Mixed Strategy Nash Equilibrium for this particular 3x3 matrix Suppose I am given the following matrix:

I would like to find all MSNE
I started by doing the double underline method to find any PSNE. I discovered that none exist. I then looked at which strategies are strictly dominated. I noticed that Player 1 will never play M, because player 1 can always get a better payoff by playing L or R. So I eliminated the middle row "m".
After doing this, I get the following reduced matrix:

I assigned Player 2 a probability of $p_1$ for strategy A, $p_2$ for strategy B, and $1-p_1-p_2$ for strategy C. Similarly I assigned Player 2 a probability of $q$ for strategy L and $1-q$ for strategy R.
So now, we can see that Player 1's expected payoff of choosing L, that is $E(L)$, is $(1/2)(p_1)+(2/3)(p_2)+(1)(1-p_1-p_2)$
= $(p_1/2)+(2p_2/3)+(1-p_1-p_2)$
= $(3p_1/6)+(4p_2/6)+((6)(1-p_1-p_2)/6)$
= $3p_1/6+4p_2/6+(6-6p_1-6p_2)/6$
= $(3p_1+4p_2+6-6p_1-6p_2)/6$
= $(6-3p_1-2p_2)/6$
= Thus, $p_1=(6-2p_2)/3)$ and $p_2=(6-3p_1)/2$
Player 1's expected payoff of choosing R, that is $E(R)$, is $(1)(p_1)+(2/3)(p_2)+(1/3)(1-p_1-p_2)$
=$3p_1/3+2p_2/3+(1-p_1-p_2)/3$
=$3p_1+2p_2+1-p_1-p_2$
=$2p_1+p_2+1$
=$p_2=-1-2p_1$
=$p_1=(-p_2-1)/2$
Did I do this correctly?
Similarly, Player 2's expected payoff for choosing strategy A, $E(A)$, is $(1/2)(q)+(1)(1-q)$
= $q/2-1-q$
= $q/2-2/2-2q/2$
=$q-2-2q$
=$-q-2$
=> $-2=q$
Player 2's expected payoff for strategy B, $E(B)$, is $(2/3)(q)+(2/3)(1-q)$
=$2q/3+(2-2q)/3$
=$2q+2-2q$
=$2$
Player 2's expected payoff for strategy C is $(1)(q)+(1/3)(1-q)$
=$q+(1/3)-(q/3)$
=$(3q+1-q)/3$
=$2q+1$
=$q=-1/2$
I am not sure if I'm doing this correctly.

You generally have the right approach with expected payoffs correctly, but there are some errors in your logic.
First, take a look at your reduced matrix. You're missing a way to reduce it further and simplify the math a bit! You've left an extra strategy in place for Player 2. Player 2 knows that Player 1 will never play $M$, so Player 2 only needs to consider best responses to $L$ and $R$.
Second, note that you're using Player 1's payoffs in your expected payoff calculations for Player 2. For example, you have
$$E[A] = \frac{1}{2}q + 1(1-q)$$
The payoffs of $\frac{1}{2}$ and $1$ are to Player 1, not to Player 2. You want to use $\frac{1}{2}$ and $0$ in your calculation.
Third, the way you find a mixed strategy Nash equilibrium is by setting players' expected payoffs to be equal. Player 1 and Player 2 each need to be indifferent between their strategies, and that occurs when they play their strategies with probabilities so that the other player's payoffs are equal.
So, for Player 2's equilibrium strategy, you'll take Player 1's expected payoffs and set them equal: $E[L] = E[R]$. If they aren't equal, then one's greater than the other. Say $E[L] > E[R]$. Then, Player 1 will play $L$, and Player 2 will want to play $C$, then Player 1 will want to play $R$, and you end up in a cycle (and not an equilibrium). When the payoffs are equal, you have a stable solution, and neither player has an incentive to deviate from that strategy.
The same rationale applies to Player 1's equilibrium strategy - it's the set of probabilities that result in all of Player 2's expected payoffs being equal, and your Nash equilibrium is the set of all the strategies and their corresponding probabilities.


How is money created on net? I have the impression that everyone has more net money than in the past. By net money I means cash + money lent to others - money borrowed from others. If this is true, where does the extra net money come from? Is it right to say that originally all the extra net money comes to the world as interest paid by the central bank for the reserve deposit of commercial banks?

I read that commercial banks create money by making loans. But when one person borrows money from banks, his net money doesn't increase. And when people make transactions, money just goes from one to another. How does it come that finally everyone has more net money than before?

Edit:

I have a second thought that my impression is simply wrong. It's only true to say that generally everyone is wealthier than in the past. If we look at the richest businessmen in the world, their "net money" as defined above can often be hugely negative, but they are still wealthy since they possess a lot of other things like buildings, factories etc.

And besides those business men, the "net money" of the government is also hugely negative(almost every country's government has a large public debt). So if the "net money" of the popluation as a whole remains more or less constant(in the spirit of "loans + cash == liability deposits" mentioned by @Lumi), a few entities having hugely negative "net money" make others's net money increase, so one could have the impression that the "net money" of the majority of the population has increased.

Suppose I define "net appliances" as dishwashers plus appliances lent to others minus appliances borrowed from others.

Suppose I build a refrigerator and lend it to you.  Then your "net appliances" have been reduced by one, my "net appliances" have increased by one, and the total of the world's "net appliances" has not changed.

On the other hand, the world does now have one more refrigerator, which suggests that "net appliances" was never a very interesting notion in the first place.


US Real GDP Growth Rate I am interested in finding the quarterly real GDP growth rate of US and have found the following two measures from IMF International Financial Statistics:

Which one should I choose (Dark Green or Light Green)?

It depends on what you want to look at. The blue line compares GDP of this period to the same period of the previous year. This is referred to "year-on-year" or "year-over-year" growth. The green line compares GDP of this period to the GDP of the previous period, "quarter-on-quarter (QoQ)" growth.

Because there's seasonality in the GDP (usually Q4 is the highest because of the holiday shopping), when you do QoQ growth you have to adjust for it, and that's where "seasonally adjusted" comes from.

Usually the year-on-year growth is what gets reported in the news.


Can small countries use a foreign currency as their official currency? Having one of the "big currencies" (US-Dollar, Euro, Japanese Yen) is of several advantages:

Tourism: There is a huge amount of people who can directly use it (317*10^6 US citizens, 337*10^6 people in the Eurozone, 128*10^6 Japanese).
Trade barriers: I guess trade might also get easier, at least for small companies.
Reliability: Citizens and companies can probably trust more in the value being stable of those 3 currencies than smaller ones.
Security:  I'm not too sure about the Dollar / Yen, but Euro bank notes have quite a lot of security mechanisms which make the forgery of banknotes harder.

Especially for small countries, I would guess having one of those big currency would have the advantage of not having to pay for producing the bank notes / coins.

So why do contries like Seychelles (Seychellois rupee), São Tomé and Príncipe (São Tomé and Príncipe dobra), Cape Verde (Cape Verdean escudo) ... have their own currencies? Can you give one example which shows the effect if such a country took one of the big currencies?

Are countries not allowed to use another countries currency officially?

Having your own currency means that you can conduct your own monetary policy. Adopting another country's currency means that you trade your ability to make decisions about your country's quantity of money, inflation target, etc. to a tested and solid mean of payment (the advantages you listed are good reasons).

You might consider European countries adopting the euro as an example of countries adopting a single currency. Ecuador adopting the U.S. dollar in 2000 might be a good place to look if you want to see the effect in a specific country.

There are quite a few countries in the world which use another country's currency as their official currency. This article lists them all (as of 2014):
http://qz.com/260980/meet-the-countries-that-dont-use-their-own-currency/


Sending your paper around in Economics As a PhD student I made a few connections over the course of time with professors from around Europe (had brief chats with them at conferences, invited them at conferences, etc..). Some explicitly said, send me your paper once it is ready, other haven't.

Is it common in Economics to send your paper, without an explicit invitation, asking for feedback (assuming the speaker to be in the relevant field)? Or should one wait or look for a chance to present it in a seminar?

Is it common in Economics to send your paper, without an explicit invitation, asking for feedback (assuming the speaker to be in the relevant field)?

I am not sure this is common in Econ but I have definitely done it! Note that you increase the probability of getting feedback if

you know or met the author,
he/she asked you to send your paper,
you cite their work.

Or should one wait or look for a chance to present it in a seminar?

This is probably your best chance to get feedback given that profs are very busy. A bunch of universities and associations organize PhD seminars, workshops, conferences or poster sessions. Look at inomics. You may also contact profs with the intention to present your work in their seminars.


Assumptions in GDP calculation The standard approaches for calculating GDP are:
$$
\text{GDP} = \text{Consumer Spending + Capital Investments + Govt. Spending + Net Exports}
$$
And
$$
\text{GDP} = \text{Total wages + Profits + Taxes + Return on Capital Investment}
$$
I have an issue in seeing the equivalence of these two approaches in different cases. Say we pay the government taxes. In the second approach that gets counted in "taxes", but in the first approach it doesn't get directly counted. Yes, the government spending usually comes out of tax revenue, but not all of tax revenue goes to government spending. So how does the "taxes" in the second approach get divided in the first approach. A good chunk of it goes to government spending, but what about the rest? Are we making an assumption that it's all spent? What if in a simple "two good economy", we have an individual/firm paying taxes but we don't add government spending. Does the tax money go "waste" here in our GDP calculation?

Secondly, we don't count wages in "capital investments" since we assume that the wages paid by firms (counted in the second approach) become consumer spending; but are we assuming that consumers spend ALL their income? How do we account for savings and simply models in which wages do not necessarily equal spending?

Yes the two approaches are equivalent. However, that does not mean that the respective individual variables are equivalent. Taxes are not equivalent to government spending but the both equations equally capture all Government output. For example in the first approach:

$$GDP = C+ I + G +NX$$

Where $C$ is consumer spending, $I$ is investment and $G$ government spending, $I$ is also equal to private and public saving $I=S + T-G$, so if government spend less than what it collect in taxes the public savings and public portion of investment increases, and when it runs budget deficit vice versa, so the possibility of running either surplus or deficit or balanced budget is already accounted for there. No assumption that its all spent is necessary.

Second, any income, whether it is wage or not, can be only consumed or saved. The consumption part is explicitly included in the formula as $C$ the saving part is the $S$ which represent the private savings from which investment is created. So if a person spend less their income investment increases thanks to private saving, and if a person lives on debt investment decreases to reflect that.

Also, both formulas are just accounting formulas. By itself they have no behavioral assumptions/spending assumptions. They are national equivalent of the kind of accounting that you could see in firms book just track the sources of income and spending.


separable utility function and cross price effect Suppose that consumer's utility function for three goods is separable, that is,

$U(x_1, x_2, x_3) = f_1(x_1) + f_2(x_2) + f_3(x_3)$ ...(i)

where $f_i$ is increasing and strictly concave, i=1,2,3. Show that

$ df_i/dP_1 $ for i = 2,3 can be either positive or negative, but they must be of the same sign where $f_i$ is the demand function for good i and $P_1$ is price of good 1.

i reasoned using the equimarginal principle where at optimum we must have

$ MU_1/P1 = MU_2/P2 = MU_3/P3 $.

suppose good 1 is normal, if $P_1$ rises demand for good 1 falls, that is $df_1/dP_1$ < 0. Due to law of diminishing marginal utility $MU_1$ rises, however to maintain equilibrium $ MU_2,  MU_3$ must also rise. So, $df_2/dp_1 < 0$ and $ df_3/dP_1 < 0$. But i couldn't do it more mathematically, taking the derivative of (i) w.r.t $P_1$ isn't of much use, please help.

The following argument assumes that we are dealing only with interior solutions. Let $(x_1,x_2,x_3)$ be an optimal demand bundle at prices $(p_1,p_2,p_3)$ and income $m$ and assume that $(x_1,x_2,x_3)$ is an optimal demand bundle at prices $(p_1',p_2,p_3)$ and income $m$. We want to show that one of the following three cases holds:

$x_2=x_2'$ and $x_3=x_3'$,
$x_2<x_2'$ and $x_3<x_3'$, or
$x_2>x_2'$ and $x_3>x_3'$.

What is not allowed to happen is that $x_2\leq x_2'$ and $x_3>x_3'$ or $x_2>x_2'$ and $x_3\leq x_3'$. Assume one of these cases happens, without loss of generality, we can assume it is the first.

By the strict concavity of $f_2$ and $f_3$, we have
$$MU_2(x_1,x_2,x_3)=\frac{\partial f_2(x_2)}{\partial x_2}\geq \frac{\partial f_2(x_2')}{\partial x_2}=MU_2(x_1',x_2',x_3')$$
and
$$MU_3(x_1,x_2,x_3)=\frac{\partial f_3(x_3)}{\partial x_3}< \frac{\partial f_3(x_3')}{\partial x_3}=MU_3(x_1',x_2',x_3').$$
Therefore,
$$\frac{MU_2(x_1',x_2',x_3')}{p_2}\leq\frac{MU_2(x_1,x_2,x_3)}{p_2}=\frac{MU_3(x_1,x_2,x_3)}{p_3}<\frac{MU_3(x_1',x_2',x_3')}{p_3},$$
in contradiction to the equimarginal principle.


What is the appeal of DSGE models? As far as I understand people like them, because they fit the data quite well when compared to VAR's for example while also having an economic interpretation.
They appear to explain observations in a more general way than VAR's.

However for me personally that point falls flat as I can not convince myself to see the assumptions (everything is differentiable instead of discrete, goods don't depend on each other for production, people have no skills, etc.) to be a sensible simplification of reality. So I'm left wondering if DSGE models fit the data despite their assumptions. After all they have quite a number of parameters, which might make them quite flexible.

Or do DSGE models fit the data better than VAR's or other models like neural networks?

Did people investigate the "expressiveness" of DSGE models? With expressiveness I mean the set of functions(DSGE models predict inflation as a function of time for example) you can approximate by choosing the parameters of a given DSGE model.

To summarize what I wrote below, there seem to be at least two points:

In the Smets and Wouters (ECB) research, which is apparently responsible for a lot of the fame of DSGE, they indeed found it superior in forecasting accuracy to (B)VARs, especially long-term. On the other hand, other research (including some by other ECB researchers) doesn't seem to be so uniformly conclusive in this (accuracy) regard. Alas, it doesn't look like there is anything resembling a systematic review on this issue; perhaps the variations in data sets and methodology preclude one.
In the more academic realm, proponents of DSGE (e.g. Christiano) argue that DSGE has deep explanatory powers for some inflation-related lags, making them easy to understand.

I'm sure someone will give you a more technical answer, but basically DSGE works well for monetary policy (inflation targeting) etc.

  Part of the recent popularity of DSGE models is due to work by Smets and
  Wouters (2003), who document that a modified version of a New Keynesian model
  developed by Christiano, Eichenbaum, and Evans (2005) is able to track and forecast
  euro area time series as well as, if not better than, a vector autoregression (VAR) estimated with Bayesian techniques.

In other areas like fiscal policy DSGE hasn't seen that much success/application, insofar anyway.

However, the New Keynesian DSGEs have their critics, particularly in the Minneapolis Fed; see Chari, Kehoe, and McGrattan.

  Proponents of the New Keynesian model argue that it is promising for two reasons. It
  represents a detailed economy that can generate the type of wedges we see in the data from
  interpretable primitive shocks; and second, it has enough microfoundations that both their
  shocks and parameters are structural, in that they can reasonably be argued to be invariant
  to monetary policy shocks. A model with both of these features would potentially be useful
  for monetary policy analysis.

  We disagree. We argue that these models cannot generate the type of wedges we see
  in the data from interpretable primitive shocks. And it is doubtful that many of the features
  added on in the quantitative implementation of the models are structural. Hence, the models
  are not yet useful for policy analysis.

(The first paper I quoted from is from the Atlanta Fed.)

Also, VAR and DSGE are not orthogonal or alternative as you suggest; from the Atlanta paper:

  It has long been recognized (for example, Sims 1980) that a tight relationship exists between dynamic
  equilibrium models and VARs. Imagine the following thought experiment, where for
  the moment the vector of DSGE model parameters is fixed. We generate 1 million
  observations from the DSGE model—that is, we generate a sequence of shocks
  (monetary policy, technology, etc.), feed them trough the DSGE model, and obtain
  artificial data. Next, we estimate a VAR with p lags on these artificial data. If the
  DSGE model is covariance stationary, then the estimated VAR provides an approximation to the DSGE model with the property that its first p autocovariances are
  equivalent to the first p autocovariances of the DSGE model. By including more and
  more lags we can in principle match more and more autocovariances and increase the
  accuracy of the VAR approximation of the DSGE model. Now imagine that the data
  generation is repeated using different parameter values for the DSGE model. As long
  as the DSGE model parameter space is small compared to the VAR parameter space,
  a restriction function can be traced that maps the DSGE parameters into a VAR
  parameter subspace. Hence, estimating a DSGE model is (almost) like estimating a
  VAR with cross-equation restrictions.

That paper is somewhat limited (empirically) in that it looks at a single (New Keynesian) DSGE and VAR-izes it.

For a more general comparison see: Raffaella Giacomini, The Relationship Between DSGE and VAR Models. It does mention some caveats e.g.

  a meaningful discussion of the relationship between DSGE and VAR
  models can only be carried out in the context of log-linearized DSGE models, taking for granted
  the adequacy of the linear approximation and ignoring possible nonlinear dynamics that cannot
  be replicated by linear VAR models.

It goes on to point out that non-linear DSGEs are (still) a minority in current research, but that that sub-field appears to be growing pretty fast.

The claim to DSGE empirical superiority (as estimated by the more widespread Bayesian techniques, rather than by embedding in VARs) is probably in the narrow(er) context of specific papers; the 2007-updated Smets and Wouter does indeed make such claims. In the short term, they only find a a difference for unconstrained VARs and they find that a BVAR model does as well as their DSGE; but for a longer forecast they indeed found their DSGE superior to both VAR/BVAR.

  In this Section we compare the out-of-sample forecast performance of the estimated DSGE model with
  that of various VARs estimated on the same data set. The marginal likelihood, which can be interpreted as
  a summary statistic for the model’s out-of-sample prediction performance, forms a natural benchmark for
  comparing the DSGE model with alternative specifications and other statistical models. However, a Sims (2003) has pointed out it is important to use a training sample in order to standardize the prior
  distribution across widely different models. In order to check for robustness, we also consider a more
  traditional out-of-sample RMSE forecast exercise in this section.

  Table 2 compares the marginal likelihood of the DSGE model and various unconstrained VAR models,
  all estimated over the full sample period (1966:1 – 2004:4) and using the period 1956:1 – 1965:4 as a
  training sample. Several results are worth emphasizing. First, the tightly parameterized DSGE model
  performs much better than an unconstrained VAR in the same vector of observable variables, Υt (first
  column of Table 2). The bad empirical performance of unconstrained VARs may not be too surprising, as
  it is known that over-parameterized models typically perform poorly in out-of-sample forecast exercises.
  One indication of this is that the marginal likelihood of the unconstrained VAR model deteriorates
  quickly as the lag order increases. For that reason, in the second column of Table 2, we consider the
  Bayesian VAR model proposed by Sims and Zha (1998). This BVAR combines a Minnesota-type prior
  (see Litterman, 1984) with priors that take into account the degree of persistence and cointegration in the
  variables. In order to allow the data to decide on the degree of persistence and cointegration, in this
  BVAR we enter real GDP, consumption, investment and the real wage in log levels. When setting the
  tightness of the prior, we choose a set of parameters recommended by Sims (2003) for quarterly data.
  The second column of Table 2 shows that the marginal likelihood of the Sims-Zha BVAR increases
  significantly compared to the unconstrained VAR. Moreover, the best BVAR model (BVAR(4)) does as
  well as the DSGE model.

  Overall, the comparison of marginal likelihoods shows that the estimated DSGE model can compete with
  standard BVAR models in terms of empirical one-step-ahead prediction performance. These results are
  confirmed by a more traditional out-of sample forecasting exercise reported in Table 3. Table 3 reports
  out-of-sample RMSEs for different forecast horizons over the period 1990:1 to 2004:4. For this exercise the VAR(1), BVAR(4) and DSGE model were initially estimated over the sample 1966:1 - 1989:4. The
  models were then used to forecast the seven data series contained in Υt from 1990:1 to 2004:4, whereby
  the VAR(1) and BVAR(4) models were re-estimated every quarter, whereas the DSGE model was reestimated every year. The measure of overall performance reported in the last column of Table 3 is the
  log determinant of the uncentered forecast error covariance matrix.

  The out-of-sample forecast statistics confirm the good forecast performance of the DSGE model relative
  to the VAR and BVAR models. At the one-quarter ahead horizon, the BVAR(4) and the DSGE model
  improve with about the same magnitude over the VAR(1) model, confirming the results from Table 2.
  However, over longer horizons up to three years, the DSGE model does considerably better than both the
  VAR(1) and BVAR(4) model. Somewhat surprisingly, the BVAR(4) model performs worse than the
  simple VAR(1) model at longer horizons. Moreover, the improvement appears to be quite uniform across
  the seven macro variables.

However, there's somewhat newer (2009) ECB paper by different authors (Kolasa, Rubaszek, and Skrzypczyński) with less sweeping conclusions:

  In the case of ination, the DSGE and DSGE-VAR
  models with the maximum lag set to 3 and 4 are characterized by the lowest RMSFEs. The SPF [Survey of Professional Forecasters]
  and BVAR(4) are insignicantly less accurate, while the BVAR and low-order DSGE-VAR models are
  found to be the worst. Finally, the RMSFEs for interest rate forecasts formulated by all methods are
  comparable.

(There's a 2012 peer-reviewed version of that paper, if you care about that. And As an aside, somewhat disappointingly, adding (corporate) financial market frictions to their DSGE model did not uniformly improve forecasts, but adding housing market frictions did help especially with crises.)

Another paper which focuses on hybrid DSGE models (Paccagnini, 2011) has this introductory note:

  from an econometric point of view, the performance of a DSGE model is often
  tested against an estimated Vector Autoregressive model (VAR). This procedure requires a Data
  Generating Process (DGP) that is consistent with the theoretical economic model and has a finite-order VAR representation. However, the statistical representation of a DSGE model is an exact
  VAR only when all the endogenous variables are observable; otherwise, a more complex Vector
  Autoregressive Moving Average model (VARMA) is needed. As far as the VARMA representation
  is concerned, several papers (see Cooley and Dwyer (1998), Chari, Kehoe and McGrattan (2005),
  Christiano, Eichenbaum and Vigfusson (2006), Ravenna (2007) and Fernandez-Villaverde, Rubio-Ramirez, Sargent and Watson (2007)) have discussed the conditions required to find an infinite-
  order VAR representation and a infinite-order VAR truncation in general terms. Moreover, the VAR is densely parameterized and appears to be misspecified and a Bayesian approach is preferred.

And the results of this paper are not amazing for DSGE:

  Two forecasting exercises have been implemented on US quarterly economy data: the first one
  considering a simple forecasting one-step-ahead strategy with different samples, and the second a
  h-steps ahead evaluation with a rolling forecasting estimation. In the first exercise, the last part of
  the sample from 2007 onwards, which is the Great Contraction period, was not taken into account.
  The main results show that the hybrid models, such as the DSGE-VAR and the DSGE-FAVAR give
  the most accurate forecasts for smaller forecasting samples. Instead, a FAVAR model outperforms
  the other models when we consider a long forecasting sample. The second forecasting experiment
  uses a rolling sample with the Great Contraction period included. The best forecasting performance
  is produced by VAR, BVAR and FAVAR, with the exception of real GDP where for h-steps ahead
  larger than 2 the DSGE-FAVAR outperforms the alternative models.

As a side-note to that last paper, FAVAR was apparently favored/suggested by Bernanke.

These (not always clear) accuracy contests aside, DSGE advocates claim that it supposedly has deep explanatory power for inflation:

  The new monetary DSGE models are of interest not just because they represent laboratories for the analysis of important monetary policy questions. They are also of interest because
  they appear to resolve a classic empirical puzzle about the effects of monetary policy. It has
  long been thought that it is virtually impossible to explain the very slow response of inflation
  to a monetary disturbance without appealing to completely implausible assumptions about
  price frictions (see, e.g., Mankiw (2000)). However, it turns out that modern DSGE models
  do provide an account of the inertia in inflation and the strong response of real variables to
  monetary policy disturbances, without appealing to seemingly implausible parameter values.
  Moreover, the models simultaneously explain the dynamic response of the economy to other shocks. We review these important findings. We explain in detail the contribution of each
  feature of the consensus medium-sized New Keynesian model in achieving this result.

  The econometric technique that is particularly suited to the shock-based analysis described in the previous paragraph, is the one that matches impulse response functions estimated by vector autoregressions (VARs) with the corresponding objects in a model. Using
  US macroeconomic data, we show how the parameters of the consensus DSGE model are
  estimated by this impulse-response matching procedure. The advantage of this econometric
  approach is transparency and focus. The transparency reflects that the estimation strategy
  has a simple graphical representation, involving objects - impulse response functions - about
  which economists have strong intuition. The advantage of focus comes from the possibility of studying the empirical properties of a model without having to specify a full set of
  shocks.


Raising interest rates to prevent inflation I am reading a book about the Mundell-Fleming Model and I have encountered a part which says:

  The Fed raised U.S. interest rates several times during 1994 to prevent U.S. inflation.

Isn't it the other way round? I thought that rising interest rates causes the investment to decrease and so the money demand to decrease. When money demand decreases, price level increases. Am I wrong?

The increase in interest rates make borrowing more expensive and therefore businesses and people will borrow less. Therefore, investment and consumption decrease. Through the multiplier effects, this will cause a reduction in real GDP. This will also increase the unemployment rate. Therefore, people who sell these goods and services will reduce their prices. As a result, the overall price level will fall and the inflation rate is reduced. I understand that explanation where the money demand decreases cause a probable eventual reduction in the interest rates. However, this assume that the money supply is fixed. Now, you must understand how the Fed controls the interest rates. It controls the interest rates by controlling the money supply. It reduces the money supply by selling bonds into the economy. Therefore, the money supply shift to the left and initially, the interest rates soar. The demand and supply analysis:

First we must define some basics: We are going to use the supply and demand graph with the interest rates as the y axis and the money in x axis. Now since we know that there is a fixed amount of money in the economy and the Fed is controlling it, we know that the supply of money is strictly vertical and the demand for money is downward-sloping (with a certain elasticity)
The mechanism of the money diagram: In a fixed money supply, if there is an increase in demand of money, the demand curve will shift to the right. Now if there is a a positive inflation rate, there is an increase in demand of money with every inflation rate and therefore the demand curve will shift to the right.
The fed aims to  reduce inflation by increasing interest rates. They do this by reducing the amount of money in the economy and thus shifting the supply curve of money to the left. You are right when the total quantity of money in the equilibrium point will be reduced. However, I think that you are confused why the interest rates will not go down. This is because the Fed aims to reduce positive interest rates and not cause a negative inflation rate. In argument (2) I have explained that with a positive inflation rate, the money demand curve will always be shifting to the right. Therefore, the Fed only wants to reduce the speed of that shift.

Now you wonder why the Fed wants to reduce the inflation rate. This is because it is always desirable to have a steady price level. A high inflation rate causes some cost to the economy that it does not want. You need to google or search in the wikipedia for the negative effects of high inflation rates.


Does the price level in a competitive market have to be at the intersection of the Average Cost curve and the Marginal Cost curve? I could see that if the price level is say lower than the intersection point , then firms won't be able to operate , but what is wrong with the price level being above the intersection point of the AVC and the MC .

IN that case firms would earn positive profit , although I know that this not happen in a competitive market , but I fail to grasp what stops this from happening ?

That is why won't the competitive market function well enough if the price level would be higher than the intersection point ?

I thought then the positive profits would make the other firms come in , however I could;t quite make the whole connection as to how would it drive the price level down !

One of the assumptions of perfect competition is that firms are price takers. Ultimately price is determined by the quantity of goods supplied, and with perfect competition, there are infinite (or an arbitrarily large) number of firms, so a firm that changes their price by itself will simply have no business, since there are cheaper places to buy from. The quantity supplied will also not change, and will leave the prices unchanged.

So what happens if all infinite of these firms tried to unilaterally raise their prices to the same level? This is maybe in some cases a Nash equilibrium, but not a coalition-proof Nash equilibrium. So firms could also unilaterally deviate from the higher price to take the whole market between themselves.

If price (marginal benefit), was suppose, forced to be higher, so that you moved along the marginal cost curve where MC $\neq$ ATC, then the supply curve would shift, because the optimal production quantity would increase for all firms at this price control. And the market would then not clear.


Has worker productivity decreased since the election of Donald Trump? Anecdotally, I know that myself and others have felt distracted, depressed and anxious since the election of Donald Trump.

Are there any studies that have objectively sought to measure worker productivity since the election of Donald Trump?

What was their methodology, and what were the results?

If no such study does exist, can you describe any similar studies and what the methodology is?

I think it's too early to identify econometrically an effect of Trump in the economy. Recall that the election was the 8th of November, and his victory came partly as a surprise. He took some time to define his cabinet and got into office the 22nd of January. Thus, any effect of a Trump's "dummy" might only partially be reflected in data for Q4 of 2016, and perhaps not fully in Q1 2017. The release of (worker's productivity) for Q2 2017 is the 9th of July (soon), where we might see more of Trump's effect on the economy and productivity.

The best we can do at the moment is simply look at how the economy has evolved since Trump (see here for a related exercise for Obama).

For example, the favourite measure of labour productivity among economists slowed down in Q4 of 2016 and did not increase in Q1 of 2017:

(Source here).

Similarly, there was an increase in workers productivity in the manufacturing sector in Q4 of 2016, which slowed down considerably in Q1 of 2017:

(Source here).

How these developments are related to Trump is not clear though. Some news reports about these data releases make no mention of a Trump effect (e.g. here (Q4 2017), here or here (Q1 2017)).

Another example comes from the stock market. Here is an analysis showing the performance of the stock market under different presidents, after their 100th days in office. I show the main table below:


Is single-peaked preferences necessary for majority rule to be transitive and yield non-empty choice set? I understand that when individuals have single-peaked preferences, majority rule will be transitive and the choice set will be non-empty. So single peaked preferences is a sufficient condition.

Is it also necessary? If not, what other domain restriction can given majority rule a non empty choice set?

No, single-peakedness is not necessary for majority rule to be transitive.  For example, "single-dipped" preference profiles (the vertical mirror image of "single-peaked" profiles) also produce transitive majority preferences.   A much-more general condition is "triple-wise value restriction", which Sen (1966) showed generates a transitive majority preference relation.  Here is a good summary of these and related concepts, with some references to the primary literature:

https://plato.stanford.edu/entries/social-choice/#NonDicPreAggRul


Why did the rate of money supply growth accelerate from 1993-96 in the United States? Even though the rate of growth in the monetary base decelerated — and the money multiplier decreased for the most part — from 1993-96 in the United States, the growth rate of the M2 money stock still progressively sped up. How is this possible?

Reference to second graph:

https://www.alt-m.org/2016/07/21/why-the-money-multiplier-remains-so-low/

So long as the growth rate of the monetary base is greater than the growth rate of M2, the ratio of M2 over the base (velocity) will decrease. (The numerator of M2/MB is growing less slowly than the denominator.)

That is what happened during (most of) the period shown. It was only in 1996 that M2 was growing faster than the base, which would increase velocity.

Your question is effectively attempting to characterise the second time derivative (acceleration) of M2 in terms of the acceleration of the monetary base and velocity. In my answer to another question, I give the relationship for acceleration in the money supply, and it is related to the acceleration in the monetary base and the acceleration of velocity. The data shows the level of velocity, which is not enough to characterise the relationship.


Can one prove Pareto efficiency in an n-party system by showing all Pareto improvements between any two given parties are made? I've made a proof of Pareto efficiency of a funding system that I've developed. There are effectively four types of actors. I've shown all Pareto improvements are made between any two given parties are made (including between two actors within the same party). I believe that this proof by cases is valid, but I'm not 100% certain. My one concern is that maybe there is some tricky three-way or four-way trade that is somehow not captured in my proof. Thoughts?

@HerrK. got it right in his comment (he should have deleted the somewhat confusing "yes" from the beginning and then posted it as an answer) It is possible that no pairwise improvements are possible but general Pareto-improvements are still possible. A simple counterexample for three actors and three goods is as follows. Let the utility functions be the same for all actors, that is
$$
U_A(x,y,z) = U_B(x,y,z) = U_C(x,y,z) = \min(x,y,z).
$$
Let actor $A$ have 3 units of good $x$, and 0 units of the other goods, whereas actor $B$ has 3 units of good $y$, and 0 units of the other goods, and actor $C$ has 3 units of good $z$, and 0 units of the other goods. No pairwise exchange can increase utilities above zero. But the goods could be distributed so that everyone has a unit of each. This would increase all utilities to one, making the original distribution not Pareto-efficient.


What statistics and linear algebra book do i need before reading Hayashi's econometrics What statistics and linear algebra book do I need before reading Hayashi's Econometrics?

Basics linear algebra book seems too simple for the linear algebra part, and
Casealla's statistical inference is missing out detail/too basic for the statistical part

The Linear algebra part should not worry you, it is just basic linear algebra plus familiarizing yourself a bit with differentiation of vectors and matrices (and for some chapters, visualizing the Kronecker product).  Hayashi goes some length into writing out explicitly large matrices, which is virtually with no-precedent (see eg. pages 267, or 288), something that eventually facilitates understanding -as long as you don't back out from a matrix half a page large, but you really look at it.

What you should really go slow over upon is Hayashi's notation, which is non-standard in many places. So don't expect to understand through familiar notation. Be prepared for that and "read" carefully every symbol and its role. Many people's discomfort with this book is due to the notation, but they don't realize it.

As for the Statistics part: In Econometrics, since we deal almost always with non-experimental, observational data, a large part of Statistics (originating usually in Biostatistics) do not really enter (our) picture. For example, apart from proving that under certain conditions the OLS estimator is best linear unbiased, you won't see much regarding the issues of minimum variance estimation or sufficient statistics. We don't even discuss the Exponential Family of distributions and the concept of Generalized Linear Models. Also, in statistical Hypothesis testing the Fisherian spirit prevails (oozing through the Neyman-Pearson apparatus), meaning, among other things, that issues like the "power of the test" are not so often considered.

Moreover "frequentist Econometrics", which is what Hayashi presents, are considerably lighter than Bayesian Econometrics in terms of the Algebra of Random Variables and probability theory.

What really matters is a good familiarity with basic Asymptotic Theory and Stochastic Processes (for the Time Series part). Although Hayashi in most cases just states results, providing references for the proofs, nevertheless it would be good to feel comfortable with asymptotic results and properties, because in most cases, it will be all your estimators will possess. For this part, I will once more advocate A. Spanos' book, Probability Theory and Statistical Inference - Econometric Modeling with Observational Data. It is a valuable book, Hayashi or not Hayashi. It is Statistics with the Econometrics graduate student in mind.

In case you want some more specific Time Series material, Hamilton's Time Series Analysis remains a standard reference.

Finally, regarding Unit-root Econometrics and Co-Integration, the subject is inherently advanced, and I think Hayashi has done a good job in collecting and presenting the very basics.


Finding subgame perfect equilibrium The main part of the question is as follows

(if you cannot read this, I can immediately write it)

My question is how to find the subgame perfect Nash equilibrium for the both cases $\bar{g_2}\ge \bar{g_1}$ and $\bar{g_2}< \bar{g_1}$

My attempt is

For firm 2

$$max [f_2(G)-c_2(g_2)]$$
$$max [\beta ln(g_1+g_2)-g_2]$$

By FOCs

$$\beta / (g_1+g_2)- 1=0$$

$$g_2=\beta -g_1$$

For firm 1

$$max [f_2(G)-c_2(g_2)]$$
$$max [\theta ln(g_1+\beta -g_1)-g_1]$$

I cannot get FOC with respect to $g_1$

At this point I’m stuck. How can I proceed this solution?

And I have another question

For the same question, I assume the following part

Again I need to find subgame perfect Nash equilibrium of this game where player 1 contributes a positive amount of public good.?

Sorry but I could not this part completely. Any helps will be appreciated.

Since I could not understand such type of questions for the SPE, I asked lots of time. Thanks.

Note, there is a mistake in FOC---it should be
$$\beta/(g_1+g_2) - 1 =0,$$
so the response function of firm $2$ is
$$g_2 = \beta - g_1.$$

This means that a unit increase in a public good contributed by firm $1$ causes firm $2$ to decrease its contribution by the same unit. Then, notice that firm $1$, who correctly anticipates such a (optimal) response by firm $2$, is better off by not contributing anything (hint: $g_1$ only affects $C(g_1)$ up to $g_1 \in [0,\beta]$).

I guess you can take from here to solve the second part


noise traders in neo-classical economics vs behavioural economics Does neoclassical economics/finance exclude the existence of noise traders (as a contrast to rational traders)? Or do neoclassical models also sometimes accept the existence of noise traders?

The claim that financial markets are efficient is backed by an implicit argument that misinformed "noise traders" can have little influence on asset prices in equilibrium. If noise traders' beliefs are sufficiently different from those of rational agents to significantly affect prices, then noise traders will buy high and sell low. They will then lose money relative to rational investors and eventually be eliminated from the market. But De Long et al, 1987 (https://www.nber.org/papers/w2395) presented a simple overlapping-generations model of the stock market in which noise traders with erroneous and stochastic beliefs (a) significantly affect prices and (b) earn higher returns than do rational investors. Noise traders earn high returns because they bear a large amount of the market risk which the presence of noise traders creates in the assets that they hold: their presence raises expected returns because sophisticated investors dislike bearing the risk that noise traders may be irrationally pessimistic and push asset prices down in the future. The journal version of that paper is De Long, J. B., Shleifer, A., Summers, L. H., & Waldmann, R. J. (1990). Noise trader risk in financial markets. Journal of political Economy, 98(4), 703-738.
According to google there is more than 7000 citations for that article  https://scholar.google.com.br/scholar?q=Noise+Trader+Risk+in+Financial+Markets&hl=pt-BR&as_sdt=0&as_vis=1&oi=scholart


How would a 2D model of Hotelling's law outweigh the benefits of a 1D model? I'm not sure if this goes here, or on a math exchange. I could move it if you guys want...

Let's examine Hotelling's law on a 1D plain with two shops.

Both shops would do society a favour if placed on the 1/4 mark. But since both owners want to make money, the two shops will most likely be placed in the middle, right next to each other.

There have also been numerous mathematical formula's to analyse Hotelling's law in 1D with more than two players.

However, would this model work in a specific 2D plane with n players?

And if so, how would the information-benefits of a 2D model outweigh the ones of a 1D model concerning the real word?

Would a 2D model better help shop owners find a more suitable location?

There are several scientific papers analyzing this on topologies other
than the unit interval. A 2D example is Spatial competition of firms in a two-dimensional bounded market by Aoyagi and Okabe. Unfortunately there are usually no equilibria in these cases. The intuition behind this is that the consumers arriving from different directions are usually not "balanced", and one could gain by deviating to a direction where a higher number of consumers are coming from.

Also, Hotelling models are not used in practice (to my knowledge) when one is assessing where to open a new shop.


Why does the stock price of listed firm matter for that firm? As the title hints, why would the stock price matter for a firm?

Which are -in rough terms- the channels that a firm's stock price influence it?

There are multiple channels :

Debt: the cost of debt may raise significantly if the value of equity drops. Indeed, the lower the equity, the higher the risk of the debt, as the firm will have a higher gearing ratio (also called leverage). Thus, the firm might have difficulties to gain access to additional debt or face a higher cost.
Financing: A firm with a poor performance on stock markets might face difficulties to raise additional capital. Investors might indeed not be willing to buy the firm's stock if its performance is poor. Therefore the firm might not be able to raise additional capital.
Reputation: a decrease in stock price can negatively affect the reputation of a firm. Not necessarily with the customers but also with other stakeholders, such as the suppliers which could fear that the financial stability of the firm is not assured.

So overall I would say that the stock price is mainly important to the firm as it is a strong determinant of the costs it will face when raising capital or debt.

Also, note that stockholders are owners of the firm. As such, they can compel the firm to adopt a more profitable strategy, if they so wish. Of course, it might be hard, but activist investors for example show that it is possible.


Measuring growth rate when values are negative I am studying nightlights data and trying to model cross-sectional convergence in nightlights in India. However data has some stray light corrections, which has made some of the measurements below zero. Another point being, that the value of 0 has a representative meaning.
Hence any conventional way of measuring growth rates in literature is not applicable here.
In simple words: Nightlights are measured on a relative scale from 0 to 63. The corrections for cloud cover and ephemeral lights makes some of the data points negative. So:
It is analogous to ask what is the percentage growth in nightlights if it increases from - 1 DN to 0 DN
Even more problematic question is what is the percentage growth in nightlights if it increases from 0 DN to 2 DN.
I have already thought of adding an arbitrary but reasonable positive number to data points, to bring everything into a positive domain. But this is a very crude and not an elegant way to do this.

For negative values alone you can define relative change as:
$$\frac{X_t-X_{t-1}}{|X_{t-1}|}$$
This is quite common way to deal with rates of change when you have negative numbers. However, when the denominator is zero then the growth rate is not defined. This can solve any issue when zero is not a base.
When zero is the base unfortunately there is no way how you can calculate growth rate while keeping the zero there. This is because if you start from zero any change represents $\infty$ increase. Going from 0 to 1 is $\infty$ growth rate as well as going from 0 to 10 or 0 to 1000. You have to either get rid of a zero in some way or another or simply do not calculate growth rate but some other measure of change (e.g. simple change $X_t -X_{t-1}$).

I have already thought of adding an arbitrary but reasonable positive number to data points, to bring everything into a positive domain. But this is a very crude and not an elegant way to do this.

Yes, this is very crude way of doing it but perhaps there are more elegant alternatives. Using the temperature as an example a solution would be to convert degrees Celsius to Kelvin (with $T_{(K)} = T_{(°C)} + 273.15$) which would solve the problem.
Perhaps there is an another way to measure the quantity you want. Otherwise, adding an arbitrary constant would be a solution. It is hard to recommend any specific way without knowing all the details of the research.


Why is the Cobb-Douglas production function so popular? As relatively novice quantitative analyst/ Cost analyst, Ive been asked to estimate the level of a given organizations productivity more than once, and then forecast for the next couple of periods. The place I work at is a relatively small non-profit (around 30 people) dedicated to food bank donation distribution and volunteer solicitation, so Im not sure if firm size has something to do with this.

Most of the time I've been asked for specific units and not percentage changes or elasticities, so I'm forced to present one of two production functions.

$$f(x_1,...,x_n)=\Sigma_{i=1}^n\beta_i x_i$$
$$f(x_1,...,x_n)=\gamma \min(x_1,...,x_n)$$

Yet when I read  economic literature I see the cobb douglas (or some variation of it like the stone-gerry)  being used all the time.

I know it has the property of mathematically showing diminishing returns to scale for a single factor of production, however Im having difficulty seeing it in my line of work. Is it a production function exclusive to manufacturing of real goods?

As you hint at in your question, the real underlying reason (in my opinion) behind the C-D production function's popularity is mathematical convenience. The fact that the sum $\alpha + \beta$ is a nice, intuitive representation of "returns to scale" is very convenient.

I think of its use as similar to the use of exponential or power utilities in mathematical finance. Unrealistic? Perhaps, but oh so friendlier to work with.


Expenditure function. Prove that this set is bounded I need to prove that the following set is bounded in order to derive the expenditure function:
$e(p,v)=min_x px$
ST
$\{x \in R^n_+$ such that $U(x)\geq v\}$.
Knowing that $U(x):R^n \longrightarrow R$ is a continous function.
I already proved that the set is closed and I think that if the set is closed for being $U(x)$ continous, the set must be bounded. However I'm not sure.
Please help.
Thanks in advance.

The set need not be bounded. To see this, just take $U$ to be constant. Then the set will either be empty or equal to $\mathbb{R}_+^n$.
It is also possible that no minimum exists. Let $n=2$, $p=(0,1)$, $v=1$, and $U$ be given by $U(x)=U(x_1,x_2)=x_1\cdot x_2$. Clearly, $px=0$ is only possible if $x_1=0$, which would lead to a utility of $0$. But for every $\epsilon>0$, the bundle $(1/\epsilon,\epsilon)$ has utility $1$ and a price of $\epsilon$. So no expenditure minimizing bundle exists. Of course, there is also no expenditure minimzing bundle if there exists no $x$ at all such that $U(x)\geq v$. This can happen if $U$ is bounded above.
However, an expenditure minimizing bundle exists if it holds that prices are strictly positive and there is at least one bundle $x^*$ such that $U(x^*)\geq v$. To see this, note that minimizing expenditure on the set
$$\{x\in\mathbb{R}_+^n\mid U(x)\geq v\}$$
is equal to minimizing expenditure on the set
$$\{x\in\mathbb{R}_+^n\mid U(x)\geq v, px\leq px^*\}.$$
The latter set is closed and bounded.


Keynes' conception of investment Keynes defines saving as equal to investment, saying:
"Having now defined both income and consumption, the definition of saving, which is the excess of income over consumption, naturally follows ... Our definition of income also leads at once to the definition of current investment. For we must mean by this the current addition to the value of the capital equipment which has resulted from the productive activity of the period. This is, clearly, equal to what we have just defined as saving. For it is that part of the income of the period which has not passed into consumption."
To me, Keynes' assumption that all income that is not consumed is invested in augmenting capital seems problematic. It's pretty obvious that people do keep money on hand without either consuming it or investing it. Keynes himself doesn't seem to rely on this definition in the rest of The General Theory. In fact, his own concept of liquidity preference seems to contradict this definition. My understanding of liquidity preference is that it is the desire of people to hold their money in liquid form, as opposed to investing it to earn interest. Keynes himself says:  "For if a man hoards his savings in cash, he earns no interest, though he saves just as much as before," acknowledging that people can and do hold parts of their income without investing or consuming it.
Am I misunderstanding Keynes? Does Keynes address this definition further in any of his works?

The investment ($I$) equals savings ($S$) result is derived by Keynes just from national identity, as a result it just hold by definition. Keynes in the passage starts with the simplified version of national identity that omits government. That is:
$$Y=C+I \implies I=Y-C$$
And simply solves it for investment. The solution of investment tells us that private investment is equal to difference between income and consumption. But a difference between income and consumption is also by definition savings $(S)$. Hence keynes derives this result just using accounting. In the end accounting always has to hold because its just an identity based on definitions - in itself it has no economic meaning (In a proper version of identity that would include government this would still hold true but then investment would be equal to private and public saving $I =Y-C-G$).
Furthermore, later when it comes to the paradox of thrift Keynes does not abandon the above interpretation. Rather Keynes would say that during recession $I$ is fixed at some level $\bar{I}$ so any increase in savings $S=Y-C$, which can happen only by lowering consumption $C$ will be just corresponded equal fall in income $Y$. The argument is that your spending is an income for someone else - you cut your spending you will also cut their income - however by cutting their income you also force them to spend less and their spending is your income (this holds in liquidity trap where $I$ is fixed).  At least this is the contemporary interpretation of what Keynes meant as a standards of rigor in economics were not as high in the  past as they are nowadays always leaving some room for interpretation  (see for example Blanchard et al. Macroeconomics an European Perspective - the box about paradox of thrift).
Even when we go beyond mere accounting identity to the IS-LM AS-AD model which is currently the dominant model used to explain the macroeconomy the level of investment and effective demand will be determined first by peoples exogenously given expectations and preferences and the level of savings will be afterwards determined to match this (see Romer's Advanced Macroeconomics for more complex treatment of IS-LM models).

A  side note: you should also note that precautionary savings (i.e. money households set aside to have some reserve just in case) will still normally be transformed into investment provided it is held in some account even if it is at normal deposit account even though you as an account holder might never know about it. The above still applies though - I am just mentioning this because from reading your Q I thought you might be having this misconception.


Why would oil suppliers choose a lower priced contract? The West Texas Intermediate (WTI) futures contract has ranged from \$6 to \$20 in the last 48 hours. The May Shanghai International futures contract is 205 Yuan (CNY).  At 7 CNY per USD, that comes out to about \$29 per barrel, which is higher than the WTI futures contract.

In this case, why would a supplier choose a USD-denominated contract over a CNY-denominated contract (assuming they would)?

This is because for the price comparison it is not relevant what the exchange rate is now but what it will be at the time of delivery. The difference between these corresponds to different expectations of what the USD-Yuan exchange rate will be in the future.

For example consider oil supplier that is incorporated in the US and eventially needs to convert the money to USD to pay its employees/dividends/taxes. Moreover, lets suppose that the future contract specifies that the 1 barrel of oil has to be delivered at the end of next month at the 205 yuan. Well if during the month the exchange rate between USD and yuan changes to 1\$ = 15 yuan the 205 yuan you are going to receive next month are now worth only 13.66\$. Hence in such scenario you would be worse off if you would make the future to be denominated in yuan as opposed to USD (assuming \$20 price). Due to the law of one price the two futures should be priced equivalently which implies that people think that USD will most likely become stronger at the time of delivery relative to yuan.


Examples of firms having private information about negative event as the title says, I am searching for examples where a firm incurs a negative event, for instance, a stockout, a supply chain glitch or investments that went wrong. In the best case the firm was in the aftermath under financial distress or even had to file for bankruptcy as a consequence of that initially privately known event.

If you have a link to an example or just remember firm names, it would be a great help.

Best wishes
Paul

Banks that were not bailed out in the 2008 recession and went insolvent i.e. Washington Mutual, IndyMac, Franklin Bank, First National Bank of Nevada e.t.c. You could also look into firms that were sanctioned by the Securities and Exchange Commission (SEC). I do not know the names of the top of my head but a simple google search should suffice.


Barro 1977: Main Message I used to read Barro 1977 as

(1)

  Prices not moving in a long-term contract is not sufficient for these prices to be suboptimal. That is, there can be an optimal pricing sequence in a long-term contract in which prices do not change (for example, insurance reasons)

However, many papers these days (for example, Hall 2005) cite that paper as

(2)

  Price rigidity that would terminate a contract is sub-optimal and should be subject of renegotiation, if the project yields a surplus.

Both quotes my own words.

This is a rather historical question, but when did the interpretation switch from (1) to (2)? Was (2) implied all the time, and I just didn't get it immediately from reading the paper? Or was it an implied corollary that the profession came to agree about later on?

Hall (2005) mentions Barro's paper twice, but the first one in p. 51 is in the introduction and in order to alert the reader on what to expect. The essential dialogue between the two papers is in p. 56, where, Hall, after presenting his model and its workings, writes:

  "The earlier work implied inefficient outcomes, especially the loss of
  a job under conditions where both worker and employer could have been
  better off with a wage adjustment. The wage norm I consider interferes
  neither with the formation of efficient matches once the parties are
  in touch with one another nor with the preservation of jobs with
  positive surplus. Inefficient separations cannot occur. As a result,
  the model provides a full answer to the indictment of sticky wage
  models in Barro (1977) for invoking unexplained inefficiencies in
  economic arrangements."

In p. 64 moreover Hall writes

  "Stickiness is plausible, because it occurs only within the range
  where the wage does not block efficient bargains from being struck and
  maintained."

From this second quote, one could indeed indirectly validate the OP's second quote - that in order to provide a rationale for wage stickiness, we should restrain ourselves to cases and models where wage stickiness, in order to arise does not require blatant inefficiency of the contracting parties (because, after all, "blatant inefficiency" can explain everything).

The important remark here is that not all sticky-wage outcomes are necessarily inefficient.

But this essentially concurs with Barro's (1977) approach: Barro criticizes specific sticky-wage models where contracts have provisions only on the wage and not on the level of employment (or they have arbitrary such). Barro shows that not providing for employment determination may create dead-wight losses for both parties. On the other hand, providing an optimal rule for employment determination (optimal in the sense of "maximizing the pie", as he writes, available to employers and workers), would eliminate this dead-weight losses, and then, the issue of wage determination is to be considered, which may very well imply fixed nominal wages.
pp 311-312:

  "Given this form of employment rule, which maximizes the total pie
  available to firms and workers, one can then consider optimal (and
  competitive) payment arrangements that would determine the split of
  the pie. For example, it may be optimal for firms to perform the
  insurance function of guaranteeing to the workers, ex ante, a fixed
  (nominal or real) wage or income. In this case long-term contracting
  may account for ‘rigid‘ wages, and may also explain the apparent
  non-wage rationing of jobs."

So, I don't see any change in the interpretation of Barro's paper. Both papers seem to accept that it may be the case that sticky wages arise from optimal, efficient behavior. Barro criticized sticky-wage models available then for not modeling such an efficient way to obtain the stickiness. Hall's accepts Barro's critique on past sticky-wage models, and creates a model where indeed, fixed wages can be a feature of an efficient equilibrium, something that Barro also considers it possible, as the above quote shows.


Do standard definitions of substitute goods and complementary goods assume the Law of Demand? It seems to me that they do. Suppose $x$ is a Giffen good (that is, it violates the law of demand). Then when $p_x$ increases, the quantity of $x$ demanded increases. Suppose also that this increase of $p_x$ decreases the demand for $y$. Now, the standard definition for complements suggests that $x$ and $y$ are complements because the demand for $y$ decreased when $p_x$ increased. I would argue, however, that they are, in fact, better thought of as substitutes as the change in $p_x$ leads to the quantity demanded of $x$ increasing as the demand for $y$ decreases, i.e., the consumer is substituting from $y$ to $x$.

By "standard definitions" of substitutes and complements, I'm referring to:

$x$ and $y$ are substitutes if demand for $y$ increases when $p_x$ increases.
$x$ and $y$ are complements if demand for $y$ decreases when $p_x$ increases.

Is there an alternative definition out there that is robust to Giffen goods?

A quick response is that if the law of demand is violated, then the standard definition for substitutes and complements may or may not apply.

  Consider buying fast food burgers as your only choice of meal. When the price of the meal drops, you might want to consume something healthier like a bowl of salads. You consume less fast food and may increase consumption of, say, broccoli. Then, this is your example. $\frac{\partial X_F}{\partial P_F}>0$. But, $\frac{\partial X_B}{\partial P_F}<0$ where P and X are price and quantity and subscripts F and B represent Fast Food and Broccoli respectively.

Consider another example:

  Consider buying a game CD for Xbox One that is a special and limited edition. As marketing strategy, the manufacturer emails you there are only few left and price has increased 5%. You are determined to get the game now for one collection purpose and another for actual game use. But then, you were gonna get a limited edition version of wireless controller to enhance your gaming experience. It is reasonable to consider they are complements. But because you decided to buy two CDs, you buy no wireless controller. In this example, we still have $\frac{\partial X_L}{\partial P_L}>0$. But, $\frac{\partial X_C}{\partial P_L}<0$ where P and X are price and quantity and subscripts L and C represent the limited game cd and wireless controller respectively.

Could you still argue the limited special edition CD is a substitute for the wireless controller? Maybe. But notice you still desire the wireless controller given it is wireless and limited edition. One of the reasons why you forgo the chance to buy this controller is you are effectively poorer than before. And this is an important distinction to make, because the decrease in the quantity of the controller may be from the direct impact of the increase in the price of the game CD but also the induced effect through your wealth (i.e. thinner wallet).

If you want to investigate the true relationship between two goods, you have to take both wealth and price effects into account on top of the given information, say whether the good is Giffen or inferior or both or something else.

Hope this helps.


Is Price Level equivalent to Inflation when looking at AD/AS and Phillips Curve graphs? Fairly straight forward, Can I assume that Price Level and Inflation are interchangeable when looking at these graphs together?

Generally, are they equivalent in Macroeconomics?

Snoram is correct. Price level is a just that, the relative level of prices. Inflation/deflation is the act of moving up/down price levels. The inflation rate is the difference in price levels from one time period to another.

I.E. Year 1: Price level = 100 |  Year 2: Price level =105.

There was inflation in the economy (because price level increased). The inflation rate was 5%.

Another example:

I.E. Year 1: Price level = 177

In this example we do NOT know if the economy is experiencing inflation or deflation becuase we only have a single point in time and thus cannot determine the rate or direction of change.


Are symmetric equilibria monotone? Assume a two player symmetric game is given by $n\times n$ payoff matrix $A$ for the row player (and $A^t$ for the column player).

Let $B$ be a matrix such that $\forall i,j\in [n]:B_{i, j}\geq A_{i,j}$.

Assume $a$ is a symmetric equilibrium in $A$, $b$ is a symmetric equilibrium in $B$ and that $a$ and $b$ has the same support.

Does it mean player's payoff under $a$ (playing matrix $A$) can not be larger than the payoff of playing $b$ in game $B$?

Formulating the claim in linear algebra:

Let $A,B\in [0,1]^{n\times n}$ such that $\forall i,j\in [n]:B_{i, j}\geq A_{i,j}$.

Denote by $\Delta $ the set of probability distributions over $[n]$.

Let $a,b\in \Delta$ be two distribution vectors.

Does

$\forall x\in \Delta: x^tAa\leq a^tAa \ \ $ (i.e. $a$ is an equilibrium for $A$)
$\forall x\in \Delta: x^tBb\leq b^tBb \ \ \ $ (i.e. $b$ is an equilibrium for $B$)
$\forall i\in [n]: a_i>0 \iff b_i>0  \ \ $ ($a,b$ have the same support)

Imply
$$a^tAa\leq b^tBb?$$

If not, does the answer change if $A,B$ are symmetric?

Notice that without the support condition, the claim is false, for example-

$A=
 \left( \begin{array}{ccc}
1 & 0 \\
0 & 0.1 \\
\end{array} \right) $
$B=
 \left( \begin{array}{ccc}
1 & 0 \\
0 & 0.5 \\
\end{array} \right) $

$a=
 \left( \begin{array}{ccc}
1 \\
0  \\
\end{array} \right) $
$b=
 \left( \begin{array}{ccc}
0 \\
1  \\
\end{array} \right) $

For a simple counterexample let
$$
A = B = \left( \begin{array}{cc}
1 & 0 \\
1 & 0 \end{array} \right).
$$
In this game any strategy pair will constitute a Nash-equilibrium. Let
$$
a^t = \left(\frac{2}{3}, \ \frac{1}{3} \right), b^t = \left(\frac{1}{3}, \ \frac{2}{3} \right).
$$
Then the expected payoffs are larger in the symmetric equilibrium associated with $a$.

If you wish for $B$ to be strictly larger than $A$ you can easily modify this example, simply multiply all of $B$'s elements with a number larger than 1 but smaller than 2.

A counterexample where neither $A$ nor $B$ are singular:
$$
A = \left( \begin{array}{cc}
4 & 0 \\
6 & -4 \end{array} \right), \
B = \left( \begin{array}{cc}
4 & 1 \\
6 & 0 \end{array} \right)
$$
$$
a^t = \left(\frac{2}{3}, \ \frac{1}{3} \right), b^t = \left(\frac{1}{3}, \ \frac{2}{3} \right).
$$
$$
A \cdot a = \left( \begin{array}{c}
\frac{8}{3}  \\
\frac{8}{3}  \end{array} \right) >
\left( \begin{array}{c}
2  \\
2  \end{array} \right) = B \cdot b
$$


Does quasi-concave utility function imply convex indifference curve? It is well-known that convex indifference curve (i.e. the function is convex)/ preference would imply quasi-concave utility function. But does quasi-concave utility function imply convex indifference curve?

It seems that this answer give a brief sketch of the proof, but how can I show it in a more formal way?

Does quasi-concave utility function imply convex indifference curve?

No that is not true. Consider $u(x, y) = -x^2 - y^2$ defined on $\mathbb{R}^2_+$. Since $u$ is concave it is quasiconcave. Observing the graph of the indifference curves, we see that ICs of $u$ are not "convex".


Present Value at time 0 Land is an indestructible capital asset that offers a perpetual revenue flow. You own a piece of land that returns $20,000 per year forever. The relevant real interest rate to consider is 4%. What is the present value of this land at time 0?I need to use integration here

If you can get 4% annual returns elsewhere (relevant interest rate), then the asset returning 20,000 per year is worth 20,000 / 0.04 or 500,000.

In other words, 20,000 is 4% of the asset's present value and 500,000 is 100% if its present value.


Are there any economic reasons that could justify a higher tax rate on housing repairs than on construction of new houses? In the UK, a builder constructing a new home need not add tax to the price charged, but a builder undertaking repairs or renovations to an existing home must add value added tax (VAT, currently 20%).  (There are some exceptions but that's the general rule - details can be found in HMRC Notice 708).

Question: Are there any economic reasons that could justify a higher tax rate on repairs and renovations than on new construction?  I am interested in general economic arguments, whether applicable to the UK or not.

A possible argument for not taxing construction of new homes (even if most goods and services are subject to VAT) is that VAT should be regarded as a tax on consumption, and should instead be charged on the consumption of housing services (Barker K (2014) Housing: Where's the Plan? p 64). That presumably means that, for owner-occupiers, the tax authorities should determine the value of the housing services they consume each year and charge VAT on that.  However, even this argument does not seem to justify the differential taxation of new construction, since the same argument could be applied to renovations and repairs, implying that what is taxed should be any resulting increase in the value of housing services.

Addendum 14/9/2017: I've slightly changed the wording so that it invites answers on either side, either yes there are reasons or no there are not.

If I'd have to summarize the proposed explanation that unfolds in the lines that follow in a few words, I would say that, the economic reasons behind a high tax rate on repairs are related to the effectiveness of revenue gathering and are also about providing the proper set of incentives to private economic agents.

Governments tax in order to finance spending, according to textbooks. It would seem rather trivial to assume that, like all rational agents that populate textbooks, it, too, pursues its ends in the most efficient way (in a traditional means-ends kind of calculation).

In the case of taxation, it also seems trivial to assume that the government will choose to impose only those taxes that are expected to produce the greater amount of revenue with the least push-back from the economy. It is common ground in neoclassical economics that taxes distort economic outcomes.

Therefore it follows naturally that taxing would be more productive (in terms of raising revenue) when applied on abundant (or relatively abundant-no free lunches, remember?) tax bases. Also, it seems that  it would be more probable for a government, to target consumption spending rather than capital expenditures. In that way, it would avoid distorting incentives (by taxing capital income, for example).

Having set the stage thus, what needs to follow is an explanation of how exactly housing repairs and new houses construction fit in the so neatly constructed frame.

When a house owner-or a house tenant, for that matter-need to fix a leaky roof, they forgo a portion of their income-lets assume that it's 'income' and not 'wealth', for the sake of simplicity-for the purchase of repair services and relevant commodities. The amount of money that is extinguished, will provide the government coffers with 20% (as per example) revenue.

Consider now what will happen in the case where there are a lot of leaky roofs. It will come as no surprise that there will be a lot of  repairing going on and as a consequence, there will be comparable a lot 20%'s of those expenditures going into the government's coffers.

Therefore, it seems plausible, that when the stock of houses is old and in need of repairs, taxing the amount spent on repairs seems like an effective way to pile up revenue.

On the other hand, the case is a bit different if we assume that instead of many house owners there are some real estate firms that own and distribute housing services in a country or a region.

In this case, under the assumption of "leaky roofs" it is not clear before-hand if it is in their interest to expend a considerable sum of money on repairs. Especially, when spending this much would also be burdened with the excessive tax rate. Perhaps, it is in their interest to build rather than renovate.

When the government chooses to incentivize private agents like that, it seems probable to assume it expects that, the expenditure on new buildings will create such a multiplier effect in the economy, that will-hopefully-overcompensate for the loss of revenue from the other options that got dis-incentivized ('repairs'). Also, opting for building new houses increases the stock of housing in the economy, which is another way of saying that the (residential) capital stock increases.

Therefore, it would appear that, when the government selects a high tax rate on housing repair services-as compared with the tax burden of new buildings-it is effectively 1. demonstrating its urgent need for cash and it is either acknowledging that 2. the residential housing capital stock is in dire need of repairs (derelict capital stock) or that it does not expect 3. the real estate developers to actually invest in new housing that would, in turn, invigorate the economy and create new sources of tax revenue.


What would happen if someones money would disappear when they die So suppose that when anyone died all their net worth would be liquidized and the money would be removed from circulation.

how would this affect the economy? I know this question is a bit broad, but In general, what changes would occur?

Oddly enough, this is a topic that economists have covered pretty thoroughly!

Life cycle models (more info) are a model of consumption generally attributed to Franco Modigliani. These models describe how individuals consume over their lifespan.

While more advanced versions of these models, like overlapping generations models or bequeathal models, incorporate people passing resources onto their children, in the simplest versions people only worry about themselves. In effect, this gives them a goal of using up all their resources at the same time they die, in an attempt to smooth their consumption over their lifespan.

Based on extrapolation from those models, and the fact that the no-bequeathal condition in those models isn't the main thing making them unrealistic, probably not a whole lot changes!

The biggest change you'd see if this were the case is that people would work harder to consumption smooth so that they wouldn't have anything left over. Or they'd save just enough to account for the uncertainty of their lifespan.

You'd probably end up with people falling into destitution when they live longer than expected (or more people doing so than already do). But people already undersave for retirement, so this would only matter for the rich. You might get more support for elderly-care programs so people don't have to save as much with the potential for it to be erased.

You'd also see people who amass great fortunes spending way more of it and hoarding less (or just giving it to their kids earlier), basically the same predictions you get from big estate taxes, as this is effectively just a 100% estate tax.

One change is that occasionally you'd get a super rich person dying unexpectedly. This would end up being a negative money supply shock, which could have negative macroeconomic consequences, although what would likely happen is that the relevant central bank would be prepared to print more money to replace it if necessary. This would reduce inequality very slightly.

None of those are particularly exciting predictions, but that's because this is a pretty easy thing to get around by just shifting how you spend your money. There might be some interesting contract-theoretic implications with the fact that wills are no longer a thing. No waiting for the rich person to die to figure out how they're going to divvy up their stuff; it has to be given away ahead of time.


What happens to Fed's balance sheet when its asset shrink in value? What happens to Fed's balance sheet when its asset shrink in value? I noticed that Fed's balance sheet is special because I do not see any O.E. category (correct me if I am wrong). Suppsoe Fed's subprime MBS shrink in vlaue, its asset is decreased, but its liability doesn't (correct me if I am wrong), so it has an inbalance between A and L. If no O.E. is there, how can this be?

Also, Prof. Robert Shiller's "The Subprime Solution" says "if losses on collateral [during the crisis] mean that there are not enough funds to cover the defaulted loans, this will be reflected by the Fed paying less to the federal government, hence ultimately higher taxes for individuals." What does Prof. Shiller mean when he says not enough funds to cover the the defaulted loans and what does he mean by funds? What funds exactly? I mean, Fed has the ability to create reserve so how can there be not enough funds? One last question is why is the Fed paying the federal governemnt? I have never heard of Fed needing to pay the governemnt, shouldn't it be the governemnt pay the Fed due to the marturing of the T-bills and etc?

When the Fed issues say 100k in liabilities (paper dollars) to buy 100k in assets (t-bills), then they will at the end of the year take their revenue from their assets, subtract their expenses and remit the profits to congress.  This is an obscure process but it does exist.  If you see a congressional budget, you'll see an item marked as miscellaneous revenue...this is a portion of if that.  Now they do not remit as much as they should but that is another story.

If the Fed had to write off say 50k in bad debt, then that would count against their income for their year (and mean they earned 50k less).  The 50k would actually be debited away from equity and not liabilities.

The Fed (that I know of), does not issue money directly to itself nor the treasury.  It can create money to buy investments...and then spend the profits from investments on their own expenses.  It can also sell equities for a profit (rarely done) to boost their equity.

A good question is what would happen if the Fed had to write off more in assets than they had in equity.  I doubt they would shrink the monetary base to balance the books, but instead would fabricate an asset to keep the illusion going (like say a 'good will from the treasury').


Where can I look up a companies Herfindahl index? Where can I find Herfindahl indexes on companies (current or past)? Are there any published lists put out by a research institution?

HHI index cannot by definition be on companies. It is the squared sum of market shares of all the companies in a country. So, if you are looking for companies' market shares, you should look at each country individually.

But if you want HHI index on countries (which is a correct way of framing the question) then you can use this WorldBank data: https://tcdata360.worldbank.org/indicators/hh.mkt


Why would a rise in the discount rate stop foreign gold drain and make banks fail? I am reading "Capitalism and Freedom" by Milton Friedman. In Chapter 3, "The control of Money", Dr. Friedman explains how the Fed exacerbated the Great Depression of the 1930s. In particular:

  In September 1931, Britain went off the gold standard. This act was
  preceded and followed by gold withdrawals from the United States.
  Although gold had been flowing into the United States in the prior two
  years, and the U.S. gold stock and the Federal Reserve gold reserve
  ratio were at an all time high, the Reserve System reacted vigorously
  and promptly to the external drain as it had not to the previous
  internal drain. It did so in a manner that was certain to intensify
  the internal financial difficulties. After more than two years of
  severe economic contraction, the System raised the discount rate—the
  rate of interest at which it stood ready to lend to member banks—more
  sharply than it has within so brief a period in its whole history
  before or since. The measure arrested the gold drain. It was also
  accompanied by a spectacular increase in bank failures and runs on
  banks. In the six months from August 1931 through January 1932, roughly one out of ten banks in existence suspended operations and total deposits in commercial banks fell by 15 per cent.

My questions are:

Why would an increase in the discount rate arrest gold withdrawal by foreign individuals?
Why would an increase in the discount rate decrease the amount of bank deposits made by commercial banks?
Why would an increase in the discount rate make commercial banks fail?

An increase in the discount rate increases the cost of borrowing for commercial banks.  Their normal response would be to

(a) Offer higher interest rates to depositors to replace loans from the Reserve System, and

(b) Increase commercial interest rates on the loans they offer to pass on their higher costs to customers.

This makes it more attractive for individuals (including foreign ones) to deposit gold or pay back loans, together "arrest[ing] withdrawal".

I'm not sure it would and couldn't find this implied in the text.
Because their cost of borrowing has gone up sharply.  If they can't get rid of this cost by calling in loans or attracting savings, or offset it with profits, then they'll go under.  And if they quickly pass on higher interest rates to borrowing customers, this is likely to lead to bankruptcies and foreclosures, so they have to write off loans, and go under.


Sample weights in Stata: fweight vs. pweight I'm working with IPUMS ACS and Census data in Stata.  I'm interested in learning about income distributions and variability for specific subpopulations defined by education level, occupation, race and sex.

The survey data has probability weights, but I want to use commands that don't accept probability weights.  They will accept frequency weights, though.

I want to estimate:
Kernel density distribution
Mean
Coefficient of Variation
Standard Deviation
Percentiles

Can I just use frequency weights instead of probability weights?  These seem to give me accurate point estimates for the mean, but standard errors that are too small.

Will that throw off the kernel density, standard deviation, and coefficient of variation?

mean command with pweight gives you mean and sd estimates, which in turn gives you estimate of the coefficient of variation.

pctile also takes pweight. It will generate percentiles.

kdensity only gives point estimates, not confidence intervals of the density estimates, so I think using fweight instead of pweight is fine. But I'm not certain about this.

Alternatively, svy: commands may make your life easier when working with survey data. See here for a quick intro.

Also, think through whether you want to describe your sample, or to make inference about the population. See here for an example. An relevant quote from the link:

  It was intentional that summarize does not allow pweights. summarize’s purpose, as I see it, is to provide descriptive statistics for the sample, not to provide inferential statistics for the population. By this criterion, I argue that pweights do not belong here since pweights are used to provide estimates of the population parameter mu.


What does it mean when capital is immobile as opposed to having full mobility? The economist Rudolf Hilferding refers to the immobility of capital to be able to respond to market signals. What does he mean by this and why is capital immobile?

Capital Mobility is usually defined, simply,  as the ability to move Capital out of one asset into another.

If a car manufacturing firm (Carmo) is deeply invested in Honda Engines and has built their production line and engineering team around that engine. Their capital is heavily invested in assets, labor and tech related to Honda.

Now let's say tomorrow, Honda has a billion recalls on their entire line due to some severe engineering flaw. Carmo would like to switch to Toyota engines as their somewhat interchangeable with Honda Engines but this would require heavy asset replacement. Carmo's ability to respond to market preferences is hindered by the cost of replacing their asset bucket.

In summary, Capital Mobility refers to firm's capability in transferring capital from asset to asset to produce goods demanded by consumers.


Mathematical analysis of an economic model - stuck in calculations I'm not sure if it's more economic than mathematical question but it's about analyzing a model from economics so I'd rather ask it here.

There's a model with two goods, 1 and 2. The first one has both consumer demand ($D_1(P_1)$) and the government demand ($G$, the variable is predefined externally). The second one has only $D_2(P_2)$.

The supply functions for both goods are: $Q^s_{1,2}=S(P_1,P_2)$ (some quantity of good 2 is used in good 1 production and vice versa) The supply quantity of good 1 increases when its own price $P_1$ increases but decreases when there's an increase in $P_2$ (as the costs increase). Also own effects dominate, so $\frac {\partial S_1}{\partial P_1} > |\frac {\partial S_1}{\partial P_2}|$ in absolute terms. The same is true for $S_2$. Again, I'll write out all the equations below for more clarity:

$$Q^d_1 = D_1(P_1)+G$$
$$Q^d_2 = D_2(P_2)$$
$$Q^s_1 = S^1(P_1, P_2)$$
$$Q^s_2 = S^2(P_1, P_2)$$

Where I got stuck is in calculation of $\frac {\partial Q}{\partial G}$ for $Q_1, Q_2$ (the change in $Q_1$ or $Q_2$ after a change in G). The only thing that comes to my mind is:

$$\frac {\partial D_1}{\partial P_1}*\frac {dP_1}{dG} + 1 = \frac {\partial S^1}{\partial P_1}*\frac {dP_1}{dG} + \frac {\partial S^1}{\partial P_2}*\frac {dP_2}{dG}$$ for $Q_1$, but how to calculate the $\frac {\partial Q_1}{\partial G}$ from here?

There exist implicit assumptions in the set up that exclude various cross-price effects on the demand side, related to business behavior as well as to consumer behavior. Accepting the set up (and assuming downward-sloping demand and upward-sloping supply), the old-fashioned verbal treatment goes as follows:

An increase in $G$ will move the demand schedule $Q_1^d$ outwards, in the $\{Q_1, P_1\}$ space. This will tend to bring a new equilibrium for good 1, at a higher price $P_1$, and a higher quantity $Q_1$.

A higher $P_1$ increases costs for the supply of good $2$, and so it will shift upwards the supply curve for good 2 in the $\{Q_2, P_2\}$ space, while leaving the demand schedule for good $2$ unaffected. This will produce an equilibrium with higher $P_2$ and lower $Q_2$. A higher $P_2$ in turn will tend to shift upwards the supply curve for good 1 in the $\{Q_1, P_1\}$ space (again, because due to higher costs, lower quantity is supplied at any own price than previously).

This will tend to increase equilibrium $P_1$ even more, but it will tend to offset the increase in the new equilibrium $Q_1$.

So we have learned:
In market $2$, an increase in $G$ for good $1$ will lead to an equilibrium with higher $P_2$ and lower $Q_2$.
In market $1$ an increase in $G$ will lead to an equilibrium with higher $P_1$, but ambiguous effect on the new equilibrium $Q_1$.

I'll leave to the OP the task of mathematizing these results and see also whether the ambiguity can be resolved.


Where can I find economics theories to learn about? I'm a beginner to economics so I do not have much knowledge. However, I enjoy learning new economics theories. For now, I normally search for economics theories by looking at those that won nobel prize. Do you know where can I find a list of other economics (particularly microeconomics) theories that don't win the nobel prize?
Thank you very much.

You should read the fundamentals. I strongly suggest two textbooks for microeconomics:

Hal Varian - Microeconomics
Snyder, Nicholson - Microeconomic Theory

If your read any of the two and find it confusing, I suggest you go for:

Mankiw, Taylor - Economics


What does economics say about “starting from” pricing? I was wondering what economics says about what I would call the “starting from” pricing pattern in advertising. My first question would be whether there’s a more properly defined term for it.

It’s a common enough pattern: for example, an advertisement on a website that promises “Spend a weekend in Paris!” highlighting a price of “€150”, preceded by, in small type, the words “starting from”. When you click through, this price turns out to only apply to the weekend of Saturday December 25th, which most people would prefer to spend with their family and when many sights in the city are closed. Not to mention that it’s in winter time. Every other weekend the website offers and which is closer to what you had in mind when viewing the advertisement (Paris in summer!) is really priced at €300. (I just made up those numbers).

More generally stated, the pattern consists of advertising a highly desirable price for a seemingly desirable product, which really only applies to an undesirable version of the product, while offering a more desirable product at a less desirable price.

On one hand, I assume this pattern is effective in enticing people to check out the advertiser’s offerings. On the other hand, there’s an ineffectiveness in making people feel disappointed or outright deceived by the advertisement, possibly making them turn away.

I was wondering what economics says about this pattern. Some more specific subquestions:

Is there a more properly defined term for it?
Is there some more formal or experimental study on the relation between the “starting from” price point and the more realistic one and the effectiveness of such advertisements?
Is there some comparison on this advertising pattern and others, such as one in which both price points are stated? (like “Spend a weekend in Paris! Summer weekends at €300 or in winter as low as €150”)

Glenn Ellison's "A model of Add-On Pricing" seems closely related to this issue.

He addressed the question 'why don't firms compete more aggressively to attract consumers by lowering the initial price?' The answer that he offers is that doing so induces an adverse selection problem because lowering the advertised price will disproportionately attract "cheapskates" who will not pay the add-on price for a more expensive version of the goods.


Debt Held By The Public Following off the back of this question on debt-to-GDP vs. debt held by public-to-GDP - Difference between "Debt Held by the Public" and "Total Public Debt Outstanding"?:

So in principle, the difference is that with debt held by public-to-GDP, treasuries that are owned by government agencies are not included in the statistic, but could somebody please provide some more detail on this?

What sort of government agencies are we talking about?
Is the debt that they hold financed by the agencies allocation from the government budget?
Or is the debt that these agencies hold financed by more debt?
Which of the two statistics are generally considered to be more important?
What is the point in government agencies lending the government money?
What is the point in government agencies receiving interest payments from the government?

Some of these questions are probably quite broad, but hopefully someone can shed some more detail on this topic.

A down-to-earth explanation (including why) that I found: https://www.thebalance.com/who-owns-the-u-s-national-debt-3306124

FRED blogs are also helpful.


Does it matter if there's simultaneous determination between two dependent variables? For example, if I have an equation
$$
y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + u
$$

Where $x_1$ and $x_2$ are simultaneously determined, say

$$
x_1 = \gamma_0 + \gamma_1 x_2 + \gamma_2 z_1 + e
$$

$$
x_2 = \delta_0 + \delta_1 x_1 + \delta_2 z_2 + v
$$

Should I estimate using 2SLS or is this effect already contained when adding both variables to the main regression?

The concrete example I was thinking was for tax collection and drug cartels in Mexico:

$$
collection = \beta_0 + \beta_1 cartel_{memebers}+ \beta_2 GDP{per \  capita} + u
$$

Where the presence of drug cartels negatively affects GDP but cartels choose to settle on richer towns.

In your concrete example, I think 2SLS is something worth considering because the error term u (of $y$, i.e. of tax collection) is plausible in theory to be affected by presence of cartels in ways that make it more unreliable in reporting (e.g. via increased corruption). Of course you can/should test this endogeneity.


If a currency is pegged to another currency which collapses, what happens? If a currency X is pegged to another currency Y which collapses, what happens to currency X?

You need to define "pegged" and "collapses"...
Setting a fixed exchange rate is by controlling the local currency's amount of money

If the economy of currency X's owner goes bankrupt (a "collapse"), why would the Y currency owner continue to keep the attachment...?
Usually "pegging" currencies together is to a strong currency, like the US dollar

If the onwer of Y currency will keep attaching Y to X, it will create a local hyper inflation, and hurt its own economy...


Consumer Theory (Finding demand functions) Suppose that Sally’s preferences over baskets containing food (good $x$), and clothing (good $y$), are described by the utility function $u (x, y) = \sqrt{x} + y$. Sally’s corresponding marginal utilities are,
1
MU$_x=\frac{1}{2\sqrt{x}}$ and MU$_y=1$.
Use $p_x$ to represent the price of food, $p_y$ to represent the price of clothing, and $I$ to represent Sally’s income.

Question 1: Find Sally’s food demand function, and Sally’s clothing demand function. For the purposes of this question you should assume that $I/p_y \geq p_y/(4p_x)$.

I'm having a really tough time working out how to solve this problem and any kind of help would be much appreciated.

Given the data:

Utility function: $u(x, y) = \sqrt{x} + y$
Income: $I > 0$
Prices: $p_X > 0$ and $p_Y = 1$

Utility maximization problem is

\begin{eqnarray*} \max\limits_{x,y} & \ \ \sqrt{x} + y \\ \text{s.t.} & \ \ p_Xx+ y = I \\ \text{and} & \ \ x\geq 0, \ \ y\geq 0 \end{eqnarray*}
We can substitute $y = I - p_Xx$ in the objective and convert it into a single variable optimization problem:
\begin{eqnarray*} \max\limits_{x} & \ \ \sqrt{x} + I- p_Xx \\ \text{s.t.} & 0 \leq x \leq \frac{I}{p_X} \end{eqnarray*}
Differentiating the objective with respect to $x$ yields:
$\frac{1}{2\sqrt{x}} - p_X$
which is a decreasing function of $x$. The interpretation of the derivative is that it is the net marginal benefit curve of consuming X. As long as the value of the derivative is positive, it pays to spend more on X. Therefore, the utility maximizing choice will be to spend all the money on X if the net marginal benefit curve is still positive at $x = \frac{I}{p_X}$ i.e. $\frac{1}{2}\sqrt{\frac{p_X}{I}} - p_X>0$ holds, and the equilibrium choice will satisfy the property $\frac{1}{2\sqrt{x}} - p_X = 0$ otherwise.
So, the demand function for X is:
$\begin{eqnarray*} x(p_X, p_Y = 1, I) = \begin{cases} \frac{1}{4p_X^2} & \text{if } \frac{1}{2}\sqrt{\frac{p_X}{I}} - p_X\leq 0 \\ \frac{I}{p_X} & \text{if } \frac{1}{2}\sqrt{\frac{p_X}{I}} - p_X>0  \end{cases} \end{eqnarray*}$