What actually is aggregate demand? I have been tasked with teaching some students macroeconomics, and will shortly need to introduce them to the concept of 'aggregate demand'. Usually, this is defined by the following sort of equation:

$AD$ = $C + I + G + X - M$

where the symbols have the usual interpretations.

My question is whether aggregate demand is supposed to refer to the quantity that is demanded or rather the value of total demand.

Both options would seem to present difficulties:

On the one hand, if we say that aggregate demand is a quantity, one needs to ask 'of what?' Naturally, if there were just one good in the economy, answering this would be easy. But in reality, there are many different goods. Are we supposed to just add up the quantities demanded of all these different goods (e.g. if people demand 5 laptops, 3 apples and nothing else, aggregate demand is 8)?

On the other hand, we might say that aggregate demand is the value of total demand, i.e. $p_{1}q_{1} + ... + p_{n}q_{n}$ where $p_{i}$ and $q_{i}$ are the quantity demanded and price of good $i$. That seems a bit more meaningful, but then it is far from intuitive that aggregate demand falls when the 'overall price level' (whatever that is) rises. For one might have thought that if prices rise, the value of total demand would (sometimes) rise, just as a firm's total revenue can increase when the price increases (if demand is inelastic).

My apologies if the answer is obvious; I am simply not very familiar with macroeconomics.

We measure these in values.

Also, this is a macroeconomic identity, it holds always by design.

You need an economic model that will make specific behavioral and other assumptions, in order to discuss movements when the price level change.

For example, you write

  it is far from intuitive that aggregate demand falls when the 'overall
  price level' (whatever that is) rises

Even in introductory economics courses beware of "intuitive" thinking.

And indeed, where is the model and its assumptions based on which one would argue that as price level rises aggregate demand falls? It is certainly not embedded in the macroeconomic identity.

Find the model that predicts so, understand its assumptions, and then discuss whether these assumptions are "intuitive".


Why Law of Supply indicate direct relation between price and supply? According to Wikipedia, the Law of Supply states that:

  an increase in price results in an increase in quantity supplied.

However, if the market was overflowing with a particular good (meaning higher supply), wouldn't the prices be lower? In the same vein, if the price was higher, wouldn't it be because the supply was less (all other factors, including Demand, constant). Also, wouldn't this create a run-away effect where increasing prices and supply drive more increase in each other, effectively launching prices to near infinity?

Wikipedia also states, if I understand correctly, that this view belongs to a "modern mainstream economics".

Can someone explain this seeming paradox? When we talk about supply, are we talking about future supply which will be guided based on speculations on current prices? If so, what laws will govern the present supply?

You are confusing producer behavior and equilibrium.

If producers can sell at a price $p$ some of them will do so. Other producers cannot do so profitably at this price so the do not. At a price $p'>p$ more producers can produce profitably including everyone who was already selling at $p$ so total supply increases. In this story the price was given exogenously. It was simply stated that the price is $p$ or $p'$ and we did not look at the reasons behind this. We simply stated what producers would do when facing certain price levels.

If given a price $p$ supply is larger than demand $p$ is not an equilibrium price. (An exception: it can be, if $p=0$. Would you like to buy some air from me?) You can say that this price does not occur, or at least not for a long time. As you state prices will probably decrease. In this story we looked at whether a price was actually likely given the market conditions (demand and supply). We did not simply assess what each side would do facing a given price but we tried to see if the actions of the two sides constituted an equilibrium.


Example of a rational and continuous preference relation that does not admit a utility representation It is well-known that a rational, continuous and monotone preference relation $\succeq$ defined on $\mathbb{R}^L$ admits a utility representation.

I would like to understand why monotonicity is required. In other words, what is an example of a rational and continuous but non-monotone preference relation that does not have a utility representation?

A necessary condition for a preference relation to be represented by a utility function is that the preference relation is rational (where a "utility function" is a real-valued function that assigns a higher or equal numerical value to bundle A than to bundle B, when A is weakly preferred to B).

Preferences are rational when they are complete (I can express my preferences for all conceivable bundles), and transitive (If I weakly prefer A to B and B to C, then I weakly prefer A to C).

Given rationality, a sufficient condition is that the rational preference relation is continuous, i.e. if it is preserved under limits.

Then, the related utility function is also continuous.

Monotonicity is a property where we go from quantities to preferences, after assuming desirability ("goods" rather than "bads"). Local nonsatiation is actually the weaker assumption that is required for most of the theory.


OLS estimator derivation: second-order condition to prove global minimum? In deriving our ordinary least squares estimates, we can partially differentiate the sum of squared errors $\sum_{i=1}^{n} {e_i^2} = \sum_{i=1}^{n} {(Y_i- \hat{\alpha}-\hat{\beta}X_i )^2}$ with respect to our estimators $\hat{\alpha}$ and $\hat{\beta}$ to get the following first order conditions:

$$\frac{\delta SSR}{\delta \hat{\alpha}}= -2\sum_{i=1}^{n} {e_i}=-2\sum_{i=1}^{n} {(Y_i- \hat{\alpha}-\hat{\beta}X_i)}=0$$
$$\frac{\delta SSR}{\delta \hat{\beta}}= -2\sum_{i=1}^{n} {X_i e_i}=-2\sum_{i=1}^{n} X_i {(Y_i- \hat{\alpha}-\hat{\beta}X_i)}=0$$

How can we then prove that the sum of squared residuals is a global minimum?

Firstly, can I confirm that the Hessian looks like this?

\begin{array}{cc}
   2n & 2\sum_{i=1}^{n}X_i  \\
   2\sum_{i=1}^{n}X_i  & 2\sum_{i=1}^{n}(X_i)^2  \\
  \end{array}

Secondly, how can I show that the determinant of this Hessian is positive definite, i.e. $ 4[n \sum_{i=1}^{n}(X_i)^2 - (\sum_{i=1}^{n}X_i)^2]>0?$ The presentation bears some resemblance to the population variance formula, and I know that variance must be non-negative, but I'm wondering how to move on. Is there some way to factorise this? Thank you.

It seems that you working on the right lines. By multiplying out the brackets, it can easily be verified that $n\sum{X}_i^2 - (\sum{X}_i)^2 = n\sum{(X_i - \bar{X}})^2$ where $\bar{X}$ is the mean. As you yourself spotted, this is basically a standard expression for the variance. From this, it follows that $n\sum{X}_i^2 - (\sum{X}_i)^2 > 0$ provided that $X_i \neq \bar{X}$ for some $i$.

Incidentally, you also need to verify that one of the second derivatives is positive (say $SSR{_{\alpha\alpha}}>0$) which follows directly from your Hessian.


Subgame-perfect Nash equilibrium perfect information This might be a stupid question but please bear with me. I'm trying to solve this game but I'm in doubt on how to represent the strategy profile of the game. The game looks like this in extensive-form. I've marked the path with red that show the best actions of the players when it is their turn to move. The game is a game of perfect information.

The normal-form of the game looks like this:

From the normal-form we can see that there are 4 Nash equilibria of the game. Using backward induction I've come to the conclusion that $(df,\neg rr)$ is the unique subgame-perfect Nash equilibrium. My concern arises when we take a look at player 2. His pure strategy set would be $S_{2} = \{rr, r\neg r, \neg rr, \neg r \neg r\}$. In my normal-form representation of the game I've written the pure strategies of player 1 as $S_{1} = \{df, d\neg f, \neg df, \neg d \neg f\}$. For some reason I'm more tempted to write player 1's pure strategy set as $S_{1} = \{dff, df\neg f, d\neg ff, d\neg f \neg f,\neg dff, \neg df \neg f, \neg d \neg ff, \neg d \neg f \neg f\}$ and we would have a 8x4 matrix-representation of the game. Thus, the unique subgame-perfect Nash equilibrium would be $(df\neg f, \neg rr)$. Can somebody shed some light and help me with my doubts? Thanks in advanced.

The game is indeed an $8\times 4$-game. A strategy formally specifies what to do at each information set, including those information sets that can never occur under the strategy. In that sense, a strategy is not simply a "plan of action." This point has been famously made in (see Section 2):
Rubinstein, Ariel. "Comments on the interpretation of game theory."
Econometrica: Journal of the Econometric Society (1991): 909-924.


bonding curves and the market This question is related to economics on the blockchain. Bonding curves are becoming popular; however, it is a bit concerning that the price on an asset is predetermined by a mathematical function. Will the use of bonding curves distort or somehow disrupt the market? In my opinion bonding curves are the wrong mechanism to use in a market economy.

Suppose the real value of an asset is significantly smaller than the sell curve. The sell curve allows me to sell only at a specified price (the price that corresponds to the current volume of issued tokens). How is this mechanism market efficient? It seems that this mechanism will work for curation markets, but it will not work as an automated market maker for assets similar to equity securities. Please, correct me if I'm wrong.

I’ll try to succinctly explain bonding curves and then discuss benefits. Let’s look at a typical bonding curve where the buy price formula and the and sell price formula are equal:

 from https://medium.com/@simondlr/tokens-2-0-curved-token-bonding-in-curation-markets-1764a2e0bee5

The way the formula works is look at the current amount of tokens purchased (supply) and charge the price given by the formula for the next token. As people sell, the supply goes down and as people buy, the supply goes up. The total amount of money put into the token is the area under the curve.

At any point you can buy a token and sell it back and get your money. However, if you buy at $q_1$, wait and more people buy (not guaranteed!) then you can sell at a higher price at $q_2$. To make profit, you should only buy if you think others will buy after you as well.

At the end of the day, total money paid in will be total money paid out, but the smartest who buy early and sell at high supplies (buy $q_2$ and sell $q_1$) will make money while those who buy when it’s “hot” and sell when supply is low (buy $q_2$ and sell $q_1$) will lose money.

Now, sometimes the sell curve is below the buy curve:

In this case, the area between the buy and sell curve is revenue that will typically go to a company. There is money making opportunities, but because the sell curve grows slowly, it only really benefits the earliest buyers.

So what are these any good for?

The Buy curve equals the Sell curve:

This kind of market is good for content curation. It’s easiest explained by an example (borrowed from https://medium.com/@simondlr/tokens-2-0-curved-token-bonding-in-curation-markets-1764a2e0bee5):

  Meme Factory: A Game of Curation & The Trading of Dank Memes
  Meme Factory from District0x will be a game where users can create dank memes and bond tokens to each meme according to its own bonding curve. This becomes a game where users then bet on the popularity of each meme. Bonded early to a dank meme and got out at the top? You successfully traded a dank meme and just made a profit.

  The question each time is: do you think this meme is dank and funny enough that others will want to bet after you on this too?

  Ultimately, whilst this game is being played, these memes are also being curated themselves: more tokens bonded to a meme is a signal that is a funnier meme than a meme with fewer bonded tokens. This is an emergent outcome.

By people trying to make money, they will curate popular content as a byproduct (social surplus from private motives!)

The Buy curve > the Sell curve:

It’s very hard to start a community because the first members don’t have many people to interact with and it’s very laborious to create stuff that other people will want to join and see. It’s especially hard if you have to pay to join!

However, notice that if you enter early the sell curve is super close to the buy curve, so you have low risk of joining a community (because you can sell right back). And the upside is, if you work on the community to gather members and create fun content then more people will pay to enter. All of a sudden your share is worth a lot! This incentivized people to value their community and make money while doing so.


Understanding Inflation in a video game I don't understand where inflation occurs in a video games. Assuming "free market" ie unlimited new players can enter any universe at will. You will say that for an economy to form, both sides must be willing to trade. This is true, here a player trades working hours for gold (g).

Universe A:
 working for 1 hour (killing rats) rewards 1g.
 a sword can be bought for 10g.

does inflation occur ?
Time required to buy a sword will always be the same ~ 10 Hours.
New players will have to exert the same effort as old players to get a sword in universe A.

Universe B:
 Denizens of universe B can buy swords from universe A for 10g + 4g (transpotation fees).
 working for 1 hour (killing slimes) destroys a sword and rewards 15g.
 slime jars can be produced for 10g.

Does inflation occur?
Both citizens get the same profit for their hourly work = 1g per hour.
Is this what they call zero sum rule? workers sacrifice 1 hour for 1g.

Universe C:
Aliens can buy slime jars from Universe B for 10g (teleportation magic).
Alien have to eat slime jars every hour or die.
Aliens produce 20g by materializing matter out of thin air.

Does inflation occur?
Aliens get x10 gold per hour for their work. Is this what they call inflation? But humans lack the capacity for such feat, shouldn't alien be paid more?

Universe D: modify universe C as follows:
A weather effect blocks teleportation magic. We dont know how long it will last.
Buying slime jars from B now costs 21g.

Does Inflation or Deflation occur?
aliens now lose money instead gaining. they lose -1g even if they work. Shouldn't they have been paid more in the first place for the risk they took eg dying if they run out slime jars.
Assuming infinite years pass, and the weather condition pattern is 100% known. What should be a fair alien wage? Approximate 0 if averaged out, same as humans (1g) or more ?

Universe E: mmorpg simulation. Assume this world becomes available after 1000 years
Everyone can switch to this universe by paying 10g.
Working accumulates experience and increases productivity. Every 10 hours switch to the next level.
Lv0. Working produces 0g per hour.
Lv1. Working produces 0.1g per hour.
Lv2. Working produces 1g per hour.
Lv3. Working produces 10g per hour.
Cap. No more levels.

Does this cause inflation?
What will happen to the rest of the world if introduced.
Since the level is capped. This means that inflation also has a maximum cap = new player vs old player money profit for hourly wage.

Universe F: modify universe E as follows:
a time hole speeds aging: Creatures living in it have a finite lifespan of 1 month.

Does this cause inflation?
What should be a fair wage? Approximate 0 if averaged out, same as humans (1g) or more ?

11. Can other types of economy form in video games? Seems to me that all economies in games are "free markets" with an initial entrance fee. There is no competition. The rewards remain the same for everyone regardless of the amount of workers that enter a universe. This is because in a game goods are produced from thin air. Will markets with competition make sense ? or will new players be harshly punished for arriving to play the game too late?

You seem to think of a game where objects are obtained at a fixed rate by farming. Fix supply of work for a certain object (bc. Only a few people know where to find things to farm or are high enough level or have the right profession) and increase demand (new players coming in or more players buying in game currency for real money) then prices for the object will soar over time, people producing the object will find it easier to sell it, so much so that they will increase the price until people stop buying it. This will inflate the price of the object. Whether this will last over longer period of time then depends on many factors : ability of supply to adjust (e.g. How much are player willing to switch to farming that object?), rate of new player characters coming in, their propensity to buy the object etc.

There are  many other ways. One example I could think of: as a player on a WoW private server with moderate population I would routinely buy all objects from the auction house that I thought of as undervalued and put them back in auction at higher prices. This allowed me to gain arbitrage profit from less careful players and also to craft and sell the same object at higher prices.


Can't government experiment on price in the case of a monopoly? In the lecture given by Jon Gruber at MIT, he talks about the governmental regulations on monopolies, and he states that

(in short)
for government to regulate a monopoly, it needs to know the price of
that good in the case of a perfectly competitive market.However, in
reality, the government does not know the demand and supply curve.
Nevertheless, to get the demand curve the government can do
experiments on the consumer and get the demand curve.

If so, can't the government do experiment on the monopolist ? I mean, it can set a price first, and then change the price. Doing so, observing how much the firm produce, we can learn the supply curve of the monopolist. Of course, this would in some sense be not logical, but in the long run, you the government could set all the monopolies in the optimal price.
Moreover, if we look from a broader picture, this can be accomplished more easily by cooperation of different governments on collecting the data.

If I understand your question correctly, you are proposing that the government sets prices and observes the behavior of market actors to elicit the demand and supply functions.

I see two possible concerns:
Unless the monopoly is obligated to serve all customers, the market may not be in equilibrium, full demand may not be observed.
Similarly the government would have to buy any unsold goods, otherwise
a too large $p$ could result supply being larger then demand, resulting in a loss for the monopoly.

The other concern is that the monopoly's behavior significantly affects the government's observations. It could potentially benefit by behaving suboptimally now and earning more in the regulated future. One way it could do that is to make the government believe it has higher costs by supplying lower quantities given any price $p$.
-While I was writing this answer, @Dan has posted the same idea in a comment.


Daily variable for inflation I was wondering if there is a way to account for daily inflation data. I have daily short-term interest rates, and I would like to convert them to real short-term interest rates.

Can I just average the monthly CPI over the days of that month to calculate the real rate with the Fisher equation?

Any help is greatly appreciated!

The Billion Price Project offers what you want:

  Daily price indices, monthly, and annual inflation rates for Argentina
  and the US. Monthly data with annual inflation rates for Argentina,
  Brazil, China, Germany, Japan, South Africa, UK, US, 3 US sectors, and
  global aggregates (including Eurozone). Daily PPP series for Argentina
  and Australia.

However, these data, which come mostly from online transaction data, are imperfect because they end in 2015. However, I've put together some code so you can see that there is not very much high frequency price level variation for the basket of goods:

import delimited pricestats_bpp_arg_usa.csv
drop if country=="ARGENTINA"
gen date2 = date(date, "DMY")
format date2 %d
tsset date2
twoway (tsline indexps)

tssmooth ma indexps_ma30  = indexps, window(30)
twoway (tsline indexps) (tsline indexps_ma30)
gen monthly_diff = indexps - l30.indexps
gen monthly_diff_ma = indexps_ma30 - l30.indexps_ma30
gen abs_double_diff =  abs(monthly_diff -  monthly_diff_ma)

sum indexps indexps_ma30 monthly_diff monthly_diff_ma abs_double_diff, detail
twoway (tsline monthly_diff) (tsline monthly_diff_ma)\

This generates a figure comparing the 30 day moving average price level and actual price level you can see below that there is very little difference between the smoothed and actual price level. The price level of a broad basket of prices doesn't fluctuate enough for daily inflation to be very different from assuming a constant inflation (which is roughly equivalent to using the average).

I estimate, using the calculations above, that monthly inflation is about 11 basis point per month. Using a measure of inflation rather than the price level shows that the smoothed and raw inflation estimates are very similar. This variation could be because there is measurement error and bias from the high frequency calculation approach.

Bottom line, I would just stick with converting monthly series to an implied daily rate. Depending on if you care about business days or calendar days and how you feel about using real time data, this could be as simple as: $$ \hat{r}_{daily\ implied, t} = ( 1 + r_{monthly\ observed, t})^{1/30} -1 +\epsilon$$


real gdp per capita vs real gdp this site summarizes the difference between GDP and GDP per capita as:

1. GDP is a measure of a nation as economic health while GDP per capita takes into account
the reflection of such economic health into an individual citizen as perspective.
2. GDP measures the nation as wealth while GDP per capita roughly determines the standard
of living in a particular country.
3. GDP normally increase as the population increase while GDP per capita may decrease when
population increases.

Since real gdp is just gdp adjusted for inflation, would the same definition summarized for GDP vs GDP per capita hold true for Real GDP vs Real GDP per capita?

Yes.

Example. In 2017, a country's GDP was \$100 and its population was 100.

In 2018, its GDP was \$110, its population was 105, and the price level rose by 3%. Then:

2017 GDP per capita was $\$100 \div \ 100 = \$1$.
2017 Real GDP per capita (in 2017 prices) was also $\$1.$
2018 GDP per capita was $\$110 \div \ 105 \approx \$1.048$.
2018 Real GDP per capita (in 2017 prices) was $\$1.048 \div 1.03 \approx \$1.017$.


What is the difference between present value and face value? What is the difference between present value and face value?
When I search this question on Google is says they're the same in some cases and different in others. It says they are the same when the market interest rate is the same as the contractual interest rate.

I need help understanding what this means. I do not understand the difference between these  types of interest rates, etc.
And also does this have anything to do with discounting vs. coupon bonds, etc?

Suppose the face value of a bond is $M$ and its interest rate is $\tau$. This means it will pay $\tau \cdot M$ interest every year (other periods are also possible) and at the end of its run (its maturity) it will also repay the face value $M$. Government bonds are usually sold in auctions. Whatever ends up being the market price is considered to be the present value of the bond. Using the cash flow you can also calculate the yield of the bond. If and only if the face value and the present value are equal the yield will be equal to the interest rate.

For an example see the US treasury's website. Click on bonds to see face value, interest rate and maturity, click on the bond serial to see its price (present value).

Further reading here. (Link copied from a comment by @Jamzy .)


Long-,short-term interest rates and inflation I just read about the "dynamics" of long-, short-term intreset rates and inflation. Does the logic go as follows?

Centrals banks determine interest rates which in turn determine the short term rates. Inflation and expected inflation on the other hand determine how the central bank will most likely change the rates in the future(i.e what the market expects the central banks to do), hence

short term rate + expected inflation= long term rates?

Found the info here,

https://www.investopedia.com/articles/bonds/09/bond-market-interest-rates.asp

Does the logic go as follows?

  short term rate + expected inflation= long term rates?

Not exactly. There is some confusion. Inflation distinguishes between real and nominal interest rates, whereas the discrepancy between short- and long-term interest rates is derived from the preclusion of arbitrage opportunities. It is neither actual nor expected inflation, but the forward rate, what explains the discrepancy between short- and long-term interest rates.

By way of example, suppose the short- and long-term rates currently are 3% and 5%, with short- and long-term referring to 1 and 2 years, respectively. The interest rate $r_{f}$ for the 2nd year should be such that $(1+0.03)(1+r_{f})=(1+0.05)^2$. Any other rate $r_{f}$ would allow either the borrower or the lender to make profit with no risk (or somewhat equivalently, to make profit without having to invest his own funds).

It is true that a lender requires higher return for long-term loans than for short-term ones because a longer term entails greater exposure to risk. But the inflation is just one of multiple risks that the lender factors in when determining at what rate (of return) he is willing to lend money.

Edited on 7/22/2018 (at 3:29PM EDT) to supplement as per 2nd-to-last comment

There is no robust or widely-adopted method for calculation of long-term rates based on estimated future inflation (and/or short-term rates). Nor is there a mathematical expression describing how --or even whether-- market forces use the estimated future inflation for determining the rate at which lenders are willing to commit funds for a long-term period. I personally doubt that such method or expression could ever exist.

One can only resort to qualitative reasoning to sketch the generic effect that some information tends to have on long-term rates. In the case of expected/estimated future inflation, it might be implicitly (at most, but perhaps not at all) reflected in other factors and preferences that influence those market forces. Uncertainty --as you rightly point out in one of your comments--, risk aversion, and cost of opportunity are three of many other factors and preferences that influence how much a long-term rate would differ from the short-term rate.

Although it is reasonable to conjecture that these estimates, factors, and preferences are positively correlated with the duration of a long-term period, it would be very hard (or I would say futile as well as impossible) to reliably model by how much they cause a long-term rate to differ from the short-term rate.


Constant MC - Monopolstic Competition I would like to know if it is possible to have constant marginal costs (MC) in a business that is operating on a market, that is defined by monopolistic competition?

The company is a construction company, more specific a scaffolding company. My assumption is based on:

They have invested in their building materials one time. This means that they have a natural limit on how much work they can do.
They don't expect to buy more building materials in order to do more work, since they are also limited by number of employees.
All employees are on a fixed salary.
The only variable cost that is associated with each construction job is the transporation to/from site.

Since there is only one variable cost - the transportation, I am assuming that the marginal costs are constant, since transportation doesn't cost more whether they have 1 site (Q) or 10 sites (Q) to maintain.

Is this a valid assumption? Is it possible to have a constant MC such a market?

It is possible for firms to have constant marginal costs in monopolistic competition in theory. Nevertheless, they must also have fixed costs. The fixed costs prevent firms from entering in sufficient numbers such that you would have perfect competition.

As to whether constant marginal costs are realistic in you scenario, that depends on what you believe about the industry in practice. That would require detailed knowledge and expertise of this specific industry, which you are unlikely to find on this site.

Note, however, that just because the company has already bought the materials does not neessarily mean that these costs do not matter. For example, the company may still want to use less material per production output, because it could resell the unused materials. So the company in that case still cares about the costs associated with the use of each unit of material.

It is a bit unclear in your example what this company actually produces. However, if you think the costs of producing one extra unit are the same, regardless of how many units you have already produced, then you are justified in assuming constant marginal costs.


Neutral technical progress Recently I learnt that Cobb-Douglas production function has elasticity of substitution equal to 1, therefore it has neutral technical progress. Then Leontief production function has zero elasticity of substitution. Does that imply that it cannot have neutral technical progress? On the other hand, factors of production in Leontief cannot be substituted for one another so I thought it can never have labour or capital saving technical progress.

There are different notions of neutrality of technical progress in macroeocnomics.

You can have Hicks-neutral technical progress - that is a technical progress that increases the marginal productivity of all factors of production by the same proportion at the same capital-labor ratio. An example of Hicks-neutral production function would be one where $Y^*= F(AK, A L) = A F( K,L)$ and consequently $\frac{\partial Y / \partial K}{\partial Y / \partial K}= \frac{AF_k}{AF_L}= \frac{F_K}{F_L}$. Also note the technical progress would be neutral when its neither capital or labor saving, according to Hick's definition in his the theory of wages, labor saving technology would be one that improves the marginal product of labor relatively more and capital saving that which improves the marginal product of capital relative to labor.

I dont recall ever seeing Leontief production function that would be assumed to be Hicks-neutral in research papers but I think it should be possible to have special cases such as $ F = \min{ \{A K, A L}\}$ where $K$ and $L$ have to be consumed exactly in the same proportion you could say that the technology is Hicks-neutral as it is neither labor nor capital saving, also the $K$ and $L$ ratio would have to remain constant as they are perfect complements and here we would need one unit of capital for every one unit of labor.

Whether the production function is Hicks-neutral depends also on factor elasticity of substitution as well as product elasticity of demand but that is more in sense that the same production function can be or not be Hicks-netural depending on the elasticity of substitution it has.

Then you can also have Harrod-neutral technical progress. In this definition the technological change is neutral as long as capital-output ratio and the rate of profit stays constant. An example of such function would be a function where technology is labor augmenting like $F(K, AL)$.

Next, you can also have Solow-neutral technical progress which is defined as technological change that leaves
the relative input shares  unchanged for a given labour-output ratio. With example being capital augmenting technology $F(AK,L)$.

Moreover, you can even have Leontief-neutral technical change. This occurs when the augmentation effect of technology would be different for both factors of production so you would have $F(A_1 K, A_2L)$ where $A_1\neq A_2$.

None of the above definitions seem to exclude Leontief production function per se.


Reference request: Development economics I am looking for some good books on Development economics. My background is in mathemathics and statistics (with working knowledge of intermediate micro and macro), so a "good" book needs to be rigorous yet also provide intuition.

What are people reading these days when it comes to this topic?

Development economics has a distinct flavor among subfields in Economics, in that it usually opts for a more socio-economic, geopolitical and historical approach rather than mathematical modelling.
But they do use rigorous quantitative methods as regards empirical studies.

Anyway a book that can certainly show you how this subfield thinks is E. Wayne Nafziger's "Economic Development" (850 pages long - in hardcover, the book weighs 1.5 Kgr!)

See also the scientific journal "Journal of Development Economics"


Why do many occupations show a gender bias? Yesterday we had a question about the alleged underpayment of women in work, asking why employers would hire fewer cheaper female workers and would instead hire a larger number of expensive male workers. A large amount of discussion ensued.
I'd like to approach the same topic from a different angle.
Without doubt many occupations show a gender bias, and across the board it is apparent that women are more concentrated in occupations which attract lower hourly pay.
What are the economic reasons why, when encountering low pay (or anticipating it at the start of their careers), women should not simply respond to economic incentives, and choose to transfer to higher-paid occupations to increase their earnings?
I should say pre-emptively that I'm not satisfied with ideas that merely may explain the effect, as yesterday's question produced a proliferation of rationalisations and claims that lacked rigour.
I'd prefer to see an explanation that attempts to be comprehensive, or supports contentious claims (such as those about women's productivity) with research.

I should say pre-emptively that I'm not satisfied with ideas that merely may explain the effect, as yesterday's question produced a proliferation of rationalisations and claims that lacked rigour.

I'd prefer to see an explanation that attempts to be comprehensive, or supports contentious claims (such as those about women's productivity) with research.

Your question and the yesterday's one are contentious even in the literature, which means there is no consensus among the economists and no one can give an answer that satisfies everybody. Given the complexity of these questions, they can involve and interact with many different issues, all of which matter to some extent. Even in the literature, the common way is to attack them from one specific perspective rather than to offer a "comprehensive" answer. Also a convincing explanation usually requires careful data analysis, qualified modelling and many robustness checks, which suits more to an academic paper rather than to an answer in this forum.
However, I agree with you that we should avoid rationalisations and claims that lack rigour and the support of academic references. In the comments of this question someone has already mentioned that some recent papers argue that commuting requirement can be one potential reason. I thus list some recent papers that suggest other deep-in-root causes below.
Adda, Dustmann, Stevens 2017 finds that different occupations can diverge in the amenity "child raising value" and in the loss of accumulated skills when interrupting work careers. Given the fertility consideration, women would thus more likely to choose the occupations that have lower wage growth.
Occupation choice is also related with education choice. Women's underrepresentation in the math-intensive fields (i.e. STEM fileds) translates into their underrepresentation not only in high-paying occupations but also in occupations where the gender wage gap within the occupation is particularly small. A survey paper by McNally 2020 reviews many arguments behind this gender differences in tertiary education.
Hsieh, Hurst, Jones, Klenow 2019 studies the roles that the discrimination in the labor market, the barriers to forming human capital, and the differences in preferences or social norms play in individuals' occupation choice. They find that the improvement in the discrimination in forming human capital is the most important driver behind the increased participation of women in high-wage occupations in recent decades.
In additional to typical economics reasoning, Bertrand 2020 suggests that endogenous preferences and self-fulfilling prophecies caused by gender stereotypes can be important for the low share of women in STEM careers and occupations. Also, Grosjean & Khattar 2019 shows that cultural persistency can affect womens' occupational choices.


Log linearization of the technology dynamic I am still dealing with DSGE models and with log-linearization of characteristic equations of the model. The one that creates me more doubts is the technology shock, that is usually modeled as an AR(1).

Usually, we are given technology processes like
\begin{gather}
\ln(z_t)=(1-\rho) \ln(\bar z)+\rho \ln(z_{t-1})+\epsilon_t
\end{gather}
so that it is already linear and we can re-write it in deviations from the steady state just moving $\ln(\bar z)$ on both sides of equation, obtaining
\begin{gather}
\hat z_t=\rho \hat z_{t-1}+\epsilon_t
\end{gather}
where hat variables are log deviations from the steady state.

But when the process is something like
\begin{gather}
\ln(z_t)=(1-\rho) (\bar z)+\rho \ln(z_{t-1})+\epsilon_t
\end{gather}
how should I proceed?
What I cannot understand is how the log linearization should be used, taking into account that $\epsilon_t$ is a white noise process. I mean applying logs and differentiating gives me something I do not understand.

The shock process is already linear. any log linearisation will result in identical expression. The underlying non linear shock process can be something like this:$

$$ Z_t = Z^{(1-\rho)} Z_{t-1} e^{\epsilon_{t}}$$

This when you linearise, you obtain your linear shock processes.


What is meant by the sentence in the context of "Monetary Policy in India"? To quote from the book, "Indian Economy by Nitin Singhania," this is what I found out,"It is a macroeconomic policy used by RBI to influence the supply of money." What is meant by macroeconomic policy here?

From the first Google hit I got, The tools of macroeconomic policy—a short primer:

Macroeconomic policy is concerned with the operation of the economy as a whole. In broad terms, the goal of macroeconomic policy is to provide a stable economic environment that is conducive to fostering strong and sustainable economic growth, on which the creation of jobs, wealth and improved living standards depend. This brief outlines the nature of each of these policy instruments and the different ways they can help promote stable and sustainable growth.
[...]
Fiscal policy operates through changes in the level and composition of government spending, the level and types of taxes levied and the level and form of government borrowing. Governments can directly influence economic activity through recurrent and capital expenditure, and indirectly, through the effects of spending, taxes and transfers on private consumption, investment and net exports.
[...]
Monetary policy decisions are implemented by changing the cash rate (the interest rate on overnight loans in the money market).
[...]
By changing the cash rate the RBA is able to influence interest rates across the financial system. Changes in interest rates in turn can influence economic activity by affecting savings and investment behaviour, household expenditure, the supply of credit, asset prices and the exchange rate.
[...]
Exchange rate policy is concerned with how the value of the domestic currency, relative to other currencies, is determined.
[...]


Asymptotic variance vs. conditional variance in calculating regression estimator standard errors I am given regression model $y_i=x_i^T\beta+\varepsilon_i$ with heteroscedasticity.
Let $Avar(b)=E[x_ix_i^T]^{-1}E[\varepsilon_i^2x_ix_i^T]E[x_ix_i^T]^{-1}$
Hayashi's book states that regression coefficients are asymptotically normal:
$\sqrt{n}(b-\beta) \rightarrow^{D} N(0, Avar(b))$ therefore $b\sim N(\beta, Avar(b)/n)$ asymptotically for sufficiently large n.
Further, Hayashi states that the standard error of $b_k$ is precisely $\sqrt{Avar(b)_{kk}/n}$ where  $Avar(b)_{kk}$ implies the kkth element of the diagonal.
Question:
Why do we use $\sqrt{Avar(b)_{kk}/n}$ as a measure of standard error rather than $\sqrt{V(b|X)_{kk}}$ where
$V(b|X)$ is the conditional variance of b?
I am confused because earlier in the book he mentioned that the conditional variance should be used. For example, he specified that in the finite sample case under conditional homoscedasticity the standard error of $b_k$ was precisely:
$\sqrt{V(b|X)_{kk}}=\sqrt{\sigma^2(X^TX)^{-1}}$ with $\sigma^2=E[\varepsilon_i^2|X]$

So the asymptotic variance in the first expression that you give is the variance under heteroskedasticity as you note. The definition you gave of $V(b|X)$ is under homoskedasticity. As one of the comments states, we could use $V(b|X)$ (as you define it) under this assumption. It seems that Hayashi uses this notation because he wants to consider heteroskedastic errors.


Economies of scale v.s. technological change In Greene's Econometric Analysis, 7th edition, page 355, it is written that:

  A long-standing problem in the analysis of production functions has been the inability to separate economies of scale and technological change.

I know what the boldfaced terms refer to but it's not clear to me what is the source of the described "inability to separate." Can you please illustrate via a simple model, preferably one (adopted) from an article / a book that studies this very issue.

The problem is to distinguish between changes along the production function, from $f(K_1, L_1)$ to $f(K_2, L_2)$, and changes of the production function, from $f(K_1, L_1)$ to $g(K_1, L_1)$.

A very simple example/model. Imagine that the only input is labor and that this input doubles between t and t+1, but output more than doubles : $L_{t+1} = 2 L_t$, $Y_{t+1} > 2 Y_t$.

To interpret this observation you have two alternatives :

Assume that there is a production function with increasing returns to scale, i.e. $1/Y dY/dL > 1$, so that $Y_t = f(L_t)$ and $Y_{t+1} = f(L_{t+1})$.
Assume that the production function has constant returns to scale, i.e. $Y_t = \alpha L_t$ and $Y_{t+1} = \beta L_{t+1}$, but technical progress has occurred between periods $t$ and $t+1$, so that $\beta > \alpha$.
Of course any combination of the two explanations above is admissible.

During the 'Cambridge controversies on capital', this was one the arguments which led the English Keynesians to reject the notion of production function. One famous paper building a growth model without a production function is Kaldor-Mirrles (1962), A New Model of economic growth


Distribution of Wages Is there any paper that looks at the distribution of wages? I'd like to see how many workers are in each percentile of labor income. I know that you could compute it using CPS or US tax data, but I suppose somebody must have done that before..

Based on the 2010 US Census, Wikipedia has pretty much exactly what you seem to be looking for.

A sample graph:

though they of course also have tables and links to more data.

Or if you prefer raw data, the IRS SOI is available for 1996-2012.

And of course there's Piketty and Saez seminal paper on the subject (See Table 5 for their data analogous to the included Wikipedia picture)

And of course there's the BLS which publishes these things regularly by demographic, hourly only, or occupation/industry.


What is the effect of Quantitative Easing on the US budget deficit? Is the deficit getting larger because of QE?

No, the deficit is not getting larger due to QE. Certainly not directly, because that's impossible, and also not indirectly, either.

Quantitative easing is a policy of purchasing government bonds with the intent of decreasing yields while injecting cash into the economy. It affects only the demand for government bonds, not the supply of bonds created by government borrowing.

This shouldn't be a surprise, as the monetary authority (the central bank) and the fiscal authority (Congress) are independent of one another. Congress cannot (without rewriting the Federal Reserve Act) directly control monetary policy, nor can the Fed force the government to borrow more.

Indirectly, Congress could choose to borrow more as a result of QE, due to lower yields on government debt, as the lower debt payments make it cheaper to do so. However, there's not much evidence that this is the case.

The deficit has fallen since 2009 (when it significantly increased due to passage of a large-scale stimulus program consisting primarily of tax cuts but also including direct federal spending, in response to the financial crisis and recession), both in nominal terms and as a percent of GDP. As a percentage of GDP (which is the appropriate long-term comparison, as taxable income is the best indication of a nation's ability to repay a debt), the deficit returned to a normal historical range by 2014.

So it's difficult to conclude even that QE encouraged spending, thereby increasing the deficit indirectly. Given two facts— that the Federal Reserve's QE programs started in earnest in 2009 and continued until late 2014, and that the federal deficit steadily fell during this time— it would be very strange indeed to conclude that QE had increased the deficit.


How does a positive capital shock cause an increase in land price? I am trying to determine the exact theoretical mechanism for a positive capital shock to create an increase in land price.

Assuming output is a function of land ($L$), labour ($N$)  and capital ($K$) :

$$ Y = A f (L, N, K) $$

I am unsure if I am correct, but so far I have,

Positive capital shock -> increase in the MPK -> labour demand rises -> wage rises -> qty supplied of labour rises -> MPN rises -> with more workers available to work the land, each additional unit of land is able to produce more output -> MPL rises -> price of land rises.

If you know any papers that deal with this particular mechanism please let me know also.

You might want to assume a Cobb-Douglas production function for the sake of simplicity.

$Y=A L^{\alpha_1} N^{\alpha_2} K^{1-\alpha_1-\alpha_2}$

Hint: Look at to the cross derivatives.


First Price Auction with Reserve Price I'm trying to solve the following question:

"The seller wants to auction off a single item to two bidders, the valuation of each bidder is an iid draw from a uniform distribution on $[0,1]$ where the seller sets a reserve price, $r$, and has zero valuation for the item.

I was able to solve for the second price auction, such that the equilibrium bidding function is to bid your valuation for $v>r$ and to not enter if $v<r$.

For the first price auction, I usually go about solving for the bidding function by first calculating the probability that bidder i wins:

$\Pr(i\text{ wins})=\Pr(v_i > r) * \Pr(v_i > v_j)$.

Where I know that $\Pr(v_i > v_j) = (1-b^{-1}(b))$ which I can then use to derive the bidding function as usual in an ordinary FPA $(0,0)$.

My question is, how do I work the reserve price into the bidding function.

Let's forget about the reserve price for a second.

Suppose there is a symmetric increasing equilibrium bidding strategy $b(v)$. We can think of a bidder with value $v$ as choosing which $\tilde{v}$ he will "pretend to be" by submitting bid $b(\tilde{v})$. The bidder wins iff $\tilde{v}>v_j$ (where $v_j$ is his rival's value). Thus, the payoff is

$$(v-b(\tilde{v}))\Pr(\tilde{v}>v_j)=(v-b(\tilde{v}))\tilde{v}.$$

Now compute the FOC for choice of $\tilde{v}$:

$$v-b(\tilde{v})-\tilde{v}b'(\tilde{v})=0.$$

If $b$ is really an equilibrium then the optimal choice of $\tilde{v}$ should be the bidder's true value, $v$: $v-b(v)-vb'(v)=0$. This is a differential equation. To solve it we just need a boundary condition.

Anyone with $v<r$ will not bid. So the set of bidders will be the truncated uniform distribution on $[r,1]$. Intuitively, a bidder with value $r$ cannot earn a positive surplus, so a reasonable boundary condition seems to be $b(r)=r$.

Solving the initial value problem
$$v-b(v)-vb'(v)=0,\ b(r)=r$$

yields the equilibrium $$b(v)=\frac{r^2+v^2}{2v}.$$


Teaching: from Microeconomics to Open-economy macro I am a new faculty teaching MBA courses. Presently, I am teaching International Financial Management (IFM) and Macroeconomics. I have prepared the syllabus of macroeconomics based on first 9 chapters of the core module in "Macroeconomics, Blanchard and Johnson, 6/E, Pearson, 2017, 9789332587601". The idea is to keep mathematical exposition to the minimum while building a base for the discussion of open-economy macroeconomics based on chapter 20 & 21 in the above-mentioned book during IFM course.

I would also be teaching microeconomics.

How do I form the syllabus for microeconomics to support my teaching of Macroeconomics and IFM while focusing on intuition rather than extensive mathematical exposition? Suggest some appropriate textbooks for this purpose.
Any suggestions to enhance my research (maybe in Macro-Finance) based on the teaching of above subjects.

This is for Micro, entirely based on my own opinion and experience.

Syllabus:

The most useful topics would be those on production and cost and perfect competition. I see no point of talking about utility theory unless you will be covering intertemporal choice. This and basic demand-supply. If you will be covering ISLM, you might find it a good idea to discuss "shifting a curve versus moving along a curve" with demand-supply prior to moving to ISLM.

Books:
I personally find useful The Applied Theory of Price by Deirdre McCloskey. The math (read calculus) was usually in the footnotes or appendix and I really did not need calculus to cover almost all of the standard chapters - Consumer Behavior, Perfect Competition, Monopoly etc. The exposition was intuition based.

However, having used this book as an instructor, I personally needed to actually read and work through the examples before teaching it to my students - some of them could require a bit of very careful thinking.

The book is available on the author's webpage: http://www.deirdremccloskey.com/books/index.php

Depending on how much calculus you want to show your students, other open source books on micro could be the one by McAfee https://www.mcafee.cc/Introecon/
and the one by Yoram Bauman (can't find the link to it)


International emissions trading As far as I have understood emission right certificates are some kind of currency. Each company may emit as much of say CO2 as its certificates allow. Certificates may be traded, i.e. bought and sold. If a company emits more than it is allowed to it pays a fine (to the country where the pollution occurs).

My question is: How is it prevented that a wealthy company in a rich country buys lots of certificates (to a modest price) from a poorer company in a poorer country which in turn is forced to emit more pollutants than it is allowed to (because it sold all its certificates) - but its country doesn't force it to pay the fine.

Thus the intended effect of emission right certificates would be undermined. By which measures is this tried to be avoided?

There can be civil or criminal penalties applied for non-compliance.

See for example:
https://www.gov.uk/government/publications/environment-agency-enforcement-and-sanctions-policy/annex-2-climate-change-schemes-the-environment-agencys-approach-to-applying-civil-penalties

https://www.daera-ni.gov.uk/articles/euets-fees-charges-and-civil-penalties

International trading schemes depend on international law. Membership of such schemes will depend on accepting an adjudication body to rule on breaches, as with any other international contractual agreement.


How does economic theory handle full automation of production resulting in full unemployment? As advances in robotics and artificial intelligence continue, one possible outcome is a laborless economy, in which capital (means of production) is the dominant factor in production, by multiple orders of magnitude.  Looking at the current system, it would seem to me that a steady progression toward full automation within the bounds of the current market structure would lead toward an ever increasing concentration of wealth amongst those that possess capital.  (coincidentally, this seems to be occurring)  The end result of this, in my mind, seems to be a collapse of capitalism, in which supply curves are vertical, demand curves are horizontal, and they intersect near 0.

Now there are proposed solutions, which seem to move toward socialism, in general.  In this question, I am not seeking one of these solutions, but rather, theory.

My question is, it seems that traditional economic theory relies on { capital, labor }.  How does economic theory handle a zero-labor scenario, in which the capital is essentially a black box that outputs products?

If this were to occur, there are three things we need to look at.

1) Will production occur?

2) Without wages, how will households make money?

3) What will be the welfare effects?

$\textbf{1)}$ To answer the first question, if we assume that capital replaced all labor, we are assuming that capital and labor are substitutes which means that the production function will have the following form:
$$F(k,l)=\alpha k+\beta l$$
What this means is that if $l=0$, $F(k,l)$ will still be greater than zero, so production will still occur.

$\textbf{2)}$ To answer the second question, we can look at how households make money. Households make money from wages, and they make money from owning a fraction of firms (so they get that fraction of the profits the firm makes). All firms are owned by households (either through stocks or private ownership). The typical income of a household looks like the following:
$$Y(\frac{}{})=wl+\theta\Pi$$
Where $w$ is wages, $l$ is labor hours, $\theta$ is the fraction of firms which the household owns, and $Pi$ is those firms' profits. If $l=0$, our income reduces to $Y(\frac{}{})=\theta\Pi$

One thing that immediately comes to mind is "without wages, won't all households' income decrease?" Well, we don't know for sure. According to economic theory, the reason the automation will have occurred is because it will cost less. What this means is that profit will increase, so $\theta\Pi$ will also increase. It really depends on whether $\Delta\theta\Pi$ is larger than, smaller than, or equal to $wl$.

$\textbf{3)}$ The welfare effects are where we run into problems. When we look at the equation for income of a household, we can conduct a thought experiment: How does the fraction of income attributed to each term change when in different income groups? In the highest income groups, most of their income will come from $\theta\Pi$. An example of this would be the show SharkTank. In this show, companies come to the very wealthy "sharks" looking for capital, and in turn, they often offer a share of their company. Now, when we think about lower income groups, where does most of their income come from? Well, most of their income comes from wages because they cannot afford to save money (and therefore invest in stocks or entrepreneurship). What would happen as a result from full automation, we would theoretically see the income inequality grow to be even larger than it currently is. This is a very undesirable result.


Is the Ramsey model one with non negative investment? I have a very fundamental question. I am currently searching for an economic growth model with non negative investment. Can someone tell me if the Ramsey model is one with non negative investment and if so - why? Thank you very much

No it is not. The benchmark Ramsey model allows for positive and negative investment. Treating the case of non-negative (or "irreversible" investment) is considered an extension.
See Barro & Sala-i-Martin (2004). Economic growth (2nd ed)

Appendix 2B for a short discussion and
Section 5.1.2 pp 242-247 for an Endogenous growth model with irreversible investment and Human capital.

For a more deep treatment, see
Arrow and Kurz(1970).  Optimal Growth with Irreversible Investment in a Ramsey Model, Econometrica, Vol. 38(2), 331-344 .


Under what circumstances is an increase in national output called economic growth? An increase in output can be achieved in two basic ways.

The first scenario:
Aggregate demand increases, so supply extends. In this way the economy is making more use of its resources, but there is still spare capacity, and productive potential hasn't increased.

The second scenario: Aggregate supply increases. National output increases without demand increasing and productive potential of the country has increased.

Now I know that the second scenario is economic growth for sure, as economic growth is generally characterised by an increase in the productive potential of country. But is the first scenario also economic growth? That is, is it called economic growth if a country just makes use of more resources already available to satisfy increased demand?

Furthermore, can the first scenario be shown on a PPC? Perhaps a shift from a point within the curve to a point on the curve?

There are actually 2 types of economic growth. Actual growth is when output increases. Potential growth is when productive potential of the economy increases.

If long run aggregate supply increases without any change to short run AS, then you have potential growth but not actual growth. This might happen with if a new discovery is made, but has not yet been applied in industry.

If SRAS increase without any change to LRAS, then you have actual growth, but no potential growth. This might happen to an oil-dependent economy if there is a temporary fall in oil prices.

As long as there is short-term capacity in the economy, increases in aggregate demand will lead to actual growth. Aggregate demand, however, cannot lead to potential growth except by affecting LRAS (e.g. through changes in producer expectation etc).

Finally, you are correct in that actual growth is shown by moving a point closer to the PPC/ in the North East direction.

See any lecture material:
http://www.tutor2u.net/business/strategy/economy-economic-growth.html


What is the difference between Q4/Q4 and Y/Y GDP growth? Per US media, the US economy grew 3.1% in 2018 Q4/Q4 and 2.9% in 2018 Y/Y. 2.9% seems the reference number in various databases (World Bank, Reuters, Bloomberg, etc) but what exactly does Q4/Q4 mean and which measures changes from Jan 1 2017 to  Dec 31 2017 compared to Jan 1 2018 to Dec 31 2018

If you could include the source(s) you were talking about that would be great. Without further info, my initial guess is that the Q4/Q4 means you compare GDP in 2018Q4 to GDP in 2017Q4. Y/Y means you compare GDP in the whole year of 2018 to that of 2017.

Upon further inspection, if you take a look at the US's real GDP, you'd get the following:

Growth in 2018Q4 compared to 2017Q4: 2.52%
Growth in 2018Q3 compared to 2017Q3: 3.13% [Link]
Growth in 2018 compared to 2017: 2.93% [Link]

So I think your Y/Y number is right... but the number for "2018Q4/Q4" might have been growth in Q3?

Update

It seems like the number reported was the initial estimate (which gives YoY growth of 2018Q4 to be 3.1% and 2018 to be 2.9%) in February 2019. The third estimate (which is what FRED uses) was released in December 2019 and yields YoY growth as calculated above.


Does a tighter spread between occupancy and stabilized occupancy indicate higher demand? I'm trying to understand how to think about real estate markets and how to identify markets where there might be strong demand for additional housing (I'm looking at senior housing in particular) and am new to real estate, so I had a few questions about metrics.

In particular, two that seem important are occupancy rates (measured as beds filled/available beds in all facilities) and stabilized occupancy rates (measured as beds filled/available beds for facilities that are at least 2 years old.

Obviously, if there's lots of new construction, we'd expect occupancy to fall as a lot of new beds are coming online and it takes time to fill them.

What I'm wondering, however, is if there is significance in comparing the spread between occupancy and stabilized occupancy. For example, if we had a fake and overly simplistic example of two markets that looked like this:

Market 1, Occupancy Rate of 88%, Stabilized Occupancy Rate of 90%, Construction vs. Inventory of 5%
Market 2, Occupancy Rate of 50%, Stabilized Occupancy Rate of 90%, Construction vs. Inventory of 7%

then the conclusion I would draw is there is likely much more latent demand in Market 1 than Market 2 because at at the same new construction levels, the spread is so much lower in Market 1 (2%) than Market 2 (40%), indicating that properties are filling up much faster in Market 1.

Is that the right way to think about this metric? If so, how should I think about adjusting or scaling this kind of metric for the amount of new construction?

Does a tighter spread between occupancy and stabilized occupancy
  indicate higher demand?

Not necessarily. Demand is not the only factor that determines occupancy rates. A tight spread by itself only indicates market steadiness (that is, uniformity over time).

Using your example, Market 2 could have experienced a significant increase of demand in the past two years and yet present a lower occupancy rate if cost at new facilities outweighs the demand increase. The new bedrooms are available but only few consumers can afford them.

Government intervention and/or expectations about the future might also discourage suppliers from effectively releasing to the market much of the new facilities. This certainly amounts to a reduction of supply (and a higher Occupancy Rate, accordingly), but metrics might fail to capture that reduction in a market that would otherwise reflect the same demand and Occupancy Rate as Market 1.


Does savings lead to investment in physical capital? In the introductory macroecon textbook I'm reading, it's made clear that savings=investment.  Mathematically, this makes sense to me.  However, I'm having trouble understanding the qualitative implications.

After looking through other similar questions, it's clear that this is due to an accounting identity where inventory accumulation due to savings is counted as investment.

But, I stumbled across this blog post, https://mainlymacro.blogspot.com/2012/01/savings-equals-investment.html, that claims savings eventually equals investment in capital (S=DK).  From what I understand, the author of the post is saying that savings will lead to inventory accumulation, DS, which will eventually lead to output (Y) decreasing.  The output must decrease for the firm to avoid losing money.  Decreasing output will lead to income decreasing, and therefore savings further decrease to the point where savings equal DK, or investment in capital goods.

Why does the eventual decrease in savings cause savings to equal investment in capital goods (S=DK)?  Am I correctly interpreting what the author of the post is saying?

I think that part of the blog post is just saying that savings may not equal investment in capital immediately, because there can be a delay caused by firms accumulating inventory.  But firms can't continue to accumulate inventory indefinitely, so this is only a transient phenomenon.  Sooner or later, inventory will reach a new equilibrium and savings will equal capital investment again.

He then goes on to talk about the reasons that a higher savings rate is unlikely to be sustained (the paradox of thrift).


why is I included as part of GDP? GDP = C + I + G + (X-M)

If GDP is supposed to count only final goods and services, why include I? Eg if build public roads, can count as G; if build factory, can count when factory produces goods and those goods are sold.

Put differently, counting I seems to double count. Eg if one counts spending on factory as I today, when the factory produces and sells goods tomorrow and in subsequent periods, the counting is done again (eg I, followed by C).

Investing is about "new" things that did not exist. Any acquisition of a previously existing asset, such as a house, is considered as Savings rather than Investment. Moreover, Investment is not consumed at the present time and are expected to provide flows for longer periods of time.


Alternative way of deriving OLS coefficients In another question of mine, an answerer used the following derivation of OLS coefficient:

  We have a model: $$ Y = X_1 \beta + X_2 \beta_2 + Z \gamma + \varepsilon, $$ where $Z$ is unobserved. Then we have: $$\text{plim}\, \hat \beta_{1} = \beta_1 + \gamma \frac{Cov(X_1^*, Z)}{Var(X_1^*)} = \beta_1, $$ where $X_1^* = M_2 X_1$ and $M_2 = [I - X_2(X_2'X_2)^{-1}X_2']$.

This looks different from the usual $\beta = (X'X)^{-1}X'Y$ that I've seen in Econometrics. Is there a more explicit exposition of this derivation? Is there a name for the $M_2$ matrix?

The $\mathbf M = \mathbf I-\mathbf X(\mathbf X'\mathbf X)^{-1}\mathbf X'$ matrix is the "annihilator" or "residual maker" matrix associated with matrix $\mathbf X$. It is called "annihilator" because $\mathbf M\mathbf X =0$ (for its own $X$ matrix of course). Is is called "residual maker" because $\mathbf M \mathbf y =\mathbf {\hat e}$, in the regression $\mathbf y = \mathbf X \beta + \mathbf e$.

It is a symmetric and idempotent matrix. It is used in the proof of the Gauss-Markov theorem.

Also, it is used in the Frisch–Waugh–Lovell theorem, from which one can obtain results for the "partitioned regression", that says that in the model (in matrix form)

$$\mathbf y = \mathbf X_1\beta_1 + \mathbf X_2\beta_2 + \mathbf u$$

we have that

$$\hat \beta_1 = (\mathbf X_1'\mathbf M_2\mathbf X_1)^{-1}(\mathbf X_1'\mathbf M_2)\mathbf y $$

Since $\mathbf M_2$ is idempotent we can re-write the above by

$$\hat \beta_1 = (\mathbf X_1'\mathbf M_2\mathbf M_2\mathbf X_1)^{-1}(\mathbf X_1'\mathbf M_2\mathbf M_2)\mathbf y$$

and since $M_2$ is also symmetric we have

$$\hat \beta_1 = ([\mathbf M_2\mathbf X_1]'[\mathbf M_2\mathbf X_1])^{-1}([\mathbf M_2\mathbf X_1]'[\mathbf M_2\mathbf y]$$

But this is the least-squares estimator from the model

$$[\mathbf M_2\mathbf y] = [\mathbf M_2\mathbf X_1]\beta_1 + \mathbf M_2\mathbf u$$

and also $\mathbf M_2\mathbf y$ are the residuals from regressing $\mathbf y$ on the matrix $\mathbf X_2$ only.

In other words:
1) If we regress $\mathbf y$ on the matrix $\mathbf X_2$ only, and then regress the residuals from this estimation on the matrix $\mathbf M_2\mathbf X_1$ only, the $\hat \beta_1$ estimates we will obtain will be mathematically equal to the estimates we will obtain if we regress $\mathbf y$ on both $\mathbf X_1$ and $\mathbf X_2$ together at the same time, as a usual multiple regression.

Now, assume that $\mathbf X_1$ is not a matrix but just one regressor, say $\mathbf x_1$. Then $\mathbf M_2 \mathbf x_1$ is the residuals from regressing the variable $X_1$ on the regressor matrix $\mathbf X_2$. And this provides the intuition here: $\hat \beta_1$ gives us the effect that "the part of $X_1$ that is unexplained by $\mathbf X_2$" has on "the part of $Y$ that is left unexplained by $\mathbf X_2$".

This is an emblematic part of classic Least-Squares Algebra.


CDO & CDS on medical patients As far as my knowledge goes, a "collateralized debt obligation" (CDO) restructures existing bonds into "layers" of debt whereby each layer has similar kinds of bonds with similar kinds of features in it. So, for example, the lowest layer could be the riskiest layers where borrowers are expected to default the most and the uppermost layer would be one where borrowers with relatively higher credit scores would be placed. These are then sold forward to willing investors. These CDO's can be further restructured into a synthetic CDO but lets not get into that.

So now, a "credit default swap" (CDS) could be placed against a CDO thereby insuring against a loan default. So, for example, if a collective bunch of loans in the bottom most layer go bad within the stipulated time, then the insurer (bank) would be forced to pay back to the insuree (any third party).

Now, lets take the scenario of a hospital with cancer patients from Stage 0 to 5. A third party comes up to the hospital and asks the hospital to restructure the cancer patients files into "tranches" such that Stage 5 patients would be at the bottom most layer and Stage 0 at the top. He would then like to buy an insurance against the bottom most layer for a period of 1 month. So, if the insured layer goes bad in that month (which basically means a certain number of people in that layer die), the hospital would have to pay him back 50X the premium amount. The hospital could even create a separate financial subsidiary to carry out the above task.

Of course, this is completely unethical and really sad. My question is: What stops this from happening? Why is it seemingly okay to do this on a housing loan but not medical patients?

In the United Kingdom, your death bonds would be prohibited by the Life Assurance Act 1774, which still says in its entirety:

  Whereas it hath been found by experience that the making insurances on lives or other events wherein the assured shall have no interest hath introduced a mischievous kind of gaming:

  From and after the passing of this Act no insurance shall be made by any person or persons, bodies politick or corporate, on the life or lives of any person, or persons, or on any other event or events whatsoever, wherein the person or persons for whose use, benefit, or on whose account such policy or policies shall be made, shall have no interest, or by way of gaming or wagering; and every assurance made contrary to the true intent and meaning hereof shall be null and void to all intents and purposes whatsoever.
  And it shall not be lawful to make any policy or policies on the life or lives of any person or persons, or other event or events, without inserting in such policy or policies the person or persons name or names interested therein, or for whose use, benefit, or on whose account such policy is so made or underwrote.
  And in all cases where the insured hath interest in such life or lives, event or events, no greater sum shall be recovered or received from the insurer or insurers than the amount of value of the interest of the insured in such life or lives, or other event or events.
  Provided always, that nothing herein contained shall extend or be construed to extend to insurances bona fide made by any person or persons on ships, goods, or merchandises, but every such insurance shall be as valid and effectual in the law as if this Act had not been made.

and there are similar laws in other places.

There were two bases for this prohibition and regulation:

it amounted to a particularly distasteful form of gambling on people's deaths
it was dangerous for an individual to be more valuable dead than alive to another individual; insurance should solely be about compensating for losses

Housing loans are not as distasteful as human death, and there is no suggestion that purchasers of Credit Default Swaps could have acted in a similar way to murderers, though the reference in section 3 to events might also apply to their use for speculation


Fixed cost of a firm Suppose that a firm has a total cost function given by:
$TC(q) = \frac{5}{q+1} + 5 + 5q + q^2$.
What is the fixed cost?

I seem to be able to come up with two "answers", which cannot be correct. My hunch is that it is because I do not have a precise understanding of what a "fixed cost" is, as silly as that may sound.

Option 1
Fixed cost is the cost of production when $q = 0$. Evaluating $TC(0) = 10$. Thus, fixed costs are $10.

Option 2
Intuitively, fixed costs should be any term in the in the cost function that are not transformed by "q" in some way, since fixed costs should remain "fixed" and independent across any level of production. This would imply that fixed costs are $5.

I think clearly there is something I am missing here since there should be one answer. Can someone help me understand what the correct answer is and where exactly where I am going wrong with my reasoning for the incorrect option? Thank you!

It is the first one, $TC(0) = FC$. This is the definition.

Also consider that it is not clear what is "transformed by $q$ in some way". In case of
$$
\frac{5q}{q+1} + \frac{5}{q+1}
$$
are the two fractions transformed by $q$, or should I just sum them up to 5?

With your function, one can rearrange it to
$$
TC(q) = \frac{5}{q+1} + 5 + 5q + q^2 = -\frac{5q}{q+1} + 10 + 5q + q^2.
$$


Why do Australian milk farmers need to protest supermarkets' milk price? Sorry this might be borderline off-topic (and I am an economics layman at best), but I found this rather puzzling and would like to know why this is happening.

I just came across an article which documents another development in the quarrels between Australian milk farmers and big supermarket chains.

As I understand it, the farmers demand that supermarkets charge higher prices for milk and then pass on the additional revenue back to the farmers.

When I think of the free market, I would expect this to be unnecessary, as the farmers could charge more when they sell the milk to the supermarkets or, if that doesn't work (why wouldn't it?), some farmers would stop milk production leading to milk scarcity leading to higher prices or, more importantly, higher revenue for the farmers.

What am I missing?

I would like to contradict Kenny LJ explicitly on his claim that "the free market works".

It only works if the market is actually free, i.e. competition exists. Which, you can argue, is not the case in the milk market.

What you are looking at is a cartel.

(Excuse me for citing numbers for the German market, not Australia, as I am more familiar with that market and have numbers ready that I don't have for Australia. I am quite confident, however, that while the ratios might differ a bit, the overall structure will be the same.)

There are about 100.000 milk farmers in Germany, producing about 28 million tons of milk per year. As Mick pointed out, however, they are in the farming / production business, not in the transportation / processing business, so they have to sell their milk to dairies. There are just over 100 dairies in Germany.

And most of them have a monopoly on their region, meaning they're the only dairy a farmer could sell to.

Those dairies sell the processed milk to supermarket chains and other retailers / business consumers. About 60% of all the milk produced is sold by less than a half-dozen major supermarket chains.

Milk is a highly regulated food product, meaning that one dairy's milk is effectively the same as any other. There is very little competition in quality. The dairies don't even have "a product", the milk ends up packaged in the supermarket brand:

  Woolworths has bumped the cost of its own-brand milk by 10 cents a litre, but Coles has refused to follow suit because it might burden customers.

So the only competition is in the price. Whoever sells cheapest. Customers buy the milk where it's cheapest (supermarket), because they simply do not have any realistic option to go for a "premium" milk product that's provided by middle- or small-sized, or regional, producers at a sustainable price with a transparent premium for the producer as well. It's just not available. There are "bio" brands, but that label is only saying something about how the cattle is kept and fed -- the price dynamics still apply:

The supermarket buys where it's cheapest (dairy), and the dairy tells the milk farmers how much they are willing to pay, take it or leave it.

A farmer that is not willing to sell his milk at the price the dairy dictates (even if it's at a loss), will not get his milk to market at all, but still have running costs to pay. Which means he'll be out of business pretty quick, forced to sell his business, land, and lifestock to some bigger farmer that is able to use scaling effects to produce at a lower price.

You could claim that this is the result of an oversaturated market, that less milk on the market would drive the prices up. That is correct, in a way, but the market is oversaturated because producing large quantities of milk as cheap as possible is the only bargaining chip the producers have in a market where literally no-one is going to a farmer to buy produce. Rising prices would not equate to rising margins for the farmers, as they simply have no control over the supply chain.

Concentration of power at the retailer end, a lack of competition in quality, and the inability of the producer to cut out the middle man (dairies) or create a meaningful "premium" market means the retailer is dictating the price, to the point where producer's margins are minimized and the only way to be a profitable producer is by economics of scale -- large combines swallow medium and small-sized producers, and the retailers are able to push the price even lower, repeating the cycle.

This is beneficial to the customer insofar as that the product (milk in this case) is available at every supermarket and extremely cheap. But it comes at a high cost, destroying middle- and small-sized milk farms (and dairies!) in a race to the bottom. Which also includes a race for the most milk-efficient cattle, to the exclusion of all other considerations.

Refuting Kenny LJ's wholesale dismissal of regulation:

  Suppose instead that these farmers instead benefited from low grain prices and enjoyed profits of 20 cents per litre of milk sold. Should consumers then have stood outside supermarkets demanding that milk prices be lowered by 10 cents per litre?

The consumers wouldn't have had to, as the supermarket chain would already, preemptively, have realized the opportunity to lower prices (to stay competitive to the other supermarket chains who would have done the same).

Addendum:

In answer to a comment by @horns, this is a matter of official record and investigation.

Rewe was sentenced to 20.8 million Euro antitrust fine in May 2013. Spar was sentenced to 3 million Euro antitrust fine in November 2014. (Just two I was able to duckduckgo ad-hoc.)

Quoting the German Antitrust Office:

  Our investigations have shown that the contracts between milk producers and dairies in Germany have long periods of notice and duration. In addition, farmers in Germany are generally obliged to supply the milk they produce exclusively to their respective dairy. There is virtually no possibility for them to switch to another dairy. This is a problem for farmers and hinders possible newcomers on the dairy side or dairies wishing to extend their activities. Another widespread practice is that the price of raw milk is set only after delivery and is based on reference prices and market information systems.

Also from that article:

  The Bundeskartellamt questioned 89 private and co-operative dairies, which in 2015 procured approx. 30.9 million tonnes of raw milk. This is equivalent to around 98 % of the total milk supply volume. The authority's investigations have shown that in 2015 97.8% of the volume of raw milk covered by the investigations was sold subject to exclusive supply obligations. In addition, contracts for more than half of the raw milk supply volume can only be terminated with at least two years' notice.

There is no effective competition.


If Germany is the largest exporter, why do Chinese products pervade the the US market? Despite Germany being the third larger exporter in the world, I have not once seen German products on online retail sites such as Amazon.com, NewEgg, BestBuy, or any retailer in the US really. Why is this the case? Amazon in particular is plagued with Chinese counterfeits, so why haven't market forces led to the appearance of an Amazon alternative, focused on original German (or Japanese) products, for customers that are more quality-sensitive than price-sensitive?

Intermediate and capital goods used in the production of other goods are often very expensive and made by Germany. Think fancy manufacturing equipment in chemicals, semiconductors, and metal fabrication as well as precisely manufactured consumables like processed chemicals and auto-parts. Chinese goods are ubiquitous because they are skewed towards final goods like toys and white goods we consume at in our homes.

This shows the mix of German exports is heavily intermediate and capital good focused:

This shows that China is more consumer goods focused (but the trend towards this as a shrinking fraction of a growing total):


Under what condition is a cost function strictly concave in prices? Define the unit cost function as
$$
c(w) = \min_{z\geq 0} w\cdot z
$$
subject to $f(z)\geq 1$. Where $w$ is a vector of input prices, $z$ is the vector of inputs and $f$ is a production function. We know from standard results that $c$ is concave and homogenous of degree one, but I would like to establish conditions on $f$ such that $c$ is also strictly concave.

No function that is homogeneous of degree one, is at the same time strictly concave in its arguments. If the function is differentiable (or non-differentiable at a finite number of points), then the Hessian of a linear homogeneous function is singular. So if you want to end up with a unit cost function that is strictly concave, you have to drop at the same time the linear homogeneity in $w$.


Where do computational economists work Does anybody know what kind of work or where computational economists end up working? It seems most end up in research...

The most useful way of thinking of a Computational Economist is one that will be able to estimate economic models in a quantitatively meaningful way. This makes them very useful for central banks which have the need to study the macroeconomy quantitatively and also have the time and resources to invest in a computational economist...

Other ways to look at this question:

The conferences by the society for computation economics are all populated by academic economists or by central bank economists. enter link description here

The job-board sites, mostly ask for data scientists when you type in computational economics. enter link description here

Commentators at the job econ rumors site claim two things: that computational economics is forever going to be the science of the future, but never the presently hot science.enter link description here


Cobb–Douglas utility maximized by spending a "fixed fraction of income on each good"? Consider a Cobb–Douglas utility function having the form
$$u(x) = \prod_{j=1}^n x_j^{a_j} $$
where $x$ is an allocation vector and $a_j$ are utility parameters with $\sum a_j = 1$. My question has to do with the demand of a buyer with a Cobb–Douglas utility function and fixed prices budget. That is, $$\arg \max_x \lbrace u(x) : \pi^T x \leq w \rbrace$$
where $\pi$ is a fixed price vector and $w$ is the budget.
This is easy to solve, but I am confused by the following claim, which I read in an optimization textbook [1]:

It is not difficult to show that a trader with a Cobb–Douglas utility function spends a fixed fraction of her income on each good.

This is clearly true when $a_j = 1/n, \forall j$ and the prices are the same.
But suppose $n = 2$, $\pi = (1, 1)$, $w = 1$, and $a = 0.8, 0.2$. Then "spending a fixed fraction of the budget on each good" would mean spending $w / n = 0.5$ on each good, or buying $0.5$ units of each good, implying $x^* = (0.5, 0.5)$. This is clearly suboptimal, as the following table of values shows:
 x_1  x_2  u(x)
 0.0  1.0  0.0
 0.1  0.9  0.155185
 0.2  0.8  0.263902
 0.3  0.7  0.355399
 0.4  0.6  0.433789
 0.5  0.5  0.5
 0.6  0.4  0.553265
 0.7  0.3  0.590885
 0.8  0.2  0.606287   (*)
 0.9  0.1  0.579955
 1.0  0.0  0.0

Instead, the maximum is at $x = (0.8, 0.2)$, which I would describe verbally as

A trader with a Cobb–Douglas utility function allocates each good in proportion to its utility per unit cost.

In this example, resource 1 yields $a_1 / \pi_1 = 0.8$ utils per dollar, resource 2 yields $0.2$ utils per dollar, and the optimal allocation is a scalar times $(0.8, 0.2)$.
Is my interpretation correct? Is the textbook's interpretation quoted above correct? If both are correct, what explains the discrepancy in the example above?
Please note that I am not asking how to compute the demand of a trader with a Cobb–Douglas utility function. I am asking about the specific claim that the trader spends a "fixed fraction of her income" on each product.

[1] Nisan, Noam, Tim Roughgarden, Éva Tardos, and Vijay V. Vazirani, eds. 2007.
Algorithmic Game Theory. Cambridge University Press.

A "fixed fraction" doesn't mean an "equal fraction", or at least that's not the intended meaning.
It can be easily verified that the solution to
\begin{equation}
\max_{x_1,x_2}\;x_1^{a_1}x_2^{a_2}\qquad\text{s.t.}\; \pi_1x_1+\pi_2x_2\le w
\end{equation}
is
\begin{equation}
x_1^*=\frac{a_1}{a_1+a_2}\frac{w}{\pi_1}\quad\text{and}\quad x_2^*=\frac{a_2}{a_1+a_2}\frac{w}{\pi_2}.
\end{equation}
Plugging in the values you used: $a_1=0.8,a_2=0.2,\pi_1=\pi_2=1$, the solution is consistent with your numerical simulation.
Generalizing to the $n$-goods case (with $\sum_ia_i=1$), the demand for $x_i$ is
\begin{equation}
x_i^*=\frac{a_i}{\pi_i}w,
\end{equation}
where the "fixed" fraction refers to $a_i/\pi_i$.


Finding the Pareto optimal set with preferences for 3 individuals Question: Let $N=\{1,2,3\}$ be a set of three people and $X=\{a,b,c,d\}$ a set of 4 political parties. The individuals have the following preferences:

Individual 1: $a \succ_1 b \sim_1 c \succ_1 d$

Individual 2: $d \sim_2 a \succ_2 c \succ_2 b$

Individual 3: $a \succ_3 b \succ_3 c \succ_3 d$

List all pairs of $(x,y) \in X \times X$ such that $x$ Pareto dominates $y$ and deduce the optimal Pareto set.

I think I am being thrown off by the $X \times X$ bit. But it seems like if I multiply out $X$ I will get the following:

$X \times X = \{(a,a),(a,b),(a,c),(a,d),(b,b),(b,c),(b,d),(c,c),(c,d),(d,d)\}$

So if I define the Pareto outcomes as $x \succeq^P y \iff x \succeq_i y$ for all $i=1,\dots,n$. Then my answer to the question would be the pairs are:

$(a,b),(a,c)$ since those are the only two combinations which dominate in all three individuals. I don't think it makes sense to examine the $(a,a),(b,b),...$ case, but I could be completely wrong. For some reason I can't seem to wrap my head around it, and I could have gone wrong right from the beginning.

I am somewhat unsure where your exact difficulty lies (and hence what your question is). As you write the two Pareto impromevents are $(a,b),(a,c)$. Meaning $b$ and $c$ can be improved upon and are not efficient. Also $(a,d)$ is an improvement, notice that individual 2 is indifferent while others prefer $a$ to $d$. Alternative $a$ cannot be improved upon, and hence it is Pareto-efficient. So the Pareto-set would be $\left\{a\right\}$.


How to distinguish Full-time (FT) employment and Part-time (PT) employment when calculating employment rate? Which of the following is true for the Canadian labour force data for June, 2015, for unemployment, Full-time (FT) employment, and Part-time (PT) employment?

A)  Unemployment fell because FT employment rose more than PT employment fell

B)  Unemployment fell because PT employment rose more than FT employment fell

C)  Unemployment rose because FT employment rose less than PT employment fell

D)  Unemployment rose because PT employment rose less than FT employment fell

E)  Unemployment rose because FT employment and PT employment fell

The answer is A). This question indicates that PT and FT has mutual relationship. But I think we don't normally count PT when calculating unemployment rate. So how does the choice A) work?

They must be counting full time/part time equivalents rather than individuals. They are basically comparing the hours worked versus the hours people report desiring to work. Thats the only explanation.


Has the Nash Equilibrium led to any significant economic discoveries? The Nash Equilibrium provided a new look at certain economic problems and won the Nobel Memorial Prize in Economic Sciences in 1994.  Since its creation, the Nash Equilibrium has been applied to "international relations" specifically for war and arms-race scenarios. However, has the Nash Equilibrium lead to any significant economic discoveries?
I had heard rumors of the Nash Equilibrium being applied to bank-runs and other financial crises but nothing to back it up.

Two areas that have been profoundly affected by game theoretic research stemming from Nash's contribution are

Oligopoly theory

There are actually a few examples of what would come to be known as Nash equilibrium in the industrial organization literature that predate Nash's work (for example, Cournot's 1838 analysis of oligopoly competition). However, until Nash (and Selten, Harsanyi, and others) made game theory a general purpose tool, industrial economics was primarily focused on relatively naive models of competition. In the last 30-40 years there has been a revolution in industrial organisation as economists have used game theory to essentially reinvent the study of market competition around oligopoly theory and the study of strategic interaction. Our modern understanding of consumer search, limit pricing, strategic entry and entry deterrance, predatory pricing, strategic advertising, switching costs, product differentiation, platform competition, horizontal and vertical integration, etc. are all predicated on models that rely mostly on Nash equilibrium (or a refinement thereof) as the solution concept. Jean Tirole was recently awarded the Nobel prize largely for work in this area.

This work has also found great practical application in areas such as antitrust policy. Prior to the 1960s, antitrust enforcement in the US (and, to a large extent, elsewhere) was inconsistent and based on unsound economic principles. A combination of the insistence by scholars (especially those based in Chicago) on more careful analysis, and the new tools of oligopoly theory have lead to a much more robust and well-grounded approach to regulating competition.

Auction theory

The study of auctions is game theoretic by its very nature: most auctions involve very direct strategic interaction between a relatively small number of bidders. It should come as little surprise, then, that auction theory essentially did not exist prior to the work of Nash (the formal study of auctions can be traced to W. Vickrey (1961) "Counterspeculation, Auctions, and Competitive Sealed Tenders," Journal of Finance 16(1); also the recipient of a Nobel prize).

None of the cornerstones of auction theory (revenue equivalence, the linkage principle, optimal auctions—source of yet another Nobel prize, etc.) would exist without the solution apparatus that can be traced to Nash. This work, too, has been of great practical importance. From radio spectrum licenses to carbon emissions permits, and from public procurement to Google ad auctions, auction theory has had a significant effect on informing good auction design. See Klemperer (2004) Auctions: Theory and Practice, Princeton University Press for an accessible summary of the theory and its applications.


How do I calculate quantity to minimize long-run average total cost? I have a formula for the long-run total cost curve,

$$TC(Q) = 6000Q + 40Q^2 + Q^3$$

and I'm trying to find the quantity that minimizes the long-run average total cost.

I assume I'm trying to find the value $Q$ (quantity) that produces the total cost ($TC(Q)$) where $\frac{TC(Q)}{Q}$ is the lowest. But how do I do this short of trial and error?

Your are right. You have to minimize the average cost.

$$c(Q)=\frac{C(Q)}{Q}=6000 +40Q+Q^2$$

Calculate the first derivative and set it equal to zero:

$ c'(Q)=40+2Q=0 $

Solve this equation for $Q$. Denote the optimal value as $Q^*$. $Q^*$ can be a local maximum or a local minimum

If $c''(Q^*)>0$, then you have found the local minimum.

The local minimum is also the absolute minimum, because

$$\lim_{Q \to \infty } 6000 +40Q+Q^2=\infty$$

$$\lim_{Q \to -\infty } 6000 +40Q+Q^2=\infty$$


Why the source profit is not only trade markups? I'm researching the source of profit. In Marx I've found the following passage:

  If then, speaking broadly, and embracing somewhat longer periods, all
  descriptions of commodities sell at their respective values, it is
  nonsense to suppose that profit, not in individual cases; but that the
  constant and usual profits of different trades spring from the prices
  of commodities, or selling them at a price over and above their value.
  The absurdity of this notion becomes evident if it is generalized.
  What a man would constantly win as a seller he would constantly lose
  as a purchaser. It would not do to say that there are men who are buyers without being sellers, or consumers without being producers. What these people pay to the producers, they must first get from them for nothing. If a man first takes your money and afterwards returns that money in buying your commodities, you will never enrich yourselves by selling your commodities too dear to that same man. This sort of transaction might diminish a loss, but would never help in realizing a profit.

  Karl Marx - "Value, Price and Profit", 1865, the last pararaph in section VI "Value and labour"

I can't construct a numerical example which could illustrate this logic for me. It seems like even critics of Marx didn't argue against this passage just like it was very clear to them. But it not clear for me.

Please check my logic. Consider a capitalist who has costs of 10 USD per unit including others' margins of 5 USD. According to Marx she has to sell for at least 10+5=15 USD and it will be just a zero profit. But mathematically 15-10=5 USD and it's not zero. May be Marx means that these 5 USD of profit will be unavoidably spent for a bare survival of the capitalist. But why, if so?

Because an extraordinary profit can also be derived from preferences, and brand. Why would you pay 4x more on an Iphone? Apple's ability to raise its price is not due to the market power it has, but rather to consumer preference, brand preference. Just answered only what was in the title and not on the basis of Marx's theories


How to calculate gdp of a company during promotion and loss? Suppose a company is selling a good worthy of 200 dollars, but it was charging it for 100 dollars intending for promotion. And the company have to pay salaries of $200 per good, so it loses 100 dollars per good sold.

From the income side, it is 200 dollars to the employees and -100 dollars to the shareholders.

From the expenditure side, it's 100 dollars from the consumers.

Should the GDP be reckoned as 200 dollars as the good's market value or 100 dollars? And why?

As noted in a comment, GDP is associated with a country, not a firm.

But if we are talking about the contribution to GDP, the operating assumption is that calculations are based on observed (market) prices. So the value of consumption is \$100 if we are calculating GDP based on expenditures. If we are looking at domestic income, it would be \$100: \$200 wage income, and -\$100 business income.

Statisticians do not attempt to decide what goods are “really worth”, they use data based on actual transactions. Since GDP numbers are estimates based on a variety of sources, it is unlikely that they capture when particular firms have promotional sales.