texts:
Consider a typical event for which tickets are sold. The event only occurs once, and for simplicity we can assume that only one kind of ticket is provided, i.e, no VIP seats etc. $N$ tickets are available for purchase, and the $N$ highest bids win the tickets.

Does it exist any clever method for auctioning this type of good?

In a classical auction, the highest bid at any time is shown and participants can increase their bid to be the winning participant. But when auctioning this type of good that does not make any sense, since there will be multiple winning bids.

Should we perhaps display the currently lowest bid that is needed to win a ticket?

What if we think that it is desirable that all winners pay the same amount, how does this effect things?

I have tried to find existing research about this, but to no avail. Maybe there exist some other type of good with similar characteristics to tickets (oil/electricity?) that is auctioned in a similar way? Pointers to existing literature would be greatly appreciated.


texts: What topics are important to analyse a financial product?

texts:
When reading analysis papers of financial product, derivative or stock, tangible or not, I noticed that a lot of those papers seem to have similar structures.

This got me to the question if there exists some sort a basis structure to use when analysing a financial product. Or if there are some important topics we need to take in account, to have our analysis accepted by the Financial and Economic communities?

Please note that I'm referring to research/analysis that focuses on the financial product.

Edit - 2015/05/29: As commented: I'm interested in doing a theoretical analysis of, for example, a derivative that someone invented, this won't have any historical data.
Also, what is analysed when a central bank receives a proposal for a new product (i.e. new type of derivative)? What type of analysis is done? It's more in this sense, analysing a new formulation of a financial product that isn't on the market yet. How is this done?


texts: In Barro's (2009) Rare Disaster Model in AER: How to derive equation (5)

texts:
In Barro (2009) http://piketty.pse.ens.fr/files/Barro2009.pdf
My question is reference to equation #5, whereby Barro is deriving the reciprocal of the market value 1/v, and I am trying to derive this equation, and having trouble. In particular, without further specifications of distribution of v.
So far, I have:

But can't seem to arrive at the same result, without further information/assumptions on the distribution of the disasters.
Barro's Result for equation (5)

Any help would be greatly appreciated.


texts: Obtaining Wold Representation of VECM Model

texts: I'm attempting to replicate Beaudry & Portier (2006), and I'm having trouble coding up the long-run restrictions in the VECM model. Specifically I'm having a hard time finding a clear explanation of dealing with the error-correction term when getting MA($\infty$) representation. Any references would help! Most papers just assumes you know how to do it.


texts: Please help solve a bank's maximization problem

texts:
I want to solve following maximization problem:
$\underset{\{i_{t}^{l}(i),i_{t}^{d}(i),B_{t}^{l}(i),B_{t}^{d}(i),R_{t}(i)\}}{\max }
i_{t}^{r}R_{t}(i)+(i_{t}^{l}(i)-\mu ^{l})
B_{t}^{l}(i)-(i_{t}^{d}(i)
-\mu ^{d})B_{t}^{d}(i)-\Gamma(B^{l}_{t}(i), Z_{t}(i))$
where $i_{t}^{r}$ is reserve rate. $i_{t}^{l}(i)$ is bank $i$'s lending rate and $i_{t}^{d}(i)$ is bank $i$'s deposit rate.
$R_{t}(i)$, $Z_{t}(i)$, $B_{t}^{l}(i)$, and $B_{t}^{d}(i)$ are bank $i$'s reserves, profits, loans, and deposits, respectively. $\mu^{l}$ denote cost of issuing loans and $\mu^{d}$ denote benefit of receiving deposits. $\Gamma(B^{l}_{t}(i), Z_{t}(i))$ is an intermediation cost that is a function of $B^{l}_{t}(i), Z_{t}(i)$.
bank $i$ is faced with following nominal constraint.
\begin{equation}
B_{t}^{l}(i)\leq (\frac{1+i^{l}_{t}(i)}{1+i^{l}_{t}})^{-\varepsilon ^{l}}B_{t}^{l}
\end{equation}
\begin{equation}
  B_{t}^{d}(i)=\left\{
  \begin{array}{@{}ll@{}}
    (\frac{1+i_{t}^{d}(i)}{1+i^{d}_{t}})^{-\varepsilon ^{d}}B_{t}^{d} & \text{if}\ i^{d}_{t}(i)\geq 0 \\
    0 & \text{if}\ i^{d}_{t}(i)< 0
  \end{array}\right.
\end{equation}
\begin{equation}
(1+i_{t}^{d}(i))B^{d}_{t}(i)=(1+i_{t}^{l}(i)-\mu^{l})B^{l}_{t}(i)+(1+i_{t}^{r})R_{t}(i)+\mu^{d}B^{d}_{t}(i)
\end{equation}
\begin{equation}
R_{t}(i) \geq 0
\end{equation}
where (19) is a loan demand constraint and (20) is a deposit demand constraint. (21) is a zero net worth constraint. (22) is non-negative reserve requirement.
I want to verify whether the solutions are
\begin{equation}
1+i_{t}^{d}(i)=\frac{\varepsilon^{d}}{\varepsilon^{d}-1}(1+i_{t}^{r} +\mu^{d})
\end{equation}
\begin{equation}
1+i_{t}^{l}(i)=\frac{\varepsilon ^{l}}{\varepsilon ^{l}-1}(1+i_{t}^{r}+\mu
^{l})+\frac{\varepsilon ^{l}}{\varepsilon ^{l}-1}(1+i_{t}^{r})\Gamma
_{B_{t}^{l}(i)}
\end{equation}
Any help would really be appreciated! Thank you


texts: do you know where can I find data about the R&D expenditure of china from 1976 until 2020?


texts: Price Elasticity of Demand - elastic demand and impact of price reductions on total revenue

texts:
A question in relation to Price Elasticity of Demand.

My understanding is that when demand is elastic, a price reduction will increase
total revenue.

If the price of a product changes from \$100 to \$80 (20% decrease) and quantity demanded increases from 1000 to 1240 (24% increase), PED = 24/-20 = -1.2 (elastic).

Total revenue at the original price (\$100) and quantity demanded (1000) = \$100,000 Total Revenue after the price change is \$80 x 1240 = \$99,200 so total revenue has actually fallen

Can anyone reconcile this with the point that when demand is elastic a price reduction should increase total revenue?


texts: Question about Locally non-satiated preferences

texts:
If a consumer has locally non-satiated preferences, which of these 2 bundles is preferred and why?

Bundle A: (1,3)

Bundle B: (4,2)

This is what I've reasoned from my very limited understanding of LNS preferences.

The distance between the two bundles has to be less than the radius of a ball around one of the bundles for the other bundle to be preferred. A ball around bundle A can't have a radius larger than 1, thus bundle B isn't preferred. However, a ball around bundle B can have a radius large enough so that Bundle A is within the ball. So bundle A is preferred.

I'm very unsure of this reasoning and I'd appreciate it if anyone could correct me where I'm wrong or help improve my answer.


texts:
What's a singular model in economics? I've tried google, but I didn't find a definition...

In an article by Ingram et al (1994), they state:

  This linear model is singular because it predicts that the current value of consumption is an exact(non-stochastic) function of current output and lagged consumption.

Also, the paper says that any model (RBC and extensions) with a number of shocks smaller than the number of observable endogenous variables, has this particular behaviour. So, the models are not 'singular' as a dictionary definition.

From this I get that any stochastic model, which determines some observable endogenous variable to follown a non-stochastic path, then I can call it singular. Is this correct?

Also, does this definition have any relation to bifurcation? In ODE we have a 'bifurcation' of solutions, when

$\dot x = F(x,\mu)$, and at $\mu=\mu^*$, $DF(x,\mu^*)$ is singular, but non-singular at every other value of $\mu$. The equilibrium will depend continuously on $\mu$ and 'after' stability is lost, new stable equilibria will appear. (this lacks mathematical precision, but I think it suits the purpose of stating the intuition of bifurcation)

Any help would be appreciated.


texts: When does the Divine Equilibrium refinement coincide with that of Perfect Sequential Equilibrium?

texts: In signaling games, it seems that the Cho Kreps refinement (intuitive criterion) is the go to refinement for eliminating bad sequential equilibria. Divine equilibrium and perfect sequential equilibrium are also interesting refinements though. It seems more common that these are compared to Cho Kreps. Are there any interesting examples comparing the differences between perfect sequential and divine equilibrium? I've never seen the two concepts discussed together.


texts:
The Chamley-Judd result of zero optimal capital taxation says that 0 capital taxation are required in order to maximize welfare at the steady state.

The result is 30 years old. Still assuming that we only care about the steady state, what's the literature's take on that? How esoteric is it? Or in other words, are there simple extensions of the model that completely overcome the result?


texts: How to determine price per unit and quantity sold of product from financial statement

texts:
Situation

I hope I'm asking in the right place. I'm writing a paper on the application of quadratic functions in economics and intend to use the Total Revenue function as well as the Profit function for a specific product in order to derive conclusions and whatnot. For the moment, all that I require is the price (or demand) function of a given product in order to find the rest out. For the price function:

  p(Q) = m - nQ

in order to find out what m (the slope) is, I would require coordinates (Q, p). Q being the quantity demanded (or sold apparently according to this link) and p being the price per unit sold.

I require the price function in order to make the TR (Total Revenue function).

Attempted Solutions

I have looked online for methods to derive the number of units sold from financial statements made by the company but I find that:

I need the price per unit for this (that that I do not have)
financial statements pertain to all products sold by the company and
as such are an inaccurate representation of the price function for
that particular product

For the profit function which requires the cost function, I have managed to find the solution from the financial statement but once again point 2 still stands. I think that if I find a business that exclusively sells one product, I will manage to derive the second cost function from the financial statements but once again, I do not have a solution for the first one.

Question

I am really lost in regards to what I should do in order to obtain data that I can use to analyze and ultimately demonstrate the application of mathematics in economics (specifically two sets of price per unit and number of units sold). I really hope that someone can help me with these questions and provide not necessarily the aforementioned solution that I desire but any solution to the situation I am in.


texts: When does a high markup mean high productivity? Never?

texts:
I was reading this article in VoxEU, where the authors (one is a Professor of Economics at Harvard University) make the case that an increasing average mark-up has accounted for much of the late productivity growth, since it leads to an increasing allocative efficiency.

However, isn't this exactly the oposite of what one would want? It seems that they are somehow mixing up the possibility of high profits due to one would usually think of as high productivity, with high profits due to market imperfections... Also, it's also as if the authors would defend a higher 'productivity' but at a lower output, than a lower 'productivity' at a higher output.

Here's a quote from the text which I find baffling:

  «(...)this reallocation of market share from low- to high-mark-up
  firms has considerably improved the allocative efficiency of the US
  economy over the last 20 years. In fact, improvements in allocative
  efficiency account for about 50% of the cumulated growth in aggregate
  productivity during this period. This suggests that ‘true’
  technological productivity growth has been even slower than previously
  imagined.(...)A high average mark-up reduces output and depresses the
  demand for labour and capital, generating low aggregate employment and
  low aggregate investment. It reduces the aggregate labour and capital
  shares, and increases the aggregate profit share.»


texts:
If tastes are homothetic and identical, does this imply that the contract curve is the line connecting the lower left and upper right corners of the box?

My understanding: no, it does not. Consumers' indifference curves, though identical, could have the same slope along some line to the side of the line connecting the lower left and upper right corners of the box, e.g. in the case of steep indifference curves.

Is this correct?


texts: Negative Inflation, AS/AD framework, What Graph to use?

texts:
My macroeconomic homework contains the question below, and I'm not sure what graphs we're suppose to use to solve it. I believe I can answer the whole question using the IS-MP Diagram, but do I need another? Is the AS/AD question just referring to the changes in demand for funds when the new interest rate is applied in the IS-MP Diagram?

In the late 1990s and early 2000s, inflation was actually negative in Japan. I want you to consider a policy to achieve a higher inflation rate. Consider an economy that beings with output at potential and an inflation rate of ̅, so that the economy begins in steady state. A new chair of the central bank decides to raise the long-run inflation target to ̅2 (greater than the original ̅). Show how the economy responds over time using the AD/AS framework. Comment on your results.


texts: Literature on DSGE models featuring a financial sector

texts: I recently read a ECB primer on DSGE models featuring the financial sector and became interested in the field. I also started to read some of the earlier literature in that field (e.g. Gertler & Karadi, 2011) but was hoping to receive some hints on where this literature is currently evolving and if there are any more recent papers that have been widely recognized?


texts:
If country A has a free trade agreement with country B, and country B has a free trade agreement with country C, does that mean country A effectively has a free trade agreement with country C?

If the answer is “it depends what you mean by free trade”, what characteristics of the A-to-B agreement would be be conducive to it being “transitive” with the B-to-C agreement?

If A-to-B and B-to-C were perfectly “compatible” in this sense, could A ship goods directly to C or would they still have to go via B?


texts: Rosen's Diagonal Strict Concavity condition

texts:
Consider a game with $n$ players, with strategy space $S \subset \mathbb{R}$, where $S$ is bounded set, and player's $i$ payoff function  $\pi_i:S^n \rightarrow \mathbb{R}$.
Rosen's condition (J. B. Rosen. Existence and uniqueness of equilibrium points for concave n-person games. Econometrica, 33(3):520–534, 1965) for uniqueness of the Nash Equilibrium in n players game states that the  equlibrium will be unique when

payoff function $\pi_i(\textbf{s}) \; i \in N$  is concave in own strategy
There exists vector $\textbf{z}$ ($(\forall i \in N)(z_i \geq 0)\ \wedge (\exists i \in N) (z_i >0)$ such that function $\sigma(\mathbf{s}, \mathbf{z})=\sum_{i=1}^{n}z_i\pi_i({\textbf{s}})$ is diagonally strictly concave

$N$ denotes the set of players.

To define the concept of diagonal strict concavity, fist introduce 'pseudogradient' of function $\sigma$, defined with:
\begin{align}
g(\mathbf{s},\mathbf{z}) = \begin{pmatrix}
z_1\frac{\partial \pi_1(\mathbf{s})}{\partial s_1} \\
z_2\frac{\partial \pi_2(\mathbf{s})}{\partial s_2} \\
... \\
z_n\frac{\partial \pi_n(\mathbf{s})}{\partial s_n}%
\end{pmatrix}
\end{align}
Then, function $\sigma$ is said to be diagonally strictly dominant in $\mathbf{s} \in S$ for fixed $\mathbf{z} \geq 0$ if for every $\mathbf{s}^0, \mathbf{s}^1 \in S$ the following holds:
\begin{align}
(\mathbf{s}^1 - \mathbf{s}^0)'g(\mathbf{s}^{0}, \mathbf{z}) + (\mathbf{s}^0 - \mathbf{s}^1)'g(\mathbf{s}^{1}, \mathbf{z})>0
\end{align}

It is shown, in the paper I cite in the beginning, that a sufficient condition for $\sigma$ to be diagonally striclty concave is that matrix $\left[G(\mathbf{x}, \mathbf{z}) +G(\mathbf{x}, \mathbf{z})' \right]$ is negative defite for $\mathbf{s} \in S$, where $G(\mathbf{x}, \mathbf{z})$ is Jacobian of pseudogradient $g$ with respect to $\mathbf{s}$. I use ' to denote transpose of a matrix.
What is the intuition behind diagonal strict concavity condition?


texts: First-price symmetric auction with discrete value

texts:
I've been trying to work the following problem out but I can't quite seem to understand it, or the whole concept of first-place auctions. I don't understand how we get to the equilibrium.

The problem is the following: "Consider a first-price, sealed-bid auction in which a bidder’s valuation can take one of three values: 5, 7, and 10, occurring with probabilities 0.2, 0.5, and 0.3, respectively. There are two bidders, whose valuations are independently drawn by Nature. After each bidder learns her valuation, they simultaneously choose a bid that is required to be a positive integer. A bidder’s payoff is zero if she loses the auction and is her valuation minus her bid if she wins it. Determine whether it is a symmetric Bayes–Nash equilibrium for a bidder to bid 4 when her valuation is 5, 6 when her valuation is 7, and 9 when her valuation is 10."

In this case, we have discrete bids and discrete valuation, as well as different probabilities for each. Could someone help me out understand the problem?


texts: What is the difference between the discrete choice method and the generalised cost method in transport planning?

texts:
I have been using the generalised cost method in an agent based model. The generalised cost method enables each individual agent to make a decision on what mode of transport it will take given a range of options from A to B. The monetary and non-monetary aspects of the journey can be summated with different valuations of the non-monetary aspects dependent on the agent and the mode (waiting is weighted 2* travelling and so on).

Thus, the generalised cost function can be defined as:

g = f(a) + t(b)

Where

g = generalised cost
f = financial cost
t = time cost
a = Value attribution of financial cost (by socioeconomic group)
b = Value attribution of time cost (by socioeconomic group)

I have temporally dynamic time cost (t) values that has enabled me to display how congestion on the roads and dynamic timetables can result in different decisions being made for exactly the same journey but at different times.

I was intrigued by Kenneth Train's Discrete Choice Method work here.

Discrete choice models attempt to predict choices between two or more discrete alternatives. They statistically relate the choice made by each person to the attributes of the person and the output the probability of the agent making each choice in a set of alternatives.

I understand the outputs are different. The generalised cost method will result in the selection of the option with the lowest generalised cost. The Discrete choice method will result in an output of the probability per each choice.

What are the key differences between the methods?


texts: Probability of history occurring at time $t$

texts:
I am reading LS book "Recursive Macroeconomics Theory".

In this book, as well as in some online lecture notes on the Internet. They often denote, for example, $\pi_t(s^t)$ for probability that history $s^t$ happens at time $t$.

But I wonder, if we are mentioning $s^t$, it implies time is $t$. So, why don't we just make it simple by writing $\pi(s^t)$ instead?

Thank in advance for any help!


texts: Effect of a change in quality on price elasticity of demand

texts:
I am interested to know how one would expect a change in the quality of a product to affect its price elasticity of demand. Two example will illustrate my confusion:

Example 1

Suppose a producer is selling tap water at price P with quantity demanded Q. Let us call this good 'Beverage v1'. The producer changes the recipe; adding some grape juice and carbon dioxide to make Champagne. The producer continues to sell at price P but now with demand Q2>Q (in the short-run, which is probably not an equilibrium). Let us call this good 'Beverage v2'.

We would, I think, expect the price elasticity of demand for Beverage v2 to be lower than that of Beverage v1. The common intuition is that 'essential' goods have lower PEoD than 'luxury' goods.

Example 2

Now suppose a producer is selling a medicine ('Medicine v1') which treats the symptoms of an illness pretty well. It is the only medicine for this illness so patients must choose between going untreated (feeling pretty awful) and buying the drug, which makes them feel 50% better than going untreated. The medicine is sold at price P with quantity demanded Q. The producer then makes some changes and now the medicine makes patients feel 100% better. It is not quite a cure, as patients have to keep taking the medicine, but it is pretty close. Let us call this 'Medicine v2'. The producer continues to sell at price P but now with quantity demanded Q2>Q (in the short-run, which is probably not an equilibrium). Bear in mind that Medicine v1 is no longer available and that there are no other alternatives available either (except going untreated).

This seems to be similar to the beverage example above, but I feel as if the intuition is less clear in this case that PEoD for Medicine v2 would be higher than for Medicine v1. Is feeling 100% better more of a luxury than feeling 50% better? It is certainly better, but I am not certain that is therefore less essential. What do you think?


texts: How did the derivatives market 'collapse' in 2008?

texts:
I just watched the film 'The big short', and have been trying to think in context with the financial markets in 2008. I think the film does a great job of explaining how sub-prime mortgages came to be issued and sold by opportunists to investors who were blinded to their junk value.

One key thing that I feel though is brushed over though is what the market for derivatives on the mortgage industry looked like at that time, and how the eventual defaults on the mortgages caused this to 'collapse'. They claim that the derivatives market had grown to 20 times the size of the market itself. According to the film,

  if... the mortgage bonds were the kerosene soaked rags, then the 'synthetic CDOs' were the atomic bomb with the drunk president holding his finger over the button

but what did these derivatives look like? I understand how someone may invest in a mortgage, which is money lent that will have to be written off in case of default. But how did the actual defaults magnify in the event to hit investors twenty fold? What were people investing in on top of the mortgages themselves? And why did these objects all necessarily become junk when the mortgages themselves did?


texts: Implications of declining money velocity

texts:
In the United States, the velocity of both the M1 and M2 money supplies has been declining for over a decade.

The decline in the velocity of M1 could be explained by the shift away from cash to cards and online payments.

What are the causes and implications of the decline in the velocity of M2?

Does it signify that the money supply is growing faster than GDP? If so, is real GDP declining? Does it indicate some sort of lack of liquidity? How does this relate to interest rates?

Thanks!


texts: Can a complement good be free or have a fixed cost?

texts:
I was not around at this time but I know roads(existing for bikes) and gas(existing for tractors) were complements for cars.

I was looking at complements for computers and noticed the ARPANET could maybe be regarded as a complement because it appears it would increase a computers usefulness.  I'm trying to leave the history out of this but I figured an example would be helpful.

Can a complement good like the ARPANET have either a fixed cost or be free?


texts: Why does Burton Malkiel recommend investing in commodity companies instead of commodities?

texts:
Source: p 185 , ETFs for Canadians for Dummies (2013; by Russell Wild and Bryan Borzykowski).

  In a recent interview with the Journal of Indexes, famed investment guru
  Burton G. Malkiel, professor of economics at Princeton and author of A Random Walk Down Wall Street, had this to say about commodity investing:
  “I think [commodities] should be in every portfolio, but for individuals, my
  sense is that the way they should get them is through ensuring that they have
  in their portfolios companies that mine or manufacture the commodities.”

  He is not alone. Frustrated with the problems of commodity investing I’ve
  outlined in this chapter, and doubtful that commodity investing in the very
  long run will provide returns commensurate with the risk, many investment
  advisors of late have turned to Malkiel’s solution. The drawback is that
  stocks in commodity-producing companies are not going to show the
  same lack of correlation, or offer the same diversification power, as pure
  commodities do. Investing in commodities this way is a trade-off.

However, a Google search revealed this which rebuts Prof Malkiel's recommendation above.


texts: What is a supply side shock in macroeconomics?

texts:
I was hoping someone could clarify what exactly is meant when someone refers to a country as having undergone a 'supply-side shock' and generally speaking when one is evaluating the health or growth of an economy, what is meant by the supply side of the economy vs. the demand side of it? Which components of GDP are considered as which?

Despite a lot of googling, it has been pretty difficult to find answers to this as most results are either in a micro-context or fail to provide examples of these things as well as their consequences.


texts:
In the history, like Japan, in the World War II, they had a hand in the war, the root cause is the economic depression.

And in this century, some country use this method many times to remit the economic problem.

So, why war can remit the economic crisis, I just don't understand?


texts: What exactly is computational economics? For example, does certain software for calculating/predicting/visualizing cost of manufacture falls under computational economics?


texts: Why do prices go up when the central bank increases money supply?

texts:
From my understanding, when the money supply curve shifts to the right, interest rates go down, it follows that the price level decreases and the prices should go down?

Thanks in advance.


texts: Solving a LRE model in King-Watson form using alternative algorithms

texts:
I have a linear rational expectation model that is in the King-Watson form:

AE_{t}y{t+1} = By_{t} + C_{0}x_{t} + C_{1}x{t+1}  (1)

with the driving process

x_{t}     = Q \delta_{t}                          (2)
delta_{t} = \rho \delta_{t-1} + G \espilson_{t}   (3)

I have a fairly large system and would like to solve it using a different algorithm than the King-Watson one, such as the Anderson-Moore algorithm (but am completely open to anything fast). However, I have so far failed in implementing the KW in Anderson-Moore. Any ideas on (i) how to solve the problem using the Anderson-Moore algo, or (ii) a different algorithm that can be used?

Note, my system of equations in (1) is about 1000 lines.

Here is a toy example for parameterization

A  = [1,0,0,0;0,1,0,0;0,0,-1,-1;0,0,0,0];
B  = [0,0,1,0;0,0,0,1;0,0,-1.1,0;0,-0.7,0,1];
C  = [0,0;0,0;4,1;3,-2];
Q  = [1,0;0,1];
RHO= [0.9,0.1;0.05,0.2];
G  = [1,0;0,1];

which should yield

\Pi = [1,0,0,0; 0,1,0,0;0,1.225, -21.0857, 3.15714; 0, 0.7, -3, 2];
M   = [0,1.225, -21.0857, 3.15714; 0, 0.7, -3, 2; 0,0,0.9,0.1; 0,0,0.05,0.2];


texts: I am curious: what exactly are the problems caused by using representative sampling rather than random sampling whenever creating a subsample of large dataset for nonexperimental analysis. Further, how effective is propensity score matching whenever one wants to create balanced comparison groups for non-experimental analyses?


texts:
I have been hearing a lot about this metric in relation to rising fears of a Chinese financial crisis. I am wondering, what exactly does this mean? I am told it refers to the difference between current credit-to-GDP ratios and long-term trends but I don't fully understand what that would mean. What would be a nice little equation for it? I have looked at some charts and I am seeing that the US has a negative Credit-to-GDP gap, how can it be negative? I just want to know what the inputs into calculating that would be so I can understand for myself what these things signify.
Thanks.


texts: Which economic research articles or books use anthropological methods?

texts:
Most of the social sciences and even disciplines have a stable relationship with economics. And rightly so because our world is so interconnected. But there are certain fields which remained separated from this interdisciplinary connection.

One of them is anthropology. Reading on the web there isn't much work done by both researchers in collaboration. What are some examples in the literature of this? And which papers would have benefited from an interdisciplinary approach but didn't take the chance to do so?


texts:
I am very confused regarding the corporate income tax. Please explain me the following scenario:

"Teddy Bears Company" buys stocks of 1000 euro (VAT added). Then, in 1 month sells everything with 1500 euro and makes a profit of 500 euro.

Where comes the income tax? On the profit of 500 euros or on the income of 1500 euros?


texts:
Robinson Crusoe’s preferences over coconut consumption, C, and leisure, R, are represented by the utility function U(C, R) = CR. There are 48 hours available for Robinson to allocate between labor and leisure. If he works L hours, he will produce the square root of L of coconuts. He will choose to work.

The answer is 16 and I known this but confused to its working out. Can some give me a step by step?


texts: Specific question about some figures in national accounts

texts:
I have highlighted four highlighted numbers in the UN System of National Accounts (p. 31, Table 2.13). My question is: What are these numbers?

My guesses:

6 = Compensation paid by foreign firms to resident employees.
2 = Compensation paid by resident firms to foreign employees.
44 = Property income paid by foreigners to residents.
38 = Property income paid by residents to foreigners.

I'm sure the answer is somewhere in the document (700 pages and not exactly user friendly), but I can't find it.

When answering my question, please cite where in the document you found the answer.

Also, how is the number 1864 obtained from the numbers above?


texts: Applying real growth rate to nominal value

texts:
What happens if one applies a real GDP growth rate to a nominal GDP value? The result can't be a GDP figure in constant prices, since that would imply applying a real GDP growth rate to constant GDP figure.

Any thoughts?


texts: What does Sims' critique of economics models actually say?

texts:
I've been searching for answer, but I can't find a clear cut one. From what I understand it says that, in the realistic model there are no exogenous variables? Or does it say that there can be no clear cut identification of exogenous and endogenous variables?

Link: http://www.wifa.uni-leipzig.de/fileadmin/user_upload/iew-vwl/OEK-Lehre/tsa_winter2011/tsa01.pdf


texts: Can Linear Supply-Demand Equilibria Be Understood as a Feedback-Control Process?

texts:
I'm not an economist, but rather an applied mathematician working in control theory. I've recently been watching Berkeley's intro to econ course in a personal project to better understand economics and finance. The first few lectures are on linear supply-demand curves and how they create price equilibria.

To wit, suppose $\sigma(p)$ and $\delta(p)$ and the quantity supplied and demanded at price $p$ resp. Then the assumption of linearity implies

$$ \sigma(p) = S_\sigma p+\sigma_0,\ \ \delta(p) = -S_\delta p+\delta_0$$

(this is my notation). The numbers $S_{\sigma,\delta}$, $\delta_0,\sigma_0$ are presumed positive and correspond to the slope (what I believe is called "elasticity" in econ jargon) and the intercepts, which I've interpreted as the amount supplied and demanded at $p = 0$ (e.g. how much people are willing to supply or would demand if the good were free). Clearly we assume $p \geq 0$.

The equilibrium is met when supply and demand are equal--$\delta = \sigma$--and give the equilibrium price
$$
p_e = \frac{\delta_0-\sigma_0}{S_\delta+S_\sigma}.
$$

This much is trivial to a real economist.

Now to the interesting part:

Through the lecturer explaining how an out of equilibrium price eventually comes to equilibirium, I recognized the basic idea of feedback at work: the change in price is forced by the signed difference between supply and demand. I propose this is modeled by the equation

$$
\dot{p} = k(\delta-\sigma),
$$

or exactly a feedback control law ($P$-controller) with feedback gain $k$. Furthermore, since we assume the supply and demand curves are linear,   the entire equation is now a linear differential equation

$$
\dot{p} = k(\delta_0-\sigma_0)-k(S_\delta+S_\sigma)p.
$$

The equilibrium occurs when $\dot{p} = 0$ and is identical to that obtained using the graphical method.

But wait--there's more! Since we now have a differential equation, we can get a time-domain solution:
$$
p(t) = e^{-t/\tau}p_i+p_e(1-e^{-t/\tau})
$$
Here $p_i$ is the initial (out-of-equilibrium) price, $\tau = \frac{1}{k(S_\delta+S_\sigma)}$, and $p_e$ is the equilibrium price.

This implies that not only can we predict what equilibrium prices will be,  but we can also, subject to understanding $k$, predict the amount of time it will take to settle into the equilibrium. In fact, the form of this equation means that equilibrium is asmyptotic ($p_e = p(t= \infty)$) and percentages--63%, 86%, 95%, etc. for $t/\tau = 1,2,3,$ etc.--of equilibrium will be obtained. $t/\tau = 6$ is a good approximation of actual equilibrium (99.8%), so we gain the ability to state how long it will take for a price initially at $p_i$ to settle to $p_e$ (call this $t_e$, the "equilibirum time")

$$
t_e \approx \frac{6}{k(S_\delta+S_\sigma)}.
$$

Thoughts on $k$

So what is $k$ really? The short answer is I don't know. Mathematically it is a feedback gain, but that's not really so helpful.

It has the units of price/(quantity$\cdot$time), so I have pulled it into two factors $k = f_t/S_X$. I suppose $f_t$ to be the frequency at which transactions are made of the good. It makes sense that a less often traded good will reach equilibrium more slowly than a more often traded good. $S_X$ has the units of $S_{\delta,\sigma}$ but I have no good interpretation.  I've considered that we might have $S_X \approx S_\delta + S_\sigma$ to produce $\tau \approx 1/f_t$ but haven't got much farther than this.

The Bottom Line

I think I've found an interesting interpretation of supply-demand dynamics in terms of control theoretic principles, namely proportional feedback. Unfortunately I am so unknowledgeable in econ that I'm unable to know whether or not this is a fruitful line of inquiry which I should pursue, or whether I have just reconstructed a longstanding theory.

Can anyone help provide some context?


texts: How is price elasticity determined in practice?

texts:
Price elasticity of demand and Price elasticity of supply are two of the most important concepts of microeconomics, but they're generally explained from a hypothetical standpoint, and little effort is given to explaining how they are measured, or how they fluctuate (specifically the scale of fluctuation, not the contributing causes).

Can anyone explain this, and/or point to studies that document the fluctuation of $PE_{d}$ and $PE_{s}$ over time?


texts: What does it mean if a economic model is internally consistent? What happens if it is not? Is it not closed anymore? Can it still be solved? Does it still have an equilibrium?


texts: Financial Economics and Corporate Finance

texts:
In pg 4 of Principles of Corporate finance (Allen et al, 2017), in the context of explaining financing decisions are less important that investment decisions, there is a line that says:

"Financial managers say that 'value comes mainly from the asset side of the balance sheet'"

What does this mean? Why asset side? Why not shareholders equity on balance sheet?
The text did use an example of Microsoft, where they point out that successful companies finance R&D by reinvesting existing cashflow.


texts: Does it matter if there's simultaneous determination between two dependent variables?

texts:
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.


texts: Articles about the economics of non-compete contracts

texts:
Today I read in a non-scientific article that Amazon requires some physical workers to sign non-compete agreements. I used to think that the idea behind allowing non-compete clauses in contracts is to protect a companies' intellectual property. The article mentions that non-competes may also serve to protect a company's investment in case it pays for the employee's education or training. Neither of these seems to fit this case.

What scientific articles (in fields of mathematical economics, such as Industrial Organization) describe models where allowing for non-compete clauses improves the situation of both the employer and the employee?


texts:
I am trying to understand the R&D model and how to calculate the growth rate of wage in this model.

There is no equation given, but it’s stated that : household income must equal total consumption. as income is total profit plus wage income, and the two are fixed in proportions, wages grow at the same rate as output $g_w=g_y$

I tried to write down the equation of this statement, however, I don‘t really think it’s right: $\pi+w= C_t$.

Can anyone help with the equation and it’s intuition?

Addition: the R&D model introduces final good producers that sell their good in a competitive market and intermediate goods producers that produce either a produced intermediate good or “ideas” that are sold to the final good producers and used to produce the final good. The intermediate good and “ideas” are substitutes.


texts: Why does the inflation not follow the money supply?

texts:
To my understanding classical economic theory tells us that inflation occurs when the money supply is increased faster than the economic growth.
Lately there has been a sharp rise in the rate of money supply, but GDP has not increased the last year:
M2 money supply and GDP for USA

However there has been no corresponding inflation (consumer price index) increase:
M2 money supply and CPI for USA

Why is this? Does the money accumulate somewhere, if so where?


texts: AGV mechanism and Individual rationality

texts:
I have the following question. I consider AGV mechanism which is as follows:
$u_i(x,\theta_i) = v_i(k,\theta_i) + t_i $ is an utility function where $x = (k,t_1,...,t_n)$ vector of alternatives. There are N agents. We choose $k^*$ such that $\sum v_i(k^*(\theta) ,\theta_i) \ge \sum v_i(k^*,\theta_i) $ and take
$$t_i(\theta) = E_{\tilde{\theta}_{-i}}\Big[ \sum_{i \neq j}v_j(k^*(\theta_i,\tilde{\theta}_{-i}),\tilde{\theta}_j)\Big] + h_i(\theta_{-i}) = \xi_i(\theta_i) + h_i(\theta_{-i}). $$
Also we define
$$h_i(\theta_{-i}) = - \frac{1}{N-1} \sum_{i\neq j}\xi_j(\theta_j)$$

Now I want to check whether is it true or not that this mechanism satisfies ex post individual rationality. There are some sources claiming that AGV mechanism violates ex post IR but satisfies ex ante IR.

Ex post IR is the following property:
Mechanism $\phi$ satisfies ex post IR iff $\forall \ \theta, \forall \ i $ we have: $v_i(k;\theta_i)+t_i\ge 0$.

So here we have:
$$v_i(k;\theta_i) + \xi_i(\theta_i) \ge \frac{1}{N-1}\sum_{j\neq i} \xi_j(\theta_j)$$
In general there are now reasons for this inequality to hold. But what might be an example that this inequality is violated?


texts: Are convex preferences needed for the first welfare theorem? It would see so. For example, we could have a situation in which B's indifference curve is non-convex, such that, at the equilibrium X, it crosses A's indifference curve. Therefore, a movement to the left (if B's consumption is measured from the bottom left) will make A better off, and B no worse-off. Therefore, X is an equilibrium which is not pareto efficient.


texts: For the other sciences it´s easy to point to the most important equations that ground the discipline. If I want to explain Economics to a physicist say, what are considered to be the most important equations that underly the subject which I should introduce and attempt to explain?


texts:
I'm a total noob.  Please be kind.  :)

GDP is only calculated using "end products".  This seems terribly difficult to me.  For example, is a truck an end product or a method for production?  If I'm driving myself and my family around, then it seems like an end product.  But if I'm using it on my farm, then it doesn't.

How about a computer?  If I'm using it to play video games, then it seems like an end product.  But if it's used in a hospital to manage medical records, then it seems like an intermediate product.

How are these multiple uses taken into account with GDP?

I want some metric that is the total amount of goods produced (regardless of whether or not the good produced is an end product or not).  What is the best metric for this?

Thank you!


texts: Coefficient omitted due to time fixed effect and multi-collinearity

texts:
I am working on a research paper (my first one) where I am dealing with company level unbalanced panel data. There are broadly two types of control variables in the study - a) firm level control variables (market cap, return on assets, cash holdings etc.) which varies for a firm cross-sectionally as well as in time and (b) macro variables (risk free rate, excess market return etc.) which do not vary cross-sectionally across firm level but vary only across the time. When I run the regression in STATA, I get an estimated coefficient of ‘0’ for macro-economic variables if I take the time and industry fixed effect. The stata provides the warning message that such variables are perfectly correlated with the fixed effects, hence cannot be estimated and provides ‘0’ coefficients for such variables. This serial correlation is understood because the values of these control variables will remain same for the time fixed effect dummy across all the firms.  Hence, when I remove the time fixed effects, then as expected this issue does not occur and I get the estimated coefficients.
Similar macro-economic variables are used in the other studies then the results always mention that the time fixed effects and cross-sectional fixed effects are being considered. I am not able to understand why these studies did not face the same issue that I am facing?
I have tried looking in books, forums etc but did not get any inputs on this. I think I am missing something conceptually, and not able to find the correct explanation. Please let me know if I can refer to something specific to resolve this.


texts: Economic concept where turning something down heightens emotional attachment

texts:
For example, say a person has turned down an offer for a competing position with another company. That person now has an increased sense of attachment to their current position with the logic "I turned down that offer, I must really like my current job".

This sometimes looks a little like sunk cost "I just watched the first 9 out of 10 seasons of this television show. I must really like it, so I'll watch the 10th"

What's the name of this economic concept? Is this maybe a psychology concept instead?


texts: Does more variable input cause marginal product to decline?

texts:
Previously, I believed that after a certain point, additional variable input results in a decline in productivity. For example, if you hire too many waiters, they will eventually get in the way of each other, resulting in a decline in productivity.

However, I read online (https://www.amosweb.com/cgi-bin/awb_nav.pl?s=wpd&c=dsp&k=marginal+cost+and+law+of+diminishing+marginal+returns) that "The law of diminishing marginal returns means that increased production of a good requires more and more of the variable input. For example, the first 50 units of production can be had with only 5 workers. However, the next 50 units might required an additional 10 workers. "

But doesn't this contradict with the law of diminishing returns? The law states that as more and more of an input is used, there is a point at which the increase in output is at a decreasing rate. So is the website wrong? Wouldn't increasing even more variable input decrease production even more?

For example, at a car factory, at some point after hiring many workers, productivity decreases. Isn't the website stating that the solution to this is hiring even more workers, which is counter-productive?


texts:
Economic growth is frequently expressed as a % of GDP.  Proponents of a steady-state economy postulate that perpetual exponential economic growth is impossible and that any system relying on it is inherently unstable. Is this true?

Is indefinite exponential economic growth possible?

(See also: Are there fundamental reasons why (exponential) economic growth is highly desirable?)


texts: what are the categorization by industry in economics?

texts: I wanted to know what industries are there from an economics point of view, and how each industry branches into different parts. Just categories and names will do , or if you can point to a resource please do.


texts: In Austrian theory, does constant, predicted deflation distort credit markets?

texts:
Many leading Austrian thinkers propose a 100% reserve gold standard banking.  They agree that such a system leads inevitably to monetary deflation if productivity continually improves.

Austrians also believe that markets free of distortions are optimal.

Thus, some Austrians must either believe that (a) the monetary deflation resulting from the proposed monetary system doesn't distort credit markets, or (b) it does, but there is no practical alternative that does provide for free credit markets, or (c) something I've not thought of.

Which do they believe?

I am having trouble seeing how deflation could NOT distort credit markets, since if the free-market real interest rate for a given loan, as determined by time preference for consumption, is less than the expected deflation rate, no transaction will take place even though both parties would benefit by making one.

But then which rationale is given for 100% reserve banking with gold standard?


texts: How come the CBO reported the Federal Deficit for FY2014 was \$483 Billion when debt went up by \$1.1 trillion?

texts:
The Monthly Budget Review: Summary for Fiscal Year 2014 states that the deficit was \$483 billion.

Treasury Direct shows Total Public Debt Outstanding increasing over the same period from \$16.7 trillion to \$17.8 trillion.

Why is there such a huge difference in these figures?


texts:
A city has a single electricity supplier. Electricity production cost is $c$ per unit. Utility function $U(q,t)=a\ln(1+q) - t$, where $q$ is electricity consumption and $t$ is electricity tariff. What is the profit maximizing tariff?

I have figured out $\text{MC}=c$ and the supplier is monopolist so $\text{MR}=\text{MC}$ condition have to be used but I can't figure out how to get MR from the utility function.


texts: What does the Bank of England do with the interest it receives?

texts: Seeing as the Bank of England is free to create money, is the interest it receives meaningful? What does the bank do with it?


texts: What happens to a production possibilities curve whenever there is too much labor?

texts: If too much labor is added to a country's production, what happens to the production possibilities curve?


texts: The use of preference relations in choice theory and the $\succsim$ symbol

texts:
At least as from Edgeworth and Pareto we think about utility in mathematical terms. My question twofold

(i)  about the start of the usage of binary relations to model preferences in economics, and hence the start of the axiomatic utility representation exercise.

(ii) about the start of usage of the symbol $\succsim$ to represent weak preference.

About (i) the earlier reference I could find is Wold's (1943): "A synthesis of pure demand analysis I-III" pioneering work on utility representation; and about (ii) is Herstein and Milnor (1953): "An axiomatic approach to measurable utility" work on expected utility.

Does anyone know about earlier uses??

Ant further comments, references or ideas are most welcome.


texts: Consumer demand: a function of present endowment?

texts:
I don't know about you, but each time I go shopping for groceries, my purchasing decision takes into account what I already have at home. I don't make only one demand decision for my entire life the day I become a consumer, and afterward never buy anything ever again. Rather, each and every day, my daily demand for goods is a different function than it was yesterday. Similar to the concept of marginal utility, my daily demand for goods depends in part on what goods I have already have acquired yesterday (and all the days before that in which I have been a consumer).

Let's take a concrete example. Whether I want to buy a soda today depends partly on whether or not I already have one in my possession at home that I could drink. Namely, if I purchased a soda yesterday and it's still in my fridge, I don't want to buy one today; on the other hand if I don't have a soda in my fridge, I do want to buy a soda today. My particular demand function for soda, as I just described it, depends on my present endowment of soda.

However, in the way demand is traditionally modeled, the amount of a good $x$ you wish to buy, $x(p,w)$, is a function only of prices $p$ and wealth $w$. The amount of each good you already have in your possession does not enter as a parameter in the demand function.

(Admittedly, your wealth, which enters in your demand function as a single parameter $w$, CAN be calculated from your present endowment of goods, as a linear combination of their respective market prices. But it's not the actual quantities of those endowments that enter into the demand function -- only the total money-value of all your endowments, in units of the numeraire good. That is, only the amount of the numeraire good you possess actually enters as a parameter into the demand functions for non-numeraire goods.)

I am sure that classical demand theory is not flawed. At the same time, there is a disconnect in my mind between how I think about demand (which makes sense to me only in the context of one's present endowments), versus how demand is traditionally modeled. Can someone help me bridge this gap?


texts: Why does the definition of MRS follow from the implicit function theorem?

texts:
TRAIN OF THOUGHT 1:

From what I understand, $MRS$ is calculated as

$$dU = U_x dx +  U_y dy =0$$
which by rearrangement yields
$$\frac{dy}{dx}= -\frac{U_x}{U_y}$$

So suppose I have $$U(x,y) = \ln x +\ln y$$ Then
$$ \frac{dy}{dx}= -\frac{1/x}{1/y} = -\frac{y}{x}$$

Okay. So I have a function $y$ in terms of $x$.

TRAIN OF THOUGHT 2:

Now consider my $U(x,y)$ again. Let $$\mathbf{a} = \begin{bmatrix}
1\\
1
\end{bmatrix}$$
and $$U(\mathbf{a})=0$$
We have $$DU(x,y) = \begin{bmatrix}
\frac{1}{x} & \frac{1}{y}
\end{bmatrix} $$
and $$\frac{\partial U}{\partial y} (\mathbf{a}) = \begin{bmatrix}\frac{1}{y}\end{bmatrix}= 1$$ which is nonsingular since $\det(1) = 1$ and so by the Implicit Function Theorem, $$U = 0$$ defines $y$ implicitly as a function of $x$ in a neighborhood of $\mathbf{a}$.

My Question:

How are these two trains of thought connected? The first is stated in terms of differentials. But the second is not. So I am confused why the definition of $MRS$ follows from the implicit function theorem.


texts: I would need help with the following problem about consumer theory. Let us say that $X$ is the amount of days at the sea and $Y$ is the amount of days on the cottage. We have some utility function $u(X,Y)$ and constraint $ 4X+9Y=I$. I have found the optimal solution $(X^{\star}=\frac{I}{5},Y^{\star}=\frac{I}{3})$ and I am supposed to graphically illustrate and comment dependence $X^{\star}$ and $Y^{\star}$ on income $I$. I am not sure if i understand exactly the task. Could you help me with the solution? Thank you.


texts: Relationship among universal type space, Aumann's semantic knowledge model and Samet's syntactic knowledge model

texts:
What's the relationship among universal type space, Aumann's semantic knowledge model and Samet's syntactic knowledge model?

Here's my confusion:

Regarding universal type space and the model in Aumann's Agreeing to disagree, I used to think they're really the same thing from two different angles. The type space construction is a bottom-up construction. It starts with all the payoff relevant parameters from players' point of view, and generates a set of states of world in the end. Aumann's model is top-down. The set of states of world and players' knowledge as partitions are exogenous. Interesting results are derived by imposing some consistency rules.

It seems to me, there's a one-to-one correspondence between a player's type in the former and a cell( or atom, block) in the selfsame player's partition in the latter, because a player's strategy has to be measurable with respect to them in these settings.

But after having a skimming of an unpublished paper by Robert Simon,The Common Prior Assumption in Belief Spaces: An Example, I found it's not the case.

In that paper, he actually imposed a partition on Merten and Zamir's type space(he claimed so) for each player, so there's no such correspondence.

Another thing that is weird is that it seems to me he's actually not working on on a belief space. It looks like he's working on a model in Dov Samet's Ignoring ignorance and Agreeing to Disagree, which is homeomorphic to a Cantor set, a set which is generated by assigning truth values on underlying propositions and the use of non-repeated knowledge operators of the same player. It seems to me Dov Samet's model is not homeomorphic to Merten and Zamir's type space, because we might need to add operators of belief from probability 0 to probability 1 in Dov Samet's model to do that, and the generated set of state of state of world will have a cardinality strictly larger than a Cantor set.


texts:
I'm doing exercises of Chapter3 of MWG, there's a problem that I don't understand (I didn't figure out the solution manual either...).

It is about exercise 3.D.4, the full statement of the exercise is as follows:

Let $(-\infty,\infty)\times R_+^{L-1}$ denote the consumption set, and assume that preferences are strictly convex and quasilinear. Normalize $p_1=1$.

(a) Show that the Walrasian demand functions for goods $2,...,L$ are independent of wealth. What does this imply about the wealth effect of demand for good 1?

(b) Argue that the indirect utility function can be written in the form $v(p,w)=w+\Phi(p)$ for some function $\Phi(·)$.

(c) Suppose, for simplicity, that $L=2$, and write the consumer's utility function as $u(x_1,x_2)=x_1+\eta(x_2)$. Now, however, let the consumption set be $R_+^2$, so that there is a nonnegative constraint on consumption of the numeraire $x_1$. Fix prices $p$, and examine how the consumer's Walrasian demand changes as wealth $w$ varies. When is the nonnegativity constraint on the numeraire irrelevant?

My question is about the (c) part: 1. what does it mean? 2. Can anyone explain the solution to it?

The solution to (c) (from the solution manual) is:

The non-negativity constraint is binding if and only if $p_2x_2(p,0)>w$. Note that $x_2(p,0)=(\eta')^{-1}(p_2)$, because $p_1=1$. Hence the constraint is binding if and only if $p_2(\eta')^{-1}(p_2)>w$. If so, the Walrasian demand is given by $x(p,w)=(0,w/p_2)$. Thus, as $w$ changes, the consumption level of the first good is unchanged and the consumption of the second good changes at rate $1/p_2$ with $w$ until the non-negativity constraint no longer binds.


texts: What is 2nd round of rationalizability for a 1st price auction?

texts:
Consider a first-price auction.
Suppose that we have $N$ bidders, and they believe that their opponents' values is drawn from a uniform distribution on interval $[0,1]$.
Let us eliminate weakly dominated strategies.
The 1st round will clearly eliminate all bids higher than the private value $x$. But what range of prices will be eliminated in a 2nd round?
My conjecture: after elimination of bids higher than private values, bidder $i$'s objective function in a 2-bidder situation will be $(v_i-b_i)\Pr(b_{-i}\leq b_i)$. The probability $\Pr(b_{-i}\leq b_i)$ is maximized when $b_{-i}$ is approaching $v_{-i}$. So maximized form of objective functions of bidder $i$ is $(v_i-b_i)\Pr(v_{-i}\leq b_i)$, which is $(v_i-b_i)b_{i}$. (Since we assume uniform distribution on values) So after 1st round of rationalizability, a bidder's maximized payoff will be $\frac{v^2_i}{4}$. This means that in 2nd round of rationalizability, any bidder will not be bidding higher than $v_i-\frac{v^2_i}{4}$.


texts: If interest rate increases and consumption in the present increases, is present consumption a normal good?

texts:
I recently wrote an economics quiz and one of the questions was:

  Suppose "r" is the interest rate that prevails between the present and
  the future. If "r" increases and a household chooses to consume more
  in the present, then:

I answered that since the price of current consumption increases and the consumer consumes more, current consumption must be an inferior good.

However this was marked incorrectly for me and the correct answer was current consumption must be a normal good. I'm unsure of why this would be the correct answer, could somebody explain the reasoning?

Edit: The five options were:

  A) it is an irrational decision.

  B) consumption in the present must be an inferior good.

  C) consumption in the present must be a normal good.

  D) consumption in the future must be an inferior good.

  E) consumption in the future must be a normal good.

I chose chose B but the correct answer was listed as C.


texts: Recent economics theories that involve differential topology?

texts:
The original development of general equilibrium theories involved differential topology.

I wonder if there are any recently developed theories, in any field of economic theories, that utilize differential topology (DT).

I've seen some recent papers but none of them used DT. Some real analysis, topological topology, and convex analysis seem enough.


texts: Strong monotonicity and weak monotonicity

texts:
We say $\succsim$ represents weak monotonic preferences if $$x,y \in X, \,\, y >> x \implies y \succ x $$

where $y >> x$ means that every element of $y$ is greater than every element of $x$.

And we say $\succsim$ represents strong monotonic preferences if $$x,y \in X, \,\, y \geq x, y \neq x \implies y \succ x$$

where $y \geq x$ means that at least one element of $y$ is greater than an element of $x$ and all others are equal.

My question is: do strong monotonic preferences imply weak monotonic preferences?

My answer: yes. The reasoning is as follows:

Since the set $A = \{ x,y \in X: y >> x \}$ is a subset of $B = \{x,y \in X: y \geq x, y \neq x \}$, then if $B \implies y \succ x$ it must also be true that $A \implies y \succ x$ and thus strong monotonic preferences imply weak monotonic preferences.

In plain English, if a bundle with more of one commodity and the same of all others is preferred, then a bundle with more of every commodity must also be preferred.

Is my reasoning correct?

Thanks!


texts: Why must the rate of GDP growth be positive?

texts: There are always expectations that GDP should be growing at a certain rate. This is what I see in the newspapers. I am not an economics major and this is a very basic student question. After adjusting for level of prices, meaning that forget about inflation and price related issues, it is expected to grow at say $2\%$. Why is this a case and what should it be driven by? Assume there is an economy that only produces apples, for simplicity. So, it is expected to make $2\%$ more apples every year? So the growth would be driven by the larger amount of goods produced? Why is this economy expected to make more apples every year?


texts:
What is the advantage and disadvantage to have a high value of USD for USA?

China and Japan always want to keep their currency low as oppose to USA.


texts: Subgame-perfect Nash equilibrium perfect information

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

The normal-form of the game looks like this:

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


texts: Is it bad for the economy of a country if forreign firms buy companies?

texts:
If a forreign firm buys a company. For example a Russian firm buys a British company. Is this good or bad or neutral for the British economy?

As I see it, the profits of the company will be going abroad so this seems bad.

Alternatively, there's nothing to say the people making profits if the company is British owned aren't spending their money abroad anyway.

Would it even matter if every British company was forreign owned?

If it doesn't matter. Why would the Chinese government be buying British firms? Surely to help their economy at the expense of the British economy? Yet, the British government seems to encourage this as "investment" in British industry. So who is getting the best deal here? Seems like Britain is getting a short term boost at the cost of long term profits.


texts: Pareto optimal and Walrasian equilibrium

texts:
There are 100 units of good 1 and good 2 in a economy. Consumer 1 and consumer 2 have 50 units of each good.
Consumer 1 only wants good 1 whereas consumer 2 only wants good 2.

Note: Neither of these are lexicographic preferences.

Question: Find Walrasian equilibria

Here is what I have reached:

Can someone explain why red lines are WE..and why not F and G?
And P is Pareto optimal I understand, but is it Walrasian equilibrium as well?

Is every Walrasian equilibrium Pareto optimal and every Pareto optimal point Walrasian equilibrium?


texts: Unconstrained Optimization:Why is there no "profit style" function in consumer theory?

texts:
When being exposed to your equations for profit maximization you have an equation of:

$$\pi=pf(x)-c(x)$$

with this you can solve for the optimal input(s) $x$ from the first order conditions and some basic algebra.

I was wondering why in consumer theory we don't solve for the bundle that maximizes consumer surplus using a similar type of formula.

The motive behind this question is that if such a formula exists it would simplify the calculations for utility maximization in consumer theory. The profit function is convenient because it incorporates the constraint, however we can't seem to do this in consumer theory.

Why does such a function not exist?

Edit: I'm interested in understanding why we don't have a function which circumvents the use of the Lagrangian in consumer theory. I.e. Why don't we solve to maximize consumer surplus


texts: Method of Lagrange multipliers with random variables

texts:
I'll illustrate the issue I'm having with a simple problem.

Let $c_1, c_2 \in \mathbb{R}$, and $Z$ a real-valued random variable. Let $u:\mathbb{R} \rightarrow \mathbb{R} $ be a differentiable function, and $f(c_1,Z)$ be a real-valued function that is differentiable with respect to $c_1$.

The problem is:
Maximise: $u(c_1) + \mathbb{E}[u(c_2)]$
such that $c_2=f(c_1, Z)$

This problem is easily solved by direct substitution, and the answer is

$u'(c_1) + \mathbb{E}\left[u'(f(c_1,Z)) \frac{\partial f(c_1,Z)}{\partial c_1}\right] = 0 \label{answer}$

The issue is how to write down a Lagrangian whose extrema correspond to the solution of this problem in the normal way.

My first instinct was to write
$\mathcal{L} = u(c_1) + \mathbb{E}[u(c_2)] + \lambda(c_2 - f(c_1,Z))$.

However, this doesn't seem to make sense.
If you treat $c_2$ as if it is a random variable, then the derivative of  $\mathbb{E}[u(c_2)]$ with respect to $c_2$ gives zero, and this can't possibly give the right answer.
On the other hand, it doesn't make sense to treat it as non-stochastic either, since it is 'forced' to be stochastic by the constraint.

Question: How do I write a Lagrangian whose extrema correpond to the solution of the above optimisation problem?


texts: What are the issues with currencies backed by commodities?

texts:
I have seen it suggested that currencies that are backed by a commodity are generally considered to be a bad idea in most cases. However, I have done a bit of my own research into representative money etc. and I cannot find a definitive explanation of why this might be the case.

So, my question is this: Are there qualities of commodity backed currencies that make them a bad idea?


texts: Since it doesn't change the money supply, how can an "expansionary" fiscal policy alone spur economic growth?

texts:
I understand how monetary policy can be used to heat up an economy by increasing the money supply, but how can a fiscal policy do so? When the government borrows money to increase spending, it is not as if that money would have just been sitting under somebody's mattress; it would have been loaned to some other entity, whose spending of that money (as far as I know) would cause just as much economic activity as if the government spent it. In addition, the government's demand for money would should raise interest rates and/or strengthen the dollar, which is the opposite of what I generally think of when it comes to an "expansionary" policy. Also, while money could be lent by entities in other countries, that money would just have to flow back out in the form of more imports, so domestic AD shouldn't be affected, no?

The only thing I can think of is that the government can spend 100% of the money that it borrows, whereas if that money went into a bank account, a small portion would not be lent out due to reserve requirements; does that make all the difference?

It's been years since I took an econ class, and I know this is 101 stuff, but I can't figure out what I'm missing...


texts: Continuous Preference Relation Imply Continuous Utility Fn Existence

texts:
I am reading MWG's explanation in Chapter 3 when showing continuous preference relation implies the existence of continuous utility function.

First, the authors show $u(.)$ is continuous by using the definition that the image under $u(.)$ of a convergent sequence is convergent. Consider a sequences $x_n\rightarrow x$. They first claim that $u(x_n)$ must have a convergent subsequence.

I understand the big picture: Since $x_n$ converges to x, for some large N, $u(x_n)$ must all lie in some compact set, and any infinite sequence in a compact set must have a convergent subsequence.

The part I am having trouble is when they use monotonicity to show this compact set. The exact excerpt is:

  "By monotonicity, for any $\epsilon>0$, $\alpha(x')$ lies in a compact subset of $\mathbb{R_+}$, [$\alpha_0,\alpha_1$], for all $x'$ such that $\parallel x'-x\parallel$$\leq0$."

Here I used $u(.)$ and $\alpha(.)$ interchangeably to represent the utility function. Can somebody elaborate the above claim just little more in detail please?

I understand monotonicity implies local nonsatiation, hence, in any given small ball, you always have some bundle that you prefer that to x. Part of my confusion comes from the Figure they present, which is they put the bundle x on the indifference curve ($\{y\in X:y\sim x$}). But isn't $\alpha(x')$ on the diagnoal line Z?

Please help. Thank you.


texts: How can I add fixed-effect constant variable in Stata?

texts:
I want to test a model like this:

alpha denotes full set of country fixed effects and delta denotes full set of year fixed effects in the article in which this model is used.

My model is similar to above model, however I don't know how to create such a model by using Stata.

I think I should add constant or dummy variable. Is this the right way? How can I add such variables by using Stata?

Thanks a lot!


texts: Why GDP positive growth does not decrease inflation?

texts:
My understanding is : If production increases, it would imply the amount of goods increases as well for the same amount of money available in the market. Because of this, we should see prices of goods decrease as the offer got bigger.

Since we say inflation increases with GDP growth, where am I wrong thinking it should be the other way around?


texts: Does a high current account deficit devalue the national currency?

texts: I've been reading some materials about Belarus's 2011 financial crisis, and a common thread among them is this: Belarus had had a rapidly growing current account deficit, and in 2011 it came to a head helped by a number of factors that, I take it, weren't the reasons per se (for example, people rushed to buy imported foreign cars before they got more expensive due to a planned tariff hike). While I was reading that, I couldn't help thinking about another country with a high current account deficit, the US (a comparison). But, on the contrary, it has a strong currency. The US dollar, the euro, a handful of other currencies are considered the most reliable currencies in the world. Why is that? Does a high current account deficit devalue the national currency, or does it have such an effect only coupled with some other factors?


texts: What is the result of the Bellman Equation

texts:
I'm just starting with dynamic optimization and although I understant the proof's of the theorem I'm not able to fully understand whether the bellman equation is a function , a function valuated at some number (therefore a number) or both. I'm using Stokey Lucas and Prescot Recursive methods for economics dynamics.
And they state in chapter 4.1 and 4.2:
Given some assumptions about the feasibility set and the $F(x_t,x_{t+1})$ This problems are equivalent:

1) Sequential problem (SP) $sup_{x_{t+1}}(\Sigma_{t=0}^\infty\beta^tF(x_t,x_{t+1}))$ st $x_{t+1}\in\Gamma(x_{t+1})$ for all t

2) Functional Equation (FE)$\ v(x)= sup_{y\in\Gamma(x)}[F(x,y)+\beta v(y)]$

What is not clear to me is that:
In 1 the result of applying sup operator is a NUMBER (Value function valuated at $x_0$
While in 2 as there is a functional equation, the result is a function. The authors seem to talk about a number (chapter 4.1) but then (in chapter 4.2) they state that applying the contraction mapping theorem to 2 we get the solution which is the unique fixed point in the set of continous bounded function, therefore the result is a function

So the solution is a number or a function?

Thanks in advance


texts: Higher order beliefs and coherency in game theory

texts:
I am reading about the higher order beliefs. Before getting into the formal definitions, I will define some common terminology which I will need for the formal definitions.

  If $X$ and $Y$ are two spaces, denote the set of probabilities over $X$ as $\Delta(X)$, and for $\delta\in \Delta(X\times Y)$ define the marginal probability measure of $\delta$ on $X$
  $$
marg(\delta;X)(E)=\delta(E\times Y)
$$
  for every measurable subset of $E$ of $X$.

The formal definition of higher order order is as follows:

  Let $N=\{1,2,\dots, n\}$ be the set of players. For each $i\in N$, $A_i\neq\emptyset$ is the finite set of actions available to player $i$. Denote the set of mixed strategies for  the player $i$ as $\Sigma_i=\Delta(A_i)$. As usual define $\Sigma_{-i}=\times_{j\neq i} \Sigma_i$ and $\Sigma=\times_i \Sigma_i$. Define the se set of first order beliefs $B_i^1=\Delta(\Sigma_{-i})$ and $B_{-i}^1=\times_{j\neq i} B_j^1$, and $B^1=\times_i B_i^1$. Define inductively, for each $k\geq 1$
  $$
B_i^{k+1}=\Delta(\Sigma_{-i}\times B_{-i}^1\times \dots B_{i}^k)\\
B_{-i}^{k+1}=\times_{j\neq i} B_j^{k+1}\quad B^{k+1}=\times_i B_i^k
$$
  Finally, $B_i=\times_{k=1}^\infty B_i^k $

The coherent belief is described in the following way:

  $b_i=(b_i^1,b_i^2,\dots)\in\times_i B_i^k$ is coherent if for each $k\geq 1$ $marg(b_i^{k+1},\Sigma_{-i}\times B_{-i}^1\times\dots\times B_{-i}^k)=b_i^k$ where $marg$ is the marginal probability measure.

Now according to this definition for $E\subset \Sigma_{-i}$ we have $marg(b_i^2;\Sigma_{-i})(E)=b_i^1(E)$.

I try to understand this definition. So I tried to consider a game in which there are two players $i$ and $j$ and two actions for each player. So

$$
\Sigma_i=\{(p,1-p):p\in[0,1]\}\quad \Sigma_j=\{(q,1-q):q\in[0,1]\}
$$
and $b_i^1\in\Delta(\Sigma_j)$ and $b_i^2\in\Delta(\Sigma_j\times B_j^1)$. So $b_i^1$ is a probability measure over $q$, and $b_i^2$ is a joint probability measure over $q$ and the first order beliefs of $j$. Suppose $E$ is the collection of $(q,1-q)$ such that $q\leq 0.5$, which is a subset of $\Sigma_j$.
I could not convince myself why $marg(b_i^2;\Sigma_j)=b_i^1(E)$. Apologies for the length of the question and any help is greatly appreciated.


texts: Does estimating OIRFs from an SVAR (with uncorrelated errors) mean we are orthogonalizing the error structure twice?

texts:
In a normal VAR, we can orthogolize the errors via Cholesky decomposition and estimate OIRFs. Thus, transforming the structure of the errors so that they do not correlate.
In an SVAR, asumming we impose an orthogonal structure on the errors directly so that they do not correlate. And so if we estimate OIRFs from an SVAR instead of just IRFs, are we not orthogolizing the error structure twice? First, through a direct imposition of an uncorrelated error structure by specifying some matrix. And second, through Cholesky decomposition if we estimate OIRFs.


texts: What if price were a function of buyer's income?

texts:
If everyone's income were public information, would purely profit-seeking sellers benefit from charging different prices to people based on their different incomes? My intuition says yes because a buyer's demand for some good at a given price depends on that buyer's situation in life, including income. It seems to me that prices could be better optimized if customer information on an individual level were taken into consideration.

But I'm not sure about this. I lack the mathematical know-how to think about this thoroughly. It seems plausible that the optimal price would be the same for all customers due to competition causing prices to converge ...or something along those lines. The Wikipedia page on price discrimination brings up the issue of discount buyers reselling goods for a profit, but I think this could be avoided by limiting the quantity of a discounted good a customer can buy, and it's not an issue at all if the good can't be resold. That page also refrences coupons as an example of price discrimination because only people with a low enough income can benefit from spending time on clipping coupons.

So I think there are already some successful forms of mild price discrimination, but it doesn't seem all that common, possibly because there isn't a way for customers to prove his/her income. Could price discrimination based on income work at a larger scale if people could prove their incomes, and could this help reduce inequality?


texts: Meaning of «intertemporal substitution effect dominates the income effect»

texts:
Assume a household intertemporal optimisation problem, where they only either consume or labour, and one of the equilibrium conditions states that labour will be a positive function of productivity, when « the intertemporal substitution effect dominates the income effect».
The real wage is also a positive function of productivity, regardless of the above effects interaction.
How would one interpret the meaning of « the intertemporal substitution effect dominates the income effect», when there's a positive productivity shock?
My take on this is:

The intertemporal substitution effect refers to how easily the household substitutes consuming tomorrow for consuming today.
The income effect refers to how consumption by household will change, given a change in income. Income rises, and the household will want to consume more and work less.

Therefore, I would interpret the sentence «the intertemporal substitution effect dominates the income effect» as the household choses to work more today to consume more tomorrow, instead of consuming more today.
Am I correct?


texts: How to go from demand elasticities to a demand function? (merger simulation)

texts:
I am reading this paper:  https://econpapers.repec.org/article/oupjleorg/v_3a10_3ay_3a1994_3ai_3a2_3ap_3a407-26.htm (Werden and Froeb 1994) about merger simulation.

The paper is above my level, so I'm struggling through it a bit. The part I'm having the most difficulty with is how the authors go from demand elasticities to a demand function.

My general question is, if I have own-price elasticity of demand for every good $j$ $e_j$ and cross-price elasticity of demand between all goods $j$ and $k$ $e_{jk}$, how can I derive a demand function $q(p_j, p_{-j})$ where $p_j$ is the price of good $j$ and $p_{-j}$ is a vector of prices for all non-$j$ goods?

It seems to me that I would need some observed price-quantity pair and an assumption that the demand function is linear. Is this all I would need? Is this what the authors are doing?

To confirm my understanding of the overall procedure for merger simulation used in this paper, my understanding is that I would then solve the merging firms' profit maximization problems pre- and post-transaction. This problem is

$max_{p_j}  (p_j-c_j)q_j$, where $q_j$ is a function of $e_j$ and $e_{jk}$, which in turn depend on market shares, which will be the varying factor between the pre- and post-transaction calculations.

Is this what the authors are doing in this paper?


texts: Is there an index that describes how differentiated a product is?

texts: Some products are commodities, identical regardless of the producer. Others are very different an people look for specific brands of whatever they buy. Has anybody built any sort of index of how differentiated a product is or an industry? This would be very useful for research purposes!


texts: To what extent are renewables like solar driving down the cost of oil?

texts:
The price of oil has declined by roughly 66% in the past couple of years, and a lot of people want to know why:

Some people are saying that the recent trend of oil prices dropping means the global economy is consuming less oil and therefore economic leading indicators suggest financial collapse in the future.

They are wrong (today) because oil consumption has been increasing continuously over the last 20 years.

Other, more sensible ideas are that (today) oil prices have been decreasing because oil supply outpaces oil demand. But it hasn't been enough to compensate for the price drops. Its not like oil production has increased by 66%. At most, it has increased by 15%, more likely something like 10%.

So, prices have fallen faster than the production surplus have increased.

Could it be alternative energy technologies like solar (or fear of them on the part of oil producers) that are causing this additional decline in oil prices?

TED talk that provoked this question: http://www.ted.com/talks/al_gore_the_case_for_optimism_on_climate_change

could someone please add the category "substitution" to this question


texts: Choice under Uncertainty: Relation between the certainty equivalent and the coefficient of relative risk aversion

texts:
That's my question!
Propositon 6.C.4 (MWG (1995)): The following conditions for a Bernoulli utility function $u(\cdot)$ on amounts of money are equivalent:
(i) $r_R(x,u)$ is decreasing in $x$.
(iii) Given any risk $F(t)$ on $t>0$, the certainty equivalent $\bar{c_x}$ defined by $u(\bar{c_x})=\int_{}^{} u(tx) \,dF(t)$ is such that $x/\bar{c_x}$ is decreasing in $x$.
Where $r_R(x,u)$ is the coefficient of relative risk aversion at $x$.
If both functions are decreasing in $x$, can we say that one is decreasing in relation to the other? In other words, can we say that the certainty equivalent is decreasing in the coefficient of relative risk aversion?
Thanks!


texts: Effect of prediction of later catastrophe

texts:
Say a catastrophic worldwide event is predicted likely for exactly 100 years from now, but it will not affect anyone til then. Say a large meteor hit.

Would markets budge much?

My only relevant observation is governments tend to invest in the future, but begrudgingly. (Climate change). So there will be some money in disaster aversion etc.


texts: Soft Question: Economic measurement in a post-industrial economy

texts:
I have a colleague who is a mathematician by training and currently works in Risk Analysis. He has issues with current Economic theory and I have debated him over coffee a couple of times.

One question he asked stood out to me as I could not answer it.

  In terms of economic measurement, how does one know if the variables economists are looking at are relevant to the economic health of a country in a post industrial economy?

  i.e.people and firms consume and produce many services that barely make a dent in the GDP, like how some medications and computers today are much cheaper today than when they first arrived on the market.


texts: What is the reason behind the demand function of a perfect complement good?

texts:
so I know that usually the income curve is equal to:
$$x_1p_1 + x_2p_2 = m$$
if we rearrange this equation we get that the demand for good one ($x_1$) is equal to:
$$x_1 = \frac{m-x_2p_2}{p_1}$$

None the less in my book it is said that:

  The demand for good 1 is $x_1 = \frac {m}{(p_1 + p_2)}$

if anyone could explain me why $x_1 = \frac {m}{(p_1 + p_2)}$ instead of $x_1 = \frac{m-x_2p_2}{p_1}$ that would be greatly appreciated. many thanks in advance.


texts: What counts as transactions fee in Coase Theorem?

texts:
Coase Theorem says that if the transaction fee is negligible then we will have an efficient allocation of resources.

In some of the samples, they quote that it doesn't matter who has the right to pollute. If people own the river, they will sue polluters and get money. If the polluters own the river, the people will pay the polluters to stop polluting.

It seems that the Coase Theorem presume that if a deal can be made, it will be made.

What about if both the polluters and the river owners (the people) can be better off by striking some deals but they don't make deals because they wait till better deals come along.

Say the river owners want more money for pollution?

Can I say that the transaction costs go up?

Notice that once they agree they can just pay with a credit card and hence there is no transaction fee. However, they play a game of chicken first or whatever to get deals coming up.

Does that mean transaction costs go up and hence, Coase Theorem fails?


texts: Whatever happened to efficiency wage theories?

texts:
Older macroeconomics texts give much space to efficiency wage explanations of how unemployment could coexist with wages in equilibrium higher than the reservation wage of workers.

However, there seems to be very little current research on these theories, with most recent papers modelling unemployment using search frictions.

Is the decline in popularity of efficiency wage models due to their having failed in some sense? I would greatly appreciate any references to the literature.


texts:
Shall we anticipate the regression result? Saying the coefficient sign .

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


texts: Regression on default rates and backward extrapolation

texts:
Suppose that we have bankruptcy data representative for Small and Medium-sized enterprises in a country. We can therefore calculate default rates. Furthermore suppose that we found that GDP, unemployment rates and interest rates seem to be significant macro economic factors that could explain there default rates.

Now we use regression to fit the macro economic variables to the observed default rates. My question now follows: If I suppose to have a portfolio of SME companies with only default rates from the last year. How could I using the above backward extrapolate these default rates, using the macro economic factors?

Thanks for any help!


texts: Expenditure function. Prove that this set is bounded

texts:
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.


texts: Is Universal Basic Income compatible with free international trade?

texts: If one country introduces UBI, what prevents other countries from taking advantage of that and supplying cheaper (no need to finance a UBI scheme!) goods to the original country and outcompeting the local industries? Does UBI automatically mean high international trade tariffs?


texts:
I suppose that it doesn't cost most firms much to get rid of cheap labor, and that high wage workers typically have contracts that imply high compensations in case of firing.

But what about the remainder? Since Macroeconomics is mostly about the art of writing linear models, what evidence is there for average firing costs from the view point of the firm?


texts: Why does local non satiation imply the constraint is binding?

texts:
Local non satiation says that for any $x \in X$ and $\epsilon > 0$, there exists $y \in X$ such that $d(x,y) < \epsilon$ and $U(x) < U(y)$.

I don't understand why this implies that $px^* = m$ if $x^*$ sovles consumer problem. If we think of $x \in R^2$, it implies that you can find a $y$ that is strictly preferred in the small neighborhood of $x$. In that case, even $x$ is on $px = m$, LNS seems to imply that there is a $y$ that is strictly preferred than $x$, and that $y$ may not be on the boundary since LNS only says there's a increasing direction but doesn't say which direction it is increasing.


texts: What is the difference between currency manipulation, and a fixed exchange rate regime?

texts:
China is labelled by some to be a 'currency manipulator', that is supposedly pegged to the US Dollar. What is the difference between currency manipulation and a fixed regime?

Different motives?
I figure that it may be that a textbook fixed regime is undertaken to prevent instability, and is minor (just to correct volatility), whereas manipulation is done with the aim of gaining an unfair advantage.

Different means?
I have also read that it could be due to the fact that a manipulator creates domestic base money with which it can buy currency, without sterilisation.

Legality? BVJ below makes an interesting comment about the legality of the two... is there a legal framework in which some forms of fixed currency maintenance are allowed and some not?

Could anyone please clarify? Thanks.


texts:
What's the literature on Non-Constant elasticities of substitution? Say, I'm interested in the elasticity between $c_1$ and $c_2$ increasing/decreasing in income/wealth.

CES utility functions with equal spending weights are similar to

$$ \left(\sum_i c_i^\frac{\epsilon-1}{\epsilon}\right)^\frac{\epsilon}{1-\epsilon}$$

A simple way of getting non-constant elasticities would be to let $\epsilon = \epsilon(Y)$. Then the elasticity of substitution would vary with income:

$$\frac{d \log \frac{c_i}{c_j}}{d \log \frac{p_j}{p_i}} = \epsilon(Y)$$

But I feel that this mixture of preference-parameters and outcome variables is suboptimal.

Is there a common way of modeling these preferences?


texts: Have there been any structural changes in the market that would lead the indexes to be trading so high?

texts:
If you look at this graph of the SnP500:

You will see that it is trading at levels higher than pre 08 or 99. What systemic structural changes in the market have led it to be trading so high? I think the rise from 80-99 can be explained by the deregulation of the financial sector and the rise of China. What is causing it to trade so highly now?


texts: How does buying assets change net capital outflow?

texts:
I am really confused and I hope you can help me.
I know NCO is equal to acquisition of foreign assets by residents – acquisition of domestic assets by nonresidents.
But I can't understand the transactions without purchases of goods.
For example, when an American buys a share of a foreign company, acquisiton of foreign assets by residents increases, and I think acquisition of domestic assets by nonresidents(American dollars) should also increase. So these changes should offset each other and the transaction shouldn't affect the net capital. But I know this transaction increases US NCO.
So, what am I missing ?


texts: Why the stock market went up when the currency being weakened?

texts:
From Bloomberg Market Concept (BMC), in 2013, Japan is traditionally a heavy exporter, especially automobiles. When the yen being weakened, the Japanese automobile being more attractive because it seems to be cheaper to the target market.BMC also documented that "The automobile won more order as a result, so the stock market went up."
Why the stock market went up, is it because investors optimistically value these firms because of better performance? And the result seems to be triggered by the reduction in the value of the yen compared to USD, so the stock market went up, but whether the Japanese stock market still went up if the stock price being calculated in USD?


texts: Are there any instances where short run demand/supply is more elastic than long run cases?

texts:
Conventionally both demand and supply for goods and services are both more elastic in the long run than in the short run.
My Question

Is there ever an instance where demand and/or supply for a given good be more elastic in the short run than in the long run?

That being said if there is never such an instance, does there exist a general proof refuting such an instance?


texts:
I need to do data visualization of World Bank lending category for some countries using source from their page. When I was going through it I found some inconsistencies in categories they use to describe lending groups. According to the World Bank we have three lending group:

IBRD,
IDA,
BLEND

but to describe other data they used following markers:

IDA only  - IDX,
IDA total - IDA,
IDA Blend - IDB,
IBRD only - IBD,
IDA & IBR TOTAL - IBT

Which of the three lending group correspond to six following markers? I mean is IBRD same as IBD (IBRD only), etc?

Source [1] and [2].


texts: Isn't it trivial that preferences are single-peaked over two alternatives?

texts:
I'm studying Down's Median Voter Theorem which states that if voters have single-peaked preferences over two alternatives arranged along a one-dimensional political spectrum, a majority rule voting system selects the outcome most preferred by the median voter.

As I understand it, single-peaked requires that each agent has an ideal choice, and for each agent, outcomes that are further from his ideal choice are preferred less. But isn't this trivially satisfied when two alternatives are considered (provided agents are not indifferent): If I prefer Clinton to Trump, then my preferences are single peaked over all possible choices.

I understand that singele-peakedness is far from trivial in $N>2$ alternatives, but $N=2$ is required for MVT. From wikipedia:

  The third assumption (3) is that voters are only choosing between two options. This is important because when there are more than two choices for voters, the median voter may not have voted for the most popular option.


texts: Understanding the complex relationship between macro and micro economic factor: Job shift

texts: As the world knows plenty of manufacturing jobs shifted from various countries to China. This macroeconomic trend of consolidating manufacturing jobs in China has been going on for past 30 years. Please help me understand given that so many jobs have been moved out of countries like US, why there has not been significant reduction in the demand and spending of the people in these countries. As per my understanding if people start loosing their job, they start spending less and less eventually slowing down entire economy of a country. How are countries still not affected by such a massive out flux of jobs?


texts: How change in technology affects the price of labour and capital?

texts: If the technology improves how does the price of labour and capital change. We take the neo-classical assumption that demand for each factor depends on it's marginal productivity, and demand and supply are in balance. The exact change should depend on the production function, right? So how can we say what will happen.


texts: Lets say the U.S. imports a brand new Ferrari that costs $600,000. I know that it would take away from the U.S. GDP since it's considered an import. However, if a consumer buys that Ferrari from the U.S., would it also add to the GDP (consumption) and cancel out the imports? What would happen if it just sat in U.S. warehouses unsold? Is it still adding to the GDP (investment) to cancel out with imports?


texts: China benchmark rates and Shibor relationship (chart)

texts:
I made the chart below for an assignment on People's Bank of China monetary policy during the financial crisis. The problem is that it got me very confused about the relationship between these interest rates. Why does 1- year Shibor never decrease below the rediscount rate? In the period between 2008/11 and 2009/07 it even clearly copies it.

My second question would be on what happened in 2011. Both of the market rate just seem to shoot up. If the rediscount rate represents the rate at which commercial banks are able to obtain funds from the central bank, why would banks borrow for Shibor?

I wasn't able to find answers anywhere, so a big thank you to anyone who can help.


texts: Euler equation in Continuous time VS Discrete time

texts:
I have seen the euler equation in discrete time for the baseline neoclassical growth model written as:
$$\frac{U'(c_{t+1})}{U'(c_{t})}=\frac{1}{\beta(1+r)}$$
however I have also seen the euler equation for the continous time equivalent written as:
$$\frac{U''(c(t))}{U'(c(t))}\dot{c}(t)=r-f'(k)$$
Ignoring the right hand sides of these equations (which vary based on model set up) and exclusively looking at the left hand side I see two very different formulations of the same equation.
My question is: "How does the Euler equation in Continous time represent the same thing conceptually when compared to its discrete time counter part?"


texts:
I've been estimating some non-linear Macroeconomic models.

As a field, do we care about complex roots of the autoregressive matrix? Is there any reason to think the real word processes have real roots?


texts:
In a finite Bayesian game, in most textbooks, a type of player $i$ is defined as $\theta_i\in\Theta_i$. Little is said about the "nature" of the set of types.

For example, could we have a two-element set $\Theta_i=\{(a,b),(c,d)\}$? If I am not mistaken this means that $\Theta_i$ is a subset of $\mathbb{R^2}$, right?

For the common prior then, we could have, for example, $\mathbb{P}((a,b))=p$ and $\mathbb{P}((c,d))=1-p$. Both probabilities describe the joint probability distribution that Nature assigns the types to the players.

Is this allowed in the definition of a Bayesian game?

I'd appreciate any help. Thank you.


texts:
I am having some troubles in distinguishing, from a theoretical point of view, between contract curve and Pareto set.

I have looked around books and internet, and I have found that contract curve should be a subset of Pareto set, i.e. the locus of Pareto efficient allocations that can occur as a result of mutually beneficial trading between agents.

Am I right or there is something I did not understand properly? Someone can give me a formal definition of the two objects (if there is some differences)?


texts: The factor elasticities from a Cobb-Douglas function in Romer's macroeconomy book

texts:
Good night, I'm reading the Romer's macroeconomy book in the page 42, "A complication" section title. The begin of third paragraph say:

  This is not a general property of production functions, however. With Cobb–Douglas production, the elasticity of substitution between inputs is 1.  ...

I understand that the factors elasticity of sustitution is defined like $El_x(y)=\frac{d\,\ln(y)}{d\,\ln(x)}$ in this case will be $El_K(L)=\frac{d\,\ln(L)}{d\,\ln(K)}=\frac{d L}{d K}\frac{K}{L}$.
From Cobb-Douglas simplest function $Y=K^\alpha L^{1-\alpha}$ we have, for $Y=const$, $K=(YL^{\alpha-1})^{1/\alpha}$ then
$$\frac {d K}{d L}=\frac{ \alpha - 1}{\alpha}\left(\frac{Y}{L}\right)^{1/\alpha}$$
now replacing in the formula:
$$El_L(K)=\frac{ \alpha - 1}{\alpha}\left(\frac{Y}{L}\right)^{1/\alpha}\times\frac{L}{K}$$ operating we have
$$El_L(K)=\frac{\alpha-1}{\alpha}$$
like $El_L(K)=\frac{1}{El_K (L)}$ then $El_K (L)=\frac{\alpha}{\alpha-1}$.
The point is that this values are unequal to one.

Am I interpreting wrong the affirmation? Thanks for your help.