Introductory book for asset pricing and financial economics I am going to complete a continuous time finance course in  the upcoming semester. Although all my higher education is in economics I have not encountered a financial economics setting of contingent markets,i.e, of the geometric representation of the state space of the aforementioned. I have a solid knowledge on investments, financial markets and financial products such as derivatives but I was looking for the mathematical finance formulation of contingent markets. What introductory book would be good for an introduction in the simpler settings before jumping to the Black-Scholes setting for example which is the end-goal of the class I am going to take. Cochrane's book "Asset Pricing" is similar to what I am looking for but I would like to know if there are any alternatives.

If you are looking for something simpler before jumping to Black-Scholes, consider the textbook "Investments" from Bodie, Kane, and Marcus.

You can look at the table of contents. The book assumes that the reader does not know stochastic calculus and continuous time finance, but it still gets to the Black-Scholes formula.


In econometrics what are induced jobs? Specifically, in the RIMS II model espoused by the BEA, capital spending in a region induces job creation therin, based off of specific multipliers.

Where do these multipliers come from, and what do they mean?

Induced jobs are those created by the spending of those employed directly by the primary source or indirectly by suppliers to the source.  For example, you have a project to build a bridge.  That project hires a worker.  That worker stops at a convenience store every morning and buys a coffee and a bagel.  The people responsible for selling the coffee and bagel are induced jobs.  This includes the cashier, the stock person, the delivery person, the baker, etc.

Obviously this particular worker is only responsible for a small fraction of the overall cost of these others.  However, if you aggregate all the effects across all the workers on the project, you may find that the convenience store has to hire an extra cashier, that the part-time stock person has to work full-time, that an additional delivery person has to be hired to share the stops, that another baker needs to be hired, etc.

The multiplier is simply an estimate of how much spending on the project will then be respent on labor indirectly.  It can be given either in terms of jobs or in money.  Economists use survey information and other studies to estimate how much this will be.


Continuity of preference relation (iff?) I have a question about the following definition of a continuous preference relation. I apologize for not providing a reference and will try to add one as soon as I can find one.

Definition:

A preference relation is continuous if for all sequences x_n, y_n with x_n converges to x and y_n converges to y as n goes to infinity and x_n is at least as good as y_n for all n, then this must also hold for the limits x and y.

My simple question is:
Is the if an iff or only an if? That is, say this condition (or definition?) above is not ful-filled, can I infer that the preference relation is not continuous or might it still be continuous?

This is a definition. Definitions are always iff.

Consider this property. From now on we call this and exactly this (name of the concept here).


Is nominal/real income and nominal/real wage the same? If so, is it possible for your nominal income to rise as your real income falls? In macroeconomics, I understand that nominal wage (W) is your wage in dollars, while real wage (W/P) is what you can get for that wage (in apples, etc...). But is this the same thing as "nominal income" and "real wage"?

If so, can the nominal income go up while the real income declines? And what would be a proper example of this?

I've researched this question online, but all searches were fruitless and failed to explain this simply. All help is greatly appreciated. Thank you.

Wages are a subset of income.  Your income includes your wages but it also includes other sources of income such as dividends and interest.  If your only source of income is a job, then income and wages are the same thing.

It is certainly possible that nominal wages would rise while real wages fall.  Imagine that you earn 50,000 at a job in 2019.  Inflation runs at 5% a year.  And say that at the end of 2019 your boss says that you're getting a 2,000 raise so your salary in 2020 will be 52,000.  In nominal terms, your wages increased from 50,000 to 52,000, a 4% increase.  But since inflation was 5%, your 52,000 salary in 2020 will buy less than your 50,000 salary bought in 2019-- you would have needed a 5% raise (2,500) in order to keep pace with inflation.  Your nominal wage increased but your real wage decreased.


What is the difference between preferences lacking "completeness" and being indifferent? If two preferences are complete, at least one must have a relationship to the other.  If neither has a relationship, doesn't that mean that the consumer doesn't care which one he/she purchases?

As alluded to in the comments the distinction is roughly:

Indifference: The decision maker knows she will receive the same utility from the consumption of $x$ or $y$.
Incompleteness: The DM does not know her preference between $x$ and $y$. (Note, this could stem from a lack of information, or because no preference exists)

So, from a conceptual vantage, the difference is that indifference is the existence of knowledge, whereas incompleteness is a lack of knowledge. While interesting in a foundational/philosophical sense, the distinction is subtle and likely not the reason economists have spent so much thought on the subject. However, the difference has behavioral implications! and this is important for economics.

For example, imagine various choices between "pizza", "hot dog", or "hot dog and $\$0.05$". Perhaps, the decision maker has never had pizza or hot dogs and therefore finds them incomparable. As such, from the choice set $\{p,h\}$ she would choose either (since neither option is known to be inferior[1]). So $C(\{p,h\}) = \{p,h\}$.  Now, the decision maker also likes money, so although she does not know her preference for a hot dog, she will always choose more money to less, all else equal: $C(\{h, h+5\}) = \{h+5\}$. But her indecisiveness regarding the two foods might not be resolvable for 5 cents, so, it is reasonable that $C(\{p, h, h+5\}) = \{p, h+5\}$. But this violates the weak axiom of revealed preference. Such a choice function cannot be rationalized by a complete and transitive relation.

Notice if the decision maker was actually indifference between $h$ and $p$ then, $C(\{p, h, h+5\}) = \{h+5\}$. In summary: incompleteness can cause "thick" indifference curves, and this can violate the basic tenets of rational choice theory.

[1] There are other interpretations of choice under incompleteness, for example, allowing the choice function to return an empty set.


When will the reserves be exhausted? A rough estimate of the oil and gas reserves in some country at the beginning of 2010 was 15 billion tons. production that year was approximately 250 million tons.

when will the reserves be exhausted if production is kept at same level?

I have no clue on how to solve and tackle this problem, it seems kind of odd to me that there is nothing to indicate at which level the reserves are being consumed.

Really appreciate any hints on how to solve it.

If the country converts the reserves to 250 million per year, then in 4 years it will convert 1 billion and 15 billion will be exhausted in 15x4 years.


Decreasing and increasing returns to scale question Hi, I have deduced that this function exhibit increasing returns to scale but I am not sure how to verify part d. My answer doesn't show that there is decreasing returns to scale but I can't be sure d is wrong. I am unsure between choosing c and d.

Thanks

From your production function: $f(K,L)= 1.8(K^{0.6} + L^{0.6})^{2} \Rightarrow f(K,L) = 1.8(K^{1.2} + 2(KL)^{1.2} + L^{1.2})$

You are able to see that $f(\lambda K, \lambda L) \Rightarrow \lambda^{1.2} f(K,L)$. Say you double both your inputs. Increasing returns to scale tells you that your output will be more than doubled, which is precisely what $\lambda^{1.2}$ represents. The level of $K$ and $L$ does not affect this conclusion.  The point where the level of $K$ and $L$ play a "role" is that for levels such that $K + L >1$ each unit of input results in more than one unit of output (i.e.$f(K,L) > 1$) (again note that we are talking about levels here and not changes, which would regard the returns to scale). You can easily see this by plugging in different values into your formula. But, again, this is not to do with the returns to scale of the function so it doesn't pertain the question you are asked.


What happens if the Central Bank does not absorb a BOP deficit/surplus? The basic principle of BOP accounting is double entry bookkeeping. In short, every transaction enters twice. As a consequence of this, by definition

$$\text{Current account } (CA) + \text{Capital account } (KA) = \text{Financial account } (FA)$$

Note that this may differ depending on how you classify BOP accounts. Some sources classify it as CA = KA (and do not have an FA), but the principle is the same.

In my definition, the FA includes the official reserve account (OA).

What I don't understand is - if every transaction automatically generates a credit and debit entry, how can it be possible to have:

$$CA + KA \neq (FA \; \backslash \; OA)$$

I know I am wrong to think this, but it seems to me like the 'need' for central bank intervention to absorb a surplus/deficit in the other components violates the definition of double-entry bookkeeping, which implies BOP = 0 at any point in time.
So:

1) Why am I wrong wrt the above?

2) If the OA does not absorb the deficit/surplus from the rest of the BOP, what happens?

If OA is a part of FA. The second equation follows from the first:
$CA + KA = FA \wedge OA \neq 0 \Rightarrow FA - OA = CA +KA -OA \neq CA +KA$.

Response to your EDIT:

$CA + KA \neq \frac{FA}{OA}$ follows from the first equation as well:

$CA + KA = FA \wedge OA \neq 1 \Rightarrow  \frac{FA}{OA}= \frac{CA+KA}{OA} \neq CA +KA$ in general. (I've checked your LateX expression it really says: "(FA \backslash OA)"). I don't understand why you would think that BOP has anything to do with division. For example Feenstra and Taylor say in their textbook:

$OSB=-Reserve FA=CA+KA+Nonreserve FA$, where OSB is your OA and their version of the BOP identity is $CA + KA + FA = 0$, with your FA as their -FA.


How to interpret coefficients in a dynamic OLS model? I am trying to understand how to interpret the dynamic and static effect from coefficients in regression models.
$GDP\_growth\_rate_{t,i} = \beta_1GCF_{t,i} +\beta_2GCF_{t-1,i}+\beta_3GCF_{t-2,i} +\beta X_{t,i} +u_{t,i}$
where GCF is Gross Capital Formation and the model is estimated using OLS.
My question is am I correct in interpreting $\beta_1$ as the impact multiplier /immediate effect of GCF on GDP and $\beta_1+\beta_2+\beta_3$ as the long-run multiplier/effect?

yes the way how your model is set up $\beta_1$ would be immediate effect/multiplier and $\beta_1+\beta_2+\beta_3$ the long-run one.
However, an important caveat is that this is due to the way how you set up your model and not a general result. For example, in an ARDL model with stationary variables of the following form:
$$y_t = \alpha + \beta_1 y_{t-1} + \gamma_1 x_t + \gamma_2 x_{t-1}+ e_t$$
the long run multiplier would actually become: $ \frac{\gamma_1 + \gamma_2}{1 - \beta_1}$
or in more general case
$$y_t = \alpha + \sum_{p=1} \beta_p y_{t-p} + \sum_{q=1} \gamma_q x_{t-q+1} +e_t$$
the long run multiplier would be given by: $\frac{\gamma_1+\gamma_2+...+ \gamma_q}{1-\beta_1-\beta_2-...-\beta_p}$.
In your case you do not include any lags of dependent variable so you have a special case where the denominator is 1 and hence it is enough to add in the coefficients but I thought it might be good to mention that as long as you include lagged dependent variable the calculation of the long run multiplier changes (see Verbeek (2008) guide to modern econometrics for more details).


What physically happens when foreign currency reserves change? Assume that the United States decided to hold more yuan in the federal reserve. Which processes does that involve? I assume there is some sort of electronic exchange between the two central banks where dollars are exchanged for yuan. What happens physically? I assume that the Fed will only need to hold a portion (say, 10%) of the reserves as currency, and the other 90% will be just based on the credibility of the bank. Does that mean that the currency worth 10% of the exchange needs to be loaded in a special plane and flown from China to the US and vice versa? How often do those sorts of plane trips happen?

Typically foreign reserves will just be assets denominated in a foreign currency, most importantly government debt. Another popular reserve asset are IMF special drawing rights, which are convertible into currencies of member countries. I don't think there is any amount of physical cash currency in international reserves. You can see the makeup of US reserves here: https://www.treasury.gov/resource-center/data-chart-center/IR-Position/Pages/12302016.aspx

If the US treasury would decide to increase it's Yuan holdings, it will just buy bonds that pay are traded and denominated in Yuan.


consumer surplus decreasing MRU has the following question on a quiz:

Suppose the government forced all bread manufacturers to sell their
products at a “fair price” that was half the current, free-market
price. To keep it simple, assume that people must wait in line to get
bread at the controlled price. Would consumer surplus rise, fall, or
can’t you tell with the information given?

According to them, the correct answer is:
 b. consumer surplus decreases.

I don't understand how they arrive at this answer.  It seems to me that without the price ceiling, the surplus will be close to 0, since there will be a price equilibrium.  With the ceiling, however, people are waiting in line, indicating that they would be willing to pay more for the bread if they could (the time spent waiting theoretically converts to money).  Thus, consumer surplus increases.  Or am I misunderstanding the question?

The MU question you quote is poorly worded. Here the proper answer would be:
C Indeterminate with the given information
First we can visualize it as shown on the diagrams shown below. Consumer surplus is the difference between willingness to pay (given by demand)`and price they actually pay so for all consumers it is the area below demand curve and above market price i.e. the blue area on the picture. Producer surplus is the difference between market price and price at which they are willing to supply so for all producers it is the area below market price and above supply curve i.e. the red area on picture below (you can see Mankiw Principles of Economics Ch 7 for more discussion on consumer and producer surplus).  Without any price celling the market will be at equilibrium where supply equals demand so there will be no shortage. After price celling producers are only willing to supply $Q_S$ while people demand $Q_D$ resulting in shortage of the good of size $Q_D-Q_S$. Shortages can result in waiting lines as usually some non-market mechanism then takes over.
We know that total surplus of society shrinks because $CS+PS$ is definitely smaller as the total colored area shrinks. However, if we only look at $CS$ it is possible that it increases because consumers both loose part of their original surplus and gain part of the surplus that was originally belonging to producers. Whether $CS$ increases or decreases depends on whether the gain  from appropriating part of producer surplus offsets the loss to $CS$ from consumers that no longer can get the good anymore.
Possibly, the question has a mistake and it was supposed to be total surplus where answer b) would be correct, or there are some unstated assumptions, such as that people experience disutility from queuing (reasonable but not explicitly mentioned in the question) which would lower CS further as it would impose additional costs on consumers.


Understanding the impact of Subprime Mortgages crisis on investment banking I'm interested to know the exact magnitude of impact of Subprime Mortgages crisis on major players in investment banking.

In particular, how can I find data for percentage of revenue from Subprime Mortgages in total revenue for major banks, like Goldman Sachs, Morgen Stanley, The Bear Stearns and  Lehman Brothers?

Simply put, you can't tell exactly. It's just not possible to tell these entities' subprime losses apart from other losses, with the possible exception of Lehman Brothers, due to the detail made available through its bankruptcy proceedings. Even then, it would be an incredibly labor-intensive task.

There are a number of reasons for this. First, most subprime mortgage exposures of major banks weren't held as on-balance-sheet loans, but in the form of (usually higher-rated) tranches of private-label mortgage-backed securities, which has a number of implications, including: the exposures appeared on the balance sheet as securities, not as mortgage loans; there's no way to know what fraction of those securities contained subprime loans; and due to the structures of the securities, there's not even a linear relationship between the fraction of subprime loans in a given security and the bank's exposure to losses from those loans, among other things. Second, they often had off-balance-sheet exposures in the form of support obligations (whether explicit or implicit) on structured investment vehicles. Third, their exposures varied significantly due to differences in the amount of leverage they used in funding their assets.

As an aside: pre-crisis, none of the four entities you've named were actually banks. Though often referred to as "investment banks," all of those were nonbank broker-dealers.


What did Adam Smith mean by "putting [the pins] into the paper"? In his famous description of the division of labour:

  One man draws out the wire, another straights it, a third cuts it, a fourth points it, a fifth grinds it at the top for receiving the head; to make the head requires two or three distinct operations; to put it on, is a peculiar business, to whiten the pins is another; it is even a trade by itself to put them into the paper ...

What did he mean by "put them into the paper"? Was this just some sort of paper packaging for the pins?

(By the way, my understanding is that pins are what we'd today call nails. Please correct me if I am mistaken.)

Alecos is correct that Smith is talking about packaging, but I don't believe that "paper" refers to a paper bag.

Straight pins used to be sold on sheets of paper (usually as sets of a dozen), through which they passed twice, like so:

So by "put them into the paper" Smith means exactly what he said: the pins are put into paper before being sold.


Transforming expected utility functions I am using the following theorem:

To better understand how I can transform expected utility functions.

An example with which to work:

I want to show that the preferences represented here satisfy the three axioms [A1,A2,A3] that characterize expected utility. [order, continuity, and independence]

Where $$E_{\pi} \mu = \sum_{z \in Z} u(z)\pi(z) $$

What I want to do is transform the given E.U.F.  s.t.:

$$U(\pi) = h + k....$$
$$U(\pi)= k...$$

Then by multiplying by $\frac{1}{k}$ and using $ln$

$$U(\pi) = \sum_{i=1}^n \pi_i ln(\alpha_i)$$

EDIT

Perhaps this is actually the solution. Any feedback?

This is not Homework. I am studying because I do not understand this well

Yes. What you are doing is a solution.

The key idea here is that binary relations are necessarily ordinal relations, and do not contain cardial information. Taking (strictly positive) monotone transformations of representations preserves the preference structure. So, yes, you have shown $U(\cdot)$ (from the example) is related via a monotone transformation to an linear function with the index $ln(\alpha)$ and therefore, by the von Neumann Morgenstern theorem, satisfies the EU axioms.

Now, there is often a point of confusing here, because of the emphasis on uniqueness with regards to EU representation. But the EU representation is not the unique representation, it is the unique linear representation. While this is clearly delineated in the theorem, I think it is conflated in many people's minds with generic uniqueness.

To summarize, by choosing a particular functional form (or normalization) it is possible to act as if the preferences have a cardinal relation. But, this is just an interpretation, and not something inherent about a binary relation, even one that satisfies the independence axiom.


Price Changes in Factor and Product Markets I think something is wrong in my reasoning, and I can't really find out what it is

Lets say the supply of labor decreases in a market. That would mean that the wage rate would increase in that market. Firms hiring out of that market will experience an increase in their marginal cost, and the supply in the market for the product which uses that labor will shift left, increasing the price of that product. But that would mean that the marginal revenue product of labor would increase because of that increased price and shift the demand for labor right. At that point the wage rate would increase and everything would cycle through again.

Where am I going wrong? How does the wage rate stabilize?

Let's

distinguish exogeneous from endogenous factors,
distinguish partial versus general equilibrium analysis,
consider here the labor market of one product, i.e., a partial analysis,
consider that this labor market is perfectly competitive.

In your reasoning, the decrease in labor supply, which typically leads to an increase in the wage rate, would come from an exogenous shock. This shock causes an endogenous process that stabilizes the wage rate at a new partial equilibrium. This is a situation where the product of marginal labor income equals the wage rate.

In a competitive labor market, the wage has two properties:

It adjusts to make supply and demand for labor equal.
It equals the value of the marginal product of labor.

Suppose the labor supply decreases in our market. The supply of labor shifts to the left. At the initial wage, say $w_1$, the quantity of labor supplied falls behind the quantity of labor demanded. The wage increases from $w_1$ to $w_2$, and the firm reduces its demand for labor. As the firm lays off workers, the marginal product of a worker increases, so the value of marginal product increases. In the new (partial) equilibrium, the wage is equal to the value of the marginal product of labor and both are higher than before.

Regarding your comment and the stability of this new equilibrium

  I think where I am confused is how does the exogenous shock to the labor market cause the wage rate to stabilize? Because the firm will now get higher prices in the product market, shouldn't the demand for labor increase and wouldn't the wage rate go up again and the process would repeat again and keep on cycling upwards?

The above equilibrium is a stable partial equilibrium, but general equilibrium forces exist. As a result of the shock, the firm will initially get higher prices in the product market, but we can assume that if it is a competitive market, demand for its product will decrease. This will lower the prices of its products. Demand for labour will shift to the left ... wages will go down (not up). However, we will need a general equilibrium model to better understand these changes.


Why would using real-time settlements have helped combat some of the chaos that occurred during the January 2021 GameStop saga? I read on cnbc.com (mirror):

Tenev also advocated for real-time settlement instead of two-day settlement in order to help combat some of the chaos that occurred during the GameStop saga.

Why would using real-time settlements have helped combat some of the chaos that occurred during the January 2021 GameStop saga?

It would not prevent speculation driven bubble like GME but it would arguably prevent the situations such as Robin Hood being forced to restrict trading.  This is because when you buy stock your transaction is actually not processed immediately but takes few days to clear (usually 2 days see here).
This creates a problem because by law brokers like Robin Hood are required to keep portion of their own capital until transaction clears (e.g. SEC net capital obligations and clearinghouse deposits). This can cause a problem for a firm if people make too many transactions as it simply might not have enough capital to set aside to fulfil the regulatory requirement. In fact brokerage firms often raise additional capital even if they themselves not need it just because they anticipate that their customers could increase in trading activity but the volume of trading is not easily predictable.
This problem could be alleviated if stock trades were settled immediately instead of waiting days before actually carrying out the transaction. This is because if the stock trades are cleared immediately there is no need for brokerage firms to have capital buffers forcing them to restrict trading as the rationale for the regulatory buffer is to have some funds set aside if something happens in those 2 days.


How long can I live in the United States with my German monthly income? I see different (more or less abstract resp. specific) approaches to compare wealth (of individuals, regions, and countries):

by living standards
by living expenses
by incomes/salaries
by purchasing powers
by price levels

One such approach – to talk at large – could be:

  How long can I – coming from country X – live in country Y by spending
  my last monthly salary converted by nominal exchange rate:

  as a backpacker or as a convenience tourist?
  adapting to the other country's standards which may be lower?
  adapting to higher standards than I am used to?

  How much does this period deviate from a month?

My question is: Where do I find this approach taken?

This is tricky to answer precisely because governments vary a lot in the services they extent to visitors. There is also variation in the mix of consumption goods across countries as well as their relative prices. You might respond to local conditions by changing your consumption bundle more or less than the average person and that would change the economics for you relative to an average calculation.

The simplest approximation is to take GDP (or the C component of consumption), measured using exchange rates rather than PPP, and divide it by the population.

Think about it this way. Nominal GDP per capita in the US is about \$62,606 and in Germany is \$48,264. Assume it is safe to either ignore taxes or taxes are comparable in the two countries. If you have have saved the salary of the average German then you can afford the spending of the average American for about 9 months.

Another way to do this is to look at destination country household final consumption expenditure per capita. As of 2016 this was about \$36,373 in 2010 dollars, probably about \$43k in 2019 dollars. According to Wikipedia, average German salary, net of taxes, is about \$32,000. So if you have a pension that pays net of taxes the salary of a typical German (also net of taxes), you can afford about 75 percent of an average American's spending.

A third way is to use expatriate cost of living indices, although I've been told that these are more accurate for affluent urban households. For example, expatistan says that the cost of living is 53 percent higher in NYC than in Frankfurt. This suggests you can live for eight months in NYC for the same income that buys a year's worth of consumption in Germany.


Is there an economic theory that explains what happens when a market is saturated with a precious resource? The theoretical situation is this. What if a record breaking amount of platinum were discovered. What would happen to the economies that use, store, and/or produce platinum?

I would like to apply this theory to any kind of precious material or element. Other examples would be gold, uranium, or oil.

At the outset, discovery does not equate availability. Huge amounts of platinum (or the material at issue) might be discovered, but that does not necessarily mean that its extraction is feasible or practicable with the currently available techniques. See here and here.

Assuming that the discovered material is economically available, then supply would increase, thereby pushing prices down. At the same time, demand for that material would increase because agents (consumers) might deem that material a convenient substitute of other [now relatively costlier] alternatives. The net effect would be a higher quantity of that material being traded, and at a lower price.


What affects the interest elasticity of investment? Firstly, my understanding of the interest elasticity of investment (IEI) is that it is the responsiveness of investment to changes in interest rates. As a result, I can think of one reason why the IEI may be affected: when there's a recession, the IEI may be more inelastic because of low business confidence and a negative accelerator effect. However, I believe there are most likely other fundamental factors that affects the IEI as well, which I haven't been able to think of.

Demand:

Expected return on investments. If the expected return is much higher than interest rates, then elasticity will be low. When interest rates are close to the expected return elasticity will be high.

Supply:

Money supply. When money is scarce the elasticity will be low. When money is abundant the elasticity will be high.


Exchange Houses game - Bayesian Game Can anyone help me understand how to solve this type of asymmetric information Bayesian game?
So the game is a different version of the Tadelis 'trading house games'. It involves 2 players
that each own a house. Each player values his own house at $v_i$. The value of player $i$’s house to the other player, i.e. to player $j \ne i$, is $\alpha v_i − c$ where $\alpha > 1$. Each player knows the value $v_i$ of his own house to himself, but not the value of the opponent’s house. Both players know $\alpha$. The values $v_i$ are distributed uniformly on the interval [0, 1] and are independent across players.
I suppose that player $i$ will agree to exchange only if $v_i \leq \alpha v_j - c$ but I don't know how to go from there to find the Bayesian Nash equilibrium and how to assign probabilities. Are we suppose to use the expected value of $v_i$ through the uniform distribution, i.e. $E(v_i)=1/2$ ?
Would be very grateful for some help!!

The trick with Bayesian games is to recognize that the players learn in equilibrium from the strategies of the other players. That is, you cannot simply take the unconditional expectation of $v_i$ when calculating strategies.
For example, you may be tempted to say that both players decide to trade whenever,  $v_i\leq E(\alpha v_j-c)=0.5\alpha-c$ and $v_j\leq E(\alpha v_i - c)=0.5\alpha-c$. However, these strategies might not be mutual best responses because suppose player $i$ believes that $j$ will use that strategy and assume that $0.5\alpha-c=0.8<1$. That means that player $i$ should not expect $v_j$ to be greater than $0.8$, so a profitable deviation is to instead trade whenever $v_i\leq E(\alpha v_j-c| v_j\leq 0.8)= 0.4\alpha-c$.
A common trick to solve these games is to assume something about how the equilibrium will look like and then confirm that it indeed looks like that. For example, given the example above, it is not crazy to think that players will only trade if $v_i\leq \bar v$ (for some threshold that you will have to characterize later). It is also reasonable to assume that both players will use the same strategy since they face the same underlying uncertainty and the valuations for each other houses are symmetric.
Therefore, it must be that player I trades whenever $v_i\leq E(\alpha v_j-c | v_j\leq \bar v)= \alpha\frac{\bar v}2-c$. Since we assume that the threshold for trading or non trading is $\bar v$, it must be that $\bar v = \alpha\frac{\bar v}2-c$ which implies that $\bar v=\frac{c}{\left(\frac{\alpha}{2}-1\right)}$. This means that (assuming $c>0$), $\alpha$ must be strictly larger than 2 for some trade to exist since $\bar v <0$ means that players will never trade, and if $\bar v>1$, then trade always occurs.


why is real wage divided by marginal product of labor often called real marginal cost? As said in the title, why is real wage divided by marginal product of labor often called real marginal cost?

In mathematical formula, $mc_t = (W_t/P_t)/MPN_t$ where $MPN_t$ refers to marginal product of labor, $\partial Y_t/\partial N_t$ and $N_t$ is amount of labor. $W_t$ refers to nominal wage, and $P_t$ refers to price level.

This relation can be obtained if we realize that Total Cost can be written as a function of output (which in turn is a function of input factors), but also, that Total Cost equals total payments to factors of production. In real terms,

$$TC=TC(Q) = (w/p)N + (r/p)K$$
with the payment rates exogenous. But $Q = Q(N,K)$. Differentiate both sides by $N$:

$$\frac {\partial TC(Q(N,K))}{\partial N} = w/p $$

$$\Rightarrow \frac {\partial TC(Q(N,K))}{\partial Q}\cdot \frac {\partial Q(N,K)}{\partial N} = w/p$$

$$\Rightarrow MC \cdot MPN = w/p \Rightarrow MC = \frac {w/p}{MPN}$$

One can perform the same exercise to obtain the analogous relation with respect to capital:

$$MC = \frac {r/p}{MPK}$$


GDP type: WDA, NSA, SA What are the acronyms for? SA, WDA, NSA. I was able to find WDA: written down allowance, but I am not sure is correct and how is applicable to GDP.

SA = seasonally adjusted

WDA = working day adjusted

NSA = not seasonally adjusted


Real vs Nominal Value Concept I am having trouble understanding the meaning of the real value of an economic quantity.

The concept is easy to grasp: take a year as a base and adjust for inflation by pricing a commodity with the prices from the base-year.

As I understand it, the real value of, let's say, an orange is, or should be, close to its intrinsic value. It measures the how we value an orange by its potential. This intrinsic value is dimensionless (?).

My difficulty is to reconcile the fact that humans do not think in real terms: we observe and value everything via its nominal value.

In the hypothetical case of comparing two objects that have the same use (let's say, oranges from X country and orange from Y), we always use its nominal value to determine what to buy.

What could be an example that could convince me that the real value is a useful metric to analyze economic data?

What is the philosophical reason to use real vs nominal value?

"My difficulty is to reconcile the fact that humans do not think in
  real terms: we observe and value everything via its nominal value."

Those who do that, suffer from what is called the "money illusion".

  "In the hypothetical case of comparing two objects that have the same use (let's say, oranges from X country and orange from Y), we always
  use its nominal value to determine what to buy."

Indeed, because this is a comparison of two distinct (even if comparable) products, at a single point in time.

Now just answer the following question:

  Your wage today is 100 and the price of oranges today is
  100/kgr. Tomorrow, the price of oranges will be 200/Kgr and your wage
  will still be 100. Will your wage tomorrow be the same, as regards
  what matters, with your wage today?

Certainly, its nominal value will be the same. But what about its real value, i.e. the value in terms of what matters? (how much you can consume, is what matters).


Does a drop in GDP per capita, with the population staying around the same, mean people on average are poorer? Essentially, I'm trying to determine if there is a correlation between a drop in GDP per capita (e.g. during the 2008 financial crisis, Australia's GDP per capita dropped from USD \$49,000 to $42,000 2009) and the average income.

Regardless of the population size, what matters in terms of income is real or nominal terms. The gdp per capita may rise despite a constant population for the economy. But is it real terms that’s what matters. In an environment where the inflation skyrockets, gdp per capita is misleading.


Was there a Role of Technology in Macroeconomic Models before Solow? Was the role of technological progress formalised by Solow (1956) for the first time? or at least he provided the initial formal insight into the role of technological progress in economic growth?

The Solow model was indeed the first model to account for technological progress.

While models like the the  Harrod-Domar model and the Neo-Marxian  Feldman–Mahalanobis model conciser investment and saving as contributors to economic growth, they don't consider any measure of technology like total factor productivity to contribute to economic growth, like the Solow Residual.


To calculate cross elasticity of demand, does percentage change in quantity demanded have to be market demand instead of individual demand? If I try to calculate cross elasticity of demand (XED or CED) with individual demand quantity, it seems to break down since even small increase when the base number is small is a big increase in percentage. e.g. 1 to 2 is a 100% change.

If you calculate XED you have two relative   terms.

$XED=\frac{\Delta q_i}{q_i}\cdot \frac{p_j}{\Delta p_j}$

It is right that in your case $\frac{\Delta q_i}{q_i}=\frac{2-1}{1}=1$

Now it depends on the current price of good j and the change of the price how large XED is. From the relative change of the demand you cannot conlcude to the level of XED.


Does a price on the demand curve represent the highest or lowest price the consumer is willing to pay? My question comes out of the context of the explanation for quotas in the textbook Macroeconomics, 4th edition by Paul Krugman. The explanation is for what could've happened had a quota on cab rides not been placed. In this explanation, the price of $5.50 is apparently the minimum price consumers are willing to offer:

  Looking back at Figure 4-8, you can see that starting at the quota
  limit of 8 million rides, New Yorkers would be willing to pay at least
  $5.50 per ride when 9 million rides are offered.

In the next paragraph, there is another reference to the price as being the minimum that people were willing to pay:

  The same is true for the next 1 million riders: New Yorkers would be
  willing to pay at least $5 per ride when the quantity of rides is
  increased from 9 to 10 million...

Shouldn't this price be the maximum price that consumers are willing to pay for, instead of the minimum price, as the book suggests? Why would a consumer not want to pay less that $5.50$ dollars per ride, at $5.30$ dollars for example, if the same quantity of rides (9 million) is offered?

I have included a copy of the diagram that is referenced, which I redrew. The x axis is quantity of cab rides per year, in millions of rides. The y axis is the fare price per ride. The green, orange and red lines are the demand, supply and quota restriction lines respectively. Please click to enlarge image.

A distinction must be made between the individual demand curve and the aggregate demand curve.

An individual demand curve (or demand schedule) for a product/service, represents the pairs {price, quantity demanded} that co-optimize the consumer's utility maximization problem (together with all other quantities demanded of the other products that are present in the utility function).
It may appear that then this would be the "maximum" price, but it would be confusing to characterize it like that. Because, if the price changes, what would happen to individual quantity demanded depends on whether the good is normal or not, and in general whether there are "income-effects" or not (not all utility functions allow for income effects, by the way).
Moreover, at the individual level, the concept representing the consumer is quantity demanded, not price: the consumer observes prices and responds with quantity demanded.

Let's move now to the aggregate demand curve. It is simply the sum of individual demand curves for each price. Here we have two alternative approaches:

a) The more "traditional" one is that all consumers have a non-zero demand schedule for all price levels, each lowering its demand as price increases. Here the previous discussion applies.

b) The alternative but equally "standard" approach is to argue that for each consumer there exists a (possibly different) "threshold" price, above which the individual demands zero quantity. So as price decreases, we imagine that more consumers enter the market with non-zero demand, and this is why as price decreases aggregate quantity demanded increases.
This approach implies that the price level in each price/quantity combination is the minimum ("at least") price for some consumers, while others would be willing to pay more (and so they have contributed positive quantity demanded for higher price levels).

I believe this is the approach taken by the textbook.