10

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,...


5

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 ...


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?


4

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) ...


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

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.


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

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,...


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 ...


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 ...


2

If you look at this manuscript by Jonathan Levin (2006), pages 25-26 provide an example where there is multiple equilibria, and calculating payoffs in this case (if I am not making any calculation mistakes) gives different levels of utilities in these different equilibria.


2

One of the assumptions of perfect competition is that firms are price takers. Ultimately price is determined by the quantity of goods supplied, and with perfect competition, there are infinite (or an arbitrarily large) number of firms, so a firm that changes their price by itself will simply have no business, since there are cheaper places to buy from. The ...


2

Forgive me in advance if this is already familiar. I'll be talking about stability of equilibrium the way I (briefly) learned it. Let $\xi^j(p)$ denote the excess demand for good $j$ given price $p$. $$\xi^j(p) = \sum^m_{h=1}\left( x^j_h(p) - e^j_h \right) = x^j(p) - r^j$$ For $m$ households/consumers, $e$ being an endowment to a household, and $r^j$ ...


2

So this seems to be a known issue. Quoting from the Wilson article of 1980, The Nature of Equilibrium in Markets with Adverse Selection: Using a variant of Akerlof's model of the used car market, we examine the equlibrium of the model under three distinct conventions: (1) an auctioneer sets the price; (2) buyers set the price; (3) sellers set the price. ...


2

In order to talk about whether the competitive equilibrium is also a Nash equilibrium, you first have to properly define a game. For instance, is the buyers setting the prices or the sellers or is there bargaining. How do they meet, are there search costs etc. And importantly, what is the order of events! Your reasoning implicitly assumed that buyers would ...


2

Yes, it is possible. In the long run, firms enter until they break even. Suppose firms are symmetric. Then for each firm the break even condition is that the average costs equal the price. This is because the price is equal to the average revenue. The average revenue is given by $px/x=p$ where $p$ is price and $x$ is quantity. If revenue equals costs on ...


2

This is a paper using a competitive monopolistic framework (in GE). It is an old paper by Stratz (1989). Recent work with Stone-Geary preferences relates to the issue of structural transformation following the work of Herrendorf, Rogerson and Valentinyi (2013), although there is considerable debate on whether these preferences appropriately capture the data. ...


2

"Most likely" is not a precise term. Given the available information it is quite possible that an equilibrium does not exist. In that case we can't really tell what will happen.


2

A situation can be Pareto efficient without also being a Pareto improvement over every other situation. So, here for example, equilibrium is Pareto efficient, but -- as you have noted -- is not a Pareto improvement over every other situation. Example. Say I have 100 apples to divide between A and B. The allocation (60, 40) is Pareto efficient, but it is ...


1

There is the famous Cobweb model. Starting from a situation of equilibrium, it analyses the effect of a shock, and how long it takes to reach the equilibrium, which depends entirely on the elasticities (or slopes) of demand and supply. Thus, by estimating empirically such elasticities for a given period (e.g. year), you can predict/forecast how many periods (...


1

As a starting point, you might take a look at Stigler's model of price dispersion. Quoting from a resource I found online, George Stigler’s 1961 “The Economics of Information” begins with: "One should hardly have to tell academicians that information is a valuable resource: knowledge is power. And yet it occupies a slum dwelling in the town of ...


1

It appears we start at long-run equilibrium point. The fact that all firms operate at the level where $q^*:MC = \min AC$, means that given demand $Q^d$ and the cost structure, what is endogenously determined is the number of firms $m$: $$Q^d = mq^* \implies m^* = \frac {Q^d}{q^*}$$ Assume that aggregate demand increases. In the microeconomic setting we ...


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