$$

that is $y_t$ should always be in equilibrium/ be forecasted based on its equilibrium values/growth process (providing rationale for the use of Univariate models in economics).

My Question: Are the use of expectations augmented models useful for forecasting or is it just a way to explain forecast error?

If you prefer, think of the rational expectations framework as a benchmark -- much in the same way that perfect competition is a benchmark.  It's not about whether the benchmark is wrong, so much as what the benchmark allows us to conclude when it is wrong.

The canonical example for rational expectations is the Barro-Gordon model of central banking (or more generally, the Kydland-Prescott model of policy-making), which essentially couches monetary policy in the framework of an infinitely repeated game.

The idea there was to consider the question of whether it is better to have a central bank that sets monetary policy "by discretion" or by adhering to a stated rule.  In this case, the idealized assumption being made is that agents are rational and possess full information about the past behavior of the central bank (as well as the true value of pertinent measures like inflation & unemployment).

In the model, the bank's objective function implies a tradeoff between unemployment and inflation via the Phillips Curve.  Both inflation and unemployment are costly, but setting both to the equilibrium value is not feasible.

In a one-shot game, the bank can improve the value of its objective function by "inflation surprises" -- basically, by injecting money into the economy without announcing it, so that in the short-run there is an increase to employment but no impact on inflation.  But since realized inflation is a function of inflation expectations (because if people expect their money to be worth less tomorrow, they will spend more of it today, thus leading to increased consumption demand which drives up prices and makes the expectation self-fulfilling), in the iterated game setting rational economic agents will come to expect the central bank to generate "inflation surprises".  What is interesting about the Barro-Gordon model is that this leads to an "inflation bias" -- realized inflation is always higher than the optimal value when the bank's actual policy targets don't match with the expectations they set out through statements, etc.

So rational expectations predicts that central banking done according to a rule is more efficient, because it keeps policy inflation in line with expectations and avoids this bias.  In the literature one hears about "credible banks" and this is essentially what this is about.

Getting back to your question, is this used to "explain" forecast error?  In a sense, yes:  if the model predicts a certain value of inflation under rational expectations, and that value of inflation isn't realized, then one either questions the rational expectation model itself or (more likely) that one or more of the assumptions behind it is violated.  Usually, this is the assumption of complete information, although one should also consider the possibility of additional shocks not accounted for explicitly in the model.


What possible reasons could make arbitrage impossible between some markets? What could prevent arbitrage (not necessarily risk-free) between some markets even when price differences exist?

The seminal paper in this area with over 3,000 citations is by Shleifer and Vishney:

  Textbook arbitrage in financial markets requires no capital and
  entails no risk. In reality, almost all arbitrage requires capital,
  and is typically risky. Moreover, professional arbitrage is conducted
  by a relatively small number of highly specialized investors using
  other people's capital. Such professional arbitrage has a number of
  interesting implications for security pricing, including the
  possibility that arbitrage becomes ineffective in extreme
  circumstances, when prices diverge far from fundamental values. The
  model also suggests where anomalies in financial markets are likely to
  appear, and why arbitrage fails to eliminate them.

The Limits of Arbitrage (Andrei Shleifer and Robert W. Vishny (1997))

There are many versions online, one of them is likely ungated.


GHH Preferences: FOC Wikipedia states GHH preferences to have the general form

$$V(c, l) =  U(c - G(l))$$

with $U$ increasing concave, and $G$ increasing convex.

In interior solution w.r.t. $l$ requires

$$ U'(c - G(l))(\frac{dc}{dl} - G'(l)) = 0$$

As wikipedia says, this is given by

$$ \frac{dc}{dl} = G'(l)$$

However, what about the peculiar case where $c = G(l)$? Could someone elaborate a bit on the intuition

The first-order condition would be satisfied under the assumption $c=G(l)$ if $U'(0)=0$. But this latter requirement is incompatible with the assumptions: indeed, $U'$ is nonincreasing (by the concavity of $U$) which yields $U'(x) \leq 0$ for any $x \geq 0$, which contradicts the fact that $U$ is increasing.

If $U'(x)>0$ for all $x$, the only possibility to meet the first-order condition is indeed $\dfrac{dc}{dl}=G'(l)$.


Bellman Equation with Two Discount Factors For the following social planner's problem
$$
\max \mathbb{E_{0}}\sum_{s=0}^{\infty}\beta_{1}^{s}(\alpha U(C_{s}^{1}))+\beta_{2}^{s}((1-\alpha)U(C_{s}^{2}))
$$
$$
s.t.\ \text{some constraints including C, K, N, etc.}
$$
There are two different households with different discount factors, $\alpha$ and $1-\alpha$ are assigned weights for HH types 1 and 2, respectively. Is the following Bellman equation a correct formulation to solve the planner's problem?
$$
V(K) \equiv \max\ \alpha U(C^{1})+(1-\alpha) U\left(C^{2}\right)+\beta_{1} \alpha \mathbb{E} V\left(K^{\prime}\right)+\beta_{2}(1-\alpha) \mathbb{E} V\left(K^{\prime}\right)
$$

No. Consider the following problem: Each period, one total unit of consumption falls from the sky that can be distributed between the two agents in any way. Their per-period utility is simply how much they consume. We let $\alpha=1/2$. Assume that $\beta_1>\beta_2$; the first agent is more patient. All optimal allocations have a very simple form: The consumption unit is arbitrarily distributed in the first period, in all subsequent periods, agent 1 gets everything. This implies that the value function for continuations is completely independent of $\beta_2$, which it clearly is not in your suggested form.


What does a supply+demand curve look like for fare evasion? Consider the demand curve for fare evasion on a train. The price (I suppose) would be the average amount of money paid per ride in fines, and the quantity would be the average number of fare evaders caught. The supply curve would quantify the target number of fare evaders to catch.

Normally technological advances push the supply curve rightward. This would correspond with more people getting caught.

But this obviously isn't right. If it were easier to catch fare evaders, you'd intuitively expect that the average price in fines per ride for a rider would be higher, thus, quantity would go down.

What does the supply/demand curve really look like for fare evasion and what would be the effect of a rightward supply curve shift?

The way to get the demand curve is by deriving the utility function.

First, the utility function needs to be defined.

$E(u)=(u(0)(r)+u(200)(1-r))$

In this case, the expected utility is the utility of spending \$0 on the fare vs the utility if you get a \$200 fine. in this case, r is the probability of getting away with it.

If this is greater than the utility of paying the fare, the fare will be evaded.

$E(u)=(u(0)r+u(200)(1-r))\geq {u(5)}$

The exact utility function can take many forms. Popular choices are Decreasing Absolute Risk Aversion (DARA), Constant Absolute Risk Aversion (CARA) or others. Wikipedia is OK on this.

The next steps in this analysis are to decide on a utility function.
You will need inputs on risk of getting caught and fines.

After defining the utility function you will be able to derive the demand curve.

You will also need to define the supply curve. If the fare is something like a train ride, you may be able to set up the marginal cost=0. That allows you to only worry about the fixed cost.

A useful resource will be the wiki article mentioned earlier. This Mas Collel book is a very popular graduate text. I think it treats risk aversion relatively well, although I did find it not incredibly accessible.


Individuals vs. groups as decision makers In economics, why do people focus on the individual rather than groups of individuals as decision-makers? Wouldn't considering actions decided by a group of individuals reduce the chance of socially nonoptimal outcomes?

Many fields of economics focus on collective decision making. For example public choice theory is almost solely focused on collective decision making as opposed to individual one.

Many areas of economics focus on individual decision making because that’s where actually decisions are made in real life. When you go to the store buy shirt you go there as an individual not as some kind of collective or hive mind. This holds for many economic interactions as well.

Furthermore, collective decisions are not more socially optimal then individual ones. For example, as Arrow impossibility theorem suggests, collective decisions where there are more then 2 options will never be optimal from social welfare perspective (at least in a democracy where there is no benevolent dictator).

However, the Arrow impossibility theorem is derived in idealized conditions. In real life there are areas and cases where collective action is preferable, but as a general rule it’s not possible to say that collective action is more likely to yield socially optimal outcomes.


Minimum wage vs wage subsdies Many politicians argue that the minimum wage is essential for providing an sufficient standard of living to all. However, there are many issues binding price floors predicted by standard supply and demand theory. Why couldn't wage subsidies be used instead? I know that they are used. However, why do politicians always argue for increasing the minimum wage as opposed to increasing wage subsidies?

what advantages does the minimum wage have versus wage subsidies?

We could distinguish between two kinds of "wage subsidies":

A) The government pays to the firm part of the wage cost, usually social security fees.

B) The government pays to the employee a markup on his wage.

In scenario A, labor supply is not affected but labor demand shifts outwards: the tendency should be higher employment and higher equilibrium wage (so eventually more disposable income for the workers). Usually, what is observed is that employment rises (after all, usually such programs are on  condition of net new jobs creation in a company), but wages do not increase (i.e. firms don't share the subsidy with the employees). So no betterment of standard of living of those employed.

In scenario B, take-home income will increase at no cost to the firms. So now, workers know that if the current wage is $w$, if they work they will receive $w+s$. This will shift the labor supply curve outwards (because now it responds to $w+s$), while the labor demand curve will remain unchanged (which still responds to $w$ only). This will tend to result in higher employment and lower equilibrium wage. But this contradicts (and partly or wholly offsets) the very purpose of the measure, which is not to increase employment, but to increase disposable worker income.

So in both cases, wage subsidies are more about employment rather than income, while minimum wage is clearly about income and standard of living of those employed, even though it may hurt employment.

...and one cannot avoid in these matters a dash of political economy and political science (as well as social psychology): subsidies bear always a risk of fraud, and are always suspect of being an instance of pork-barrel politics. Moreover, they are mostly seen as measures in time of macroeconomic (or regional) recession/depression, where the main concern is to boost employment.

On the other hand, minimum wage is not about a faltering economy as regards activity and level of production/income, but about market failure as regards distribution of income. Issues of distribution are inextricably linked to issues of fairness, and this creates a more passionate political agenda, occasionally  satisfying also the expectations of the public for a "strong government" which, "when markets create unjust misery", intervenes "decisively", imposing by decree "what's fair" (or fairer).


Game Theory (continuous strategies, pure strategy) So I have this Game Theory problem, and I have a solution, but at a certain point I assume the symmetry of the problem to finally get my answer.  I'd like to be able to avoid using symmetry, though, so that in the future I can solve problems that are not symmetric.

So Alice and Beatrice are suppliers, Ashok and Bob buy from them to then sell again at retail.  Ashok only buys from Alice and Bob only buys from Beatrice.  First Alice and Beatrice set their prices simultaneously, $p_{A},p_{B}$ respectively.  Then Ashok and Bob set their quantities $q_{A},q_{B}$, and their price is determined by

$$P=1-q_{A}-q_{B}$$

The payoffs for Alice, Beatrice, Ashok, and Bob respectively are $p_{A}q_{A}, p_{B},q_{B}, q_{A}(P-p_{A}), q_{B}(P-p_{B})$.  I want to find a sub-game perfect equilibrium.

I first look at Ashok and Bob and, for any fixed prices from Alice and Beatrice, find the intersection of their best response curves.

$$\frac{dB_{A}}{dq_{A}} = 1-2q_{A}-q_{B}-p_{A}=0$$

$$\frac{dB_{B}}{dq_{B}} = 1-q_{A}-2q_{B}-p_{B}=0$$

We're solving for $q_{A},q_{B}$ so we get

$$1-3q_{A}-2p_{A}+p_{B}=0 \Rightarrow$$

$$q_{A}=-\frac{1-2p_{A}+p_{B}}{3}$$

Similarly for $q_{B}$.  Once we know those, we can substitute into the first equation for price and solve for $p_{A},p_{B}$.  But the solution will not be unique.  It becomes unique when I assume $p_{A}=p_{B}$ but if anyone can point out how I can solve this without that equation, I'd appreciate it.

I think I figured this out--I forgot to imposed the constraints on Alice and Beatrice, using the fact that they know this about Ashok and Bob and will strategize accordingly to maximize payoff.

Thus if

$$q_{A} = -\frac{1-2p_{A}+p_{B}}{3}$$

and

$$q_{B} = -\frac{1-p_{A}-2p_{B}}{3}$$

then Alice maximizes her payoff by

$$\frac{\partial B_{alice}}{\partial p_{A}} = \frac{\partial }{\partial p_{A}}\left(p_{A}\left[-\frac{1-2p_{A}+p_{B}}{3}\right]\right)$$

$$=-\frac{1}{3}(1-4p_{A}+p_{B})=0$$

With the same analysis given for Beatrice you get two linear equations in $p_{A},p_{B}$.


Levelized cost of electricity, to calculate the absolute costs? I'm doing my master thesis about the renewable energies. So my goal is to calculate how much it will cost to switch our fuel based energy generation to renewable energy generation. So my first thought was I use the levelized cost of electricity. I found some forecasts of how they will develop to 2050. So I made different scenarios in my thesis on of fast/slow the switch will be and now wanted to calculate the cost of them. So what I wanted to do is take those levelized costs of electricity (LCOE) and multiply it with the amount of electricity production different technologies have in my scenarios. After I did all those calculations I started to become sceptical if this all makes sense at all. Because I thought to myself if I look at the formula of LCOE, if you would change the amount of generated electricity it will also effect your LCOE, so lets say I produce more electricity through coal, this will decrease my LCOE and so on.

I am kinda stuck in the middle of nowhere now, because one part in me tells me that this are basically the costs per unit so it makes sense what I did and the other thoughts I have is, it makes no sense.

in other words:
Can I use the LCOE forecast of 2030 from those studies and multiply that with the amount of electricity produced for example in my 'scenario B' in the year 2030 ?

sidenote: scenario A, B, C and D have a different approach of how fast/slow the switch should be done, so lets say in scenario B I decided that in 2030 there will be already 60% of renewable energy, while scenario C is more conservative and the renewable energy is still beyond 20% of the whole generation.

Can someone please help me with my logical dilemma ?

In general, an LCoE forecast for a year, is the unit cost of electricity for generators that come online in that particular year.

Whereas, for a given year's (e.g. 2030) forecast of the cost of electricity, the average unit cost of electricity is a volume-weighted arithmetic average of the levelised costs of all the generators that have been built previously, that are operating in the forecast year. Typically, those generators will have been built in the previous 20 years.

That's not the only challenge:

you will need to check the actual definition of the LCoE data that you have. It might be the unit cost for generators that get their Final Investment Decision in that year (and so will come online sometime later, probably in the range of 1-15 years)
usually (but not always), changes to the underlying cost will affect total demand, so you've got a two-way feedback mechanism between quantity and price.
that rate at which things are deployed, and the consistency of speed with which they are deployed, affects their LCoE. There are chokepoints in various supply chains, there's exogenous and endogenous cost reductions from learning by doing, and so on.
merely averaging all the individualised costs of energy, omits the costs that are borne by the system itself: the cost of transmission and distribution networks, the costs of storage, and the costs of mechanisms to keep demand and supply in perfect balance every 20 milliseconds (or so) of the year.

So you can take historic LCoE, and multiply it by the quantity of electricity demanded in a year, to calculate total cost of electricity consumed in that year, subject to the above caveats. Note that that will give you a different answer to the amount of capital investment needed.