9

The posted quote is economic nonsense. If a lender chooses to innovate and reduce cost to borrowers in order to secure a larger share of the market, the competing lenders will instantly do the same, negating the effect. This applies to any industry without intellectual property protection -- it is hardly unique to the payday loan industry. By this logic, ...


7

Thus, the furthest we can go in terms of characterising the equilibrium in this economy/firm relates to the optimal capital-labour ratio. In effect, nothing can be said about the level of inputs and outputs, $L^*$, $K^*$, or $Y^*$. I don't think this is true. You combined two equations into one, and thereby lost information. The optimization problem is \...


7

Answer to question If we take your assumptions literally, Jim will decide not to enter the widget business. For suppose he did incur the cost of entry and that Mary is selling at price $p_m$. Jim can only sell to consumers if his price $p_j\leq p_m$. The best price for Jim is $p_m-\epsilon$ (where $\epsilon$ is some very small, positive amount). But this ...


6

Competitive Equilibrium A competitive equilibrium ("Walrasian Equilibrium")'s defining characteristic is that it's competitive. It's about an equilibrium in which market forces (say, consumers, firms)' supply and demand responds to prices, and prices respond to supply and demand, and no Pareto-improving trade possibility remains in the end. To be technical,...


6

Yes. The Debreu version of the Sonnenschein-Mantel-Debreu theorem guarantees that excess demand has to satisfy very little restrictions if there are as many consumers as commodities. An explicit example of multiple equilibria in a $2\times 2$-exchange economy can be found in Shapley, L. S., and M. Shubik. “An Example of a Trading Economy with Three ...


6

Nobody has to loose in an arbitrage. Economic relationships are not necessarily zero-sum (in fact often they will not be zero-sum). For example, if apples in city A are sold for ${\\\$}5$ and apples in city B can be sold for ${\\\$}8$, and we assume zero transaction cost there will be an arbitrage opportunity to earn ${\\\$}3$ riskless profit per apple by ...


6

Here is an example where the two are actually compatible: The consumer's utility function $U:\mathbb{R}_+\to\mathbb{R}$ is given by $U(c,1-n_ns)=c-n_s$, the initial labor endowment is $1$ and $F:\mathbb{R}_+\to\mathbb{R}$ is given by $$F(n)=n(1-e^{-n}).$$ This function has IRTS, but still turns a unit of labor into less than one unit of consumption at any ...


5

Strict convexity of preferences is not needed in existence results for competitive equilibria. Leontief preferences are quite well-behaved. They are continuous, convex, and strongly monotonic. If all endowments are strictly positive, the existence of a competitive equilibrium in an exchange economy (or a production economy satisfying standard conditions) ...


5

Let $a+b<1,\;\; a,b>0$. Pay the factors of production their marginal product: $$rK = \frac {aQ}{K} K= aQ,\;\;\ wL=\frac {bQ}{L} L=bQ$$ So total payments to factors of production will be $$rK +wL = aQ + bQ = (a+b)Q < Q$$ And the question is: who gets the rest of the output that has been produced?


5

The Pigovian taxes are non-distortionary. For example imagine situation where government optimal spending is 100e and before Pigovian tax all 100e was raised through income tax which creates distortions on Labour market. Let’s say that after imposing Pigovian tax government gets additional 30e. Now since government needs only 100e for its optimal spending it ...


5

It's important to distinguish between the effects of arbitrage on: a) the direct parties to arbitrage transactions; b) other agents in the markets in which the arbitrage takes place. Suppose arbitrageurs buy a good in market A in which its price is \$1 and sell in market B where its price is \$2. Assume further that in each market those prices have freely ...


4

Computing an equilibrium is not needed for implementing it. This was the mistake of Lange and co. and was decisively rebutted by Hayek. If you want a mathematical formulation, simply take a tatonement process. Given prices, each individual needs to compute her net demand correspondence. Under different tatonement mechanisms, which are an idealization of the ...


4

Here is another example with two consumers (A and B), two goods (X and Y): \begin{eqnarray*} u_A(x_A, y_A) & = & \min(x_A, y_A), \ \omega_A = (1, 0) \\ u_B(x_B, y_B) & = & \min(x_B, y_B), \ \omega_B = (0, 1) \end{eqnarray*} In this case, every feasible allocation $((x_A, y_A), (x_B, y_B))$ satisfying $y_A = x_A$ is a competitive equilibrium,...


4

Any constant returns to scale function is compatible witha competitive economy. Cobb-Douglas is not the only one. Google CES production function. Also, product can be wasted or be an externality, so even in non CRS competitive economy can exist.


4

Consider an economy with two commodities. Production is trivial, $Y=\{0\}$, there is a single consumer with endowment $(1,1)$ whose preferences are represented by the utility function given by $u(x_1,x_2)=\max\{x_1,x_2\}+1/2\cdot x_1 +1/2\cdot x_2$. These preferences are continuous, strictly monotone, but not convex. You can verify that there is no ...


4

Note that: (i) exploitation of returns to scale is not without limits when $n_s \leq 1 $ (this actually excludes global returns to scale for any value of $(c,n)$) (ii) the firm can produce something from nothing as $F(0) \geq 0$ In this case the Figure below illustrates that a competitive equilibrium with positive profit can exist. Given (i) and (ii), the ...


4

In the Varian textbook Intermediate Microeconomics (I am guessing in most micro textbooks), the chapter on Equilibrium discusses price controls in the presence of a demand and supply function. You can apply that discussion directly to the (competitve) labor market, were the price of labor is of course the wage.


3

As one of the comments points out, there are many models of equilibria in insurance markets. But it sounds to me like you are referring to the Rothschild-Stiglitz (1976) paradigm. I will provide a basic summary of the key takeaways here, but there is a more complete explanation in this set of slides and in those from any second-year graduate course in Public ...


3

Each curve simply shows the amount of goods that producers would supply at given prices and how many units of goods consumers would demand at all the different prices. Let's say the price of wooden chairs would be 5 million Euros. Producers would want to supply a large quantity of wooden chairs, since they're so profitable. Consumers would likely demand very ...


3

It depends on the assumptions you make. If you assume that preferences are locally insatiable then no. Without this assumption, it is easy to construct counterexamples. Consider an economy with two consumers ($A,B$) and two goods ($x,y$). Both consumers have preferences represented by their utility function $$ U_i(x_i,y_i) = \min(x_i,1) + y_i. $$ If the ...


3

Generally the fixed-points of Nash Equilibria in a market can also be reached by a dynamic process where actors myopically best-reply to the market result in the last period (see Milgrom and Roberts 1990). The process will converge to a steady state, which is the equilbrium. What this means is that actors do not need to know anything about the market ...


3

The "trick" of this question is that the fact that agents do not want to trade at the given prices does not mean the allocation is Pareto. The only thing you know is that if there is an allocation that is not a CE, there exists a vector of prices at which agents want to trade. Let me give an example: You have 2 apples and I have 2 bananas. I'm willing to ...


3

In a competitive market for a private good (y) individuals may consume different quantities but the equilibrium condition requires that: $$ \frac{\frac{\delta u^{i}}{\delta y}}{\frac{\delta u^{i}}{\delta x}} = MRS^{i}_{yx} = MRT_{yx} \; \forall \; i $$ In the case of a public good (g) individuals may have different MRS but consume the same amount of the ...


3

Still, not 100% clear whether I get the question right, but in models with constant returns to scale and decreasing marginal productivity (question to others, are these conditions even necessary?), if firms are price takers in product and labor markets (no pricing power in which case you could look into monopsony models, see for instance the textbook "...


3

Summary The equilibrium wage will decrease. The reasoning is that, due to the output constraint, total labour demand will go down. Then because of the fixed labour supply (and the fixed price of capital), this makes it that the equilibrium wage falls. Derivation We have the first order condition for the (aggregate) labor demand. $$ l = (1-\alpha)^\alpha W^{-\...


3

This is my attempt. The final result is a set of equilibrium equations, which I will not attempt at solving. The consumer: $$ \max \ln(x) + \gamma \ln(b) \text{ s.t. } p_1 x + w b = w L + \pi_0 + \pi_1. $$ This is Cobb-Douglass so: $$ \begin{align*} &x_1 = \frac{1}{1 + \gamma} \frac{(wL + \pi_0 + \pi_1)}{p_1},\tag{1}\\ &b = \frac{\gamma}{1 + \gamma} \...


2

The question "how are the first order conditions" seems very unclear to me, and I am providing a set-up for finding and writing them out, while explaining the Kuhn-Tucker conditions that are easy to struggle with. Though we try to avoid giving away basic study question answers, it's a positively voted question without an answer, and I still think these ...


2

The preferences of agent $A$ cannot be represented by any utility function and the prefeences of $B$ not by a differentiable utility function, so forget calculus approaches. Since $A$ has strictly monotone preferences, we must have $p_1>0$ and $p_2>0$ for every equilibrium. Also, $A$ is always willing to give up any amount of good $2$ to get more of ...


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