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## Hot answers tagged microeconomics

12

The full quote from the cited reference (p. 181) is Marginal cost is not the cost of producing the "last" unit of output. The cost of producing the last unit of output is the same as the cost of producing the first or any other unit of output and is, in fact, the average cost of output. Marginal cost (in the finite sense) is the increase (or decrease) in ...

7

This looks like constant relative risk aversion (CRRA) utility . Usually CRRA is written like $U = \frac{C^{1-\rho}-1}{1-\rho}$ (I omitted second part for brevity) in your case $a=1-\rho$. $\rho$ is the relative risk aversion. By extension $a$ is the function of $\rho$ so as $a$ increases (due to smaller $\rho$) the person should become less risk averse.

5

One interpretation I can offer. The demand function can be expressed as: $$Q_1 = Q_1(p_1,p_2)$$ Let us take the total differential: $$dQ_1 = \frac{\partial Q_1(p_1,p_2)}{\partial p_1}dp_1+\frac{\partial Q_1(p_1,p_2)}{\partial p_2}dp_2$$ Assume that $Q_1$ remains unchanged with respect to a change in prices. This implies that $dQ_1=0$. Solving the ...

5

Complete market is a market where every possible asset or good can be assigned a price and where you have perfect information, can make perfect contracts and zero transaction costs. Any market can be complete regardless of its market structure. So you can have complete market dominated by monopoly, or oligopoly or monopolistic competition etc. Perfectly ...

4

Yes it can be used. The theory applies regardless of what’s the source of comparative advantage. For example, if country A is able to produce 200 widgets and 50 apples and country B is able to produce 5 widgets and 45 apples you get comparative advantages - A in widgets and B in apples - and it does not really matter if these are due to technology, ...

4

With my very limited knowledge of development economics: $\left(\frac{x_m}{x}\right)^\alpha$ represents the proportion of the population that has an income larger or equal to $x$ where $x\geq x_m>0$ and $x_m$ is the minimum income amount. Example 1: Suppose $\alpha\rightarrow 1$ and the minimum income in the economy is $50,000$. We may ask the ...

4

Suppose that the vector $W=\left(w_1,w_2,\dots,w_n\right)$ represents wealth in $n$ possible states. In addition, assume the probability of each state occurring is represented by the vector $\pi=\left(\pi_1,\pi_2,\dots,\pi_n\right)$. We can express this as the simple gamble: $$g = \left(\pi_1\circ w_1,\pi_2\circ w_2, \dots, \pi_n\circ w_n\right)$$ The ...

4

Opportunity cost is the price of doing something in terms of something else. For example, cost of taking trip to Prague may be giving up new bike. In this broad sense marginal cost of producing one unit of q would be also it’s opportunity cost because you could use the same resources to produce something else. Opportunity cost of producing 1 widget at 5€ ...

4

There is no distinction between money in microeconomics or macroeconomics. In both fields money is medium of exchange, unit of account and store of value. The misconception you have probably arises from the role money plays in microeconomics and macroeconomics. In microeconomics money is almost always neutral - that is it has no impact on the real ...

3

The two statements are similar. For the website example, you could say that the marginal product of the first 5 workers is 50 units. For the next 5 workers, however, you could deduce that the marginal product is less than 50 units (otherwise "the next 50 units" would require exactly 5 workers, not 10 workers). The website is merely stating that, in order ...

3

At time $(t-1)$, the investor buys some risk free bond, $B_{t-1}$ and some risky asset $X_{t-1}$ at price $P_{t-1}$, such that the budget constraint holds, i.e. $$W_{t-1} = B_{t-1} + P_{t-1}X_{t-1}$$ At period $t$, one unit of risk free bond pays off one unit, so $B_{t-1}$ units of risk free bonds pays off $B_{t-1}$ units of wealth at $t$. For a risky ...

3

Rationality requires the following: Completeness For all $x, y \in X$, either $x \succsim y$ or $y \succsim x$ or both. Transitivity For all $x, y, z \in X$, if $x \succsim y$ and $y \succsim z$, then $x \succsim z$. Also note that if $x=y$ then completeness implies that $x\succsim x$. So reflexive preferences follow from completeness. So I would say ...

3

Your conjecture seems to be contradicted, at least for small values of $\sigma$. You can draw the function with the following R-code: qq_f = function(x,k,h,sig){ -pnorm(-k, sd=sig)*( (dnorm(h*(1-x), sd=sig))^2 ) - 0.5*dnorm(-k^2, sd=sig)*( 2*pnorm(h*(1-x), sd=sig) -1 )^2 } curve(qq_f(x,k=0,h=1,sig=0.5),col='blue',xlim=c(-1,3),type='l',main="A ...

3

Hint: find $\ln(U(x))$ and then use L'Hopital's rule to find the limit as $\rho\rightarrow0$.

2

Marshallian Theory is notoriously about computing consumer surplus (and then welfare changes). But it would be nonsensical to perform such calculations if at the level of one individual, the unit of valuation of surplus, i.e. the marginal utility of money (or the utility of one extra euro), were changing before and after changes in, say, prices. Also, what ...

2

Remember that consistency describes how the estimator behaves in the limit as N asymptotically approaches infinity. Assuming no errors in your math up to this point, you need to consider how your error terms $U_i$ behave asymptotically as well.

2

This thread has some game trees. In case you want put them on your documents, you can do like this (using LaTeX with istgame package): \documentclass{standalone} \usepackage{istgame} \begin{document} \begin{istgame}[font=\scriptsize] \setistgrowdirection{east} \cntmdistance{20mm}{20mm} \cntmAistb{q_1=0}[at end,below]{q_1=1,000}[at end,above] \...

2

The EMH applies to assets, not just stocks, and its implications are more relevant for investors who own part of the market - not the entire thing. This is important, because it's the difference between looking at a closed system versus an open one, and between populations versus samples. People make money all the time by cycling between stocks, bonds, ...

2

hint: you are supposed to show the utility function represents the same preferences not that the utility functions are exactly same. Recall that any monotonic transformations of function preserves the original order of preferences. So you only need to show that in the limit one function is monotonic transformation of the other.

2

By definition, a direct mechanism is a mechanism that asks all agents for their types and then produces some outcome. Formally, it is a mechanism $\langle M,g\rangle$ in which $M_i$ is wlog equal to $i$'s type space, usually denoted by $\Theta_i$. In your example, there is no such restriction. However, for any indirect mechanism there exists an equivalent ...

2

Yes marginal refers to the last or one more unit or person. I don’t see there any contradiction if you have 2 people in room and third person joins it’s both the last person and one more person. If you are looking for a precise definition then in economics the concept of margin is connected to the first derivative (instantaneous rate of change) of function ...

2

The idea of a rational expectations equilibrium is more general than BNE. It simply means that the belief system of agents is consistent with the model and incorporates all available information. This abstract idea can be applied for games, markets or other types of interactions. BNE is a solution concept for non-cooperative games. The expectations being ...

1

The variable unit in the quotation is the factor of production that is varied keeping the others fixed. For example it could be the amount of workers hired, while keeping the amount of machinery (capital) fixed. Or it could be the amount of machines reented, keeping the amount of workers fixed. As for your other question diminishing returns does not refer ...

1

Market sharing simply means that both platforms have some market share. So the condition can probably be obtained by finding the closed-form solution for market shares (not only implicitly as in (7)) and imposing the condition that all market shares are positive. This is akin to each platform having an interior solution. I am not sure which Hessian you are ...

1

The article Quality of Information and Oligopolistic Price Discrimination by Liu and Serfes covers this topic in great detail. It also has a rather nice literature review.

1

Captive insurance is an insurance for purpose of insuring the owners of the said insurance. It’s a kind of self-insurance where multiple agents pool their capital together to insure themselves. So the term in that sentence refers to the pool of resources for insurance. It’s called captive because the modern concept of this kind of insurance was first ...

1

If you want some simple model of stock prices consistent with efficient market hypothesis it would be random walk: $$p_{t+1}= a+ p_t +\epsilon_t$$ You don’t even need to model cycles there explicitly just due to random chance it will exhibit some ‘cyclical-like’ behavior. Although, I know it’s not actual cyclical behavior because it can diverge it’s ...

1

It seems the instructor is referring to the opp. cost of giving up the profit from selling x amount of apples. Which would be an opportunity cost. Opportunity cost isn't strictly alternative based, for example: If I'm selling 10 apples today, the opportunity cost of be only selling 9 apples tomorrow is whatever profit I stand to lose from not selling the ...

1

Utility is not the same as consumer surplus. Consumer surplus is the difference between price an individuals pay and their individual reservation price. Utility is a measure of gratification that can be completely different from consumer surplus and depending on what kind of utility we are talking about it might not even be possible to assign integer value ...

1

If the other two methods did not work out for you, another possibility, albeit a more difficult one: Set up the bordered Hessian: \bar{H}=\begin{bmatrix}0 & \frac{\partial v}{\partial p_1} & \frac{\partial v}{\partial p_2} & \frac{\partial v}{\partial p_3} & \frac{\partial v}{\partial m}\\ \frac{\partial v}{\partial p_1} & \frac{\...

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