Consider a two-person economy and both have the same utility function U(x) = x +Jx,. The ggregate endowment is (w,w,) = (200,100). The Walrasian equilibrium price ratio is а) 10 b) 2 c) 20 d) ½
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- For this and a and b problems, consider a partial equilibrium model with two households with preferences given by u1(x1, m1) = 2 ln (x1 + 1/6) + m1 and u2(x2, m2) = 3 ln(x2+1/3)+m2, and two firms with cost functions for the production of good 1 given by c1(y1) = y 2 1 and c2(y2) = y 2 2 Find the demand function for good 1 of each household and the market demand function for good 1, and illustrate each household demand and the market demand curves in a graphic. a. Find the supply function for good 1 of each firm and the market supply function for good 1, and illustrate each firm supply and the market supply curves in a graphic. b. Find the competitive equilibrium price for good 1, as well as the equilibrium demand of each household, the equilibrium supply for each firm, the households’ utility in equilibrium, the firms’ equilibrium profits, the consumer surplus, the producer surplus, and the total surplus.There is a city, which looks like chopped isosceles triangle, as shown below. Citizens live uniformly distributed all over the city. Two ice-cream vendors, A and B, must independently set up stores in the city. Each citizen buys from the vendor closest to their location and when equidistant from both vendors they choose by coin toss. Each vendor’s aim is to maximize the expected number of customers. A choice of location by the two vendors is a Nash equilibrium if no vendor can do better by deviating unilaterally. Does this game have a Nash equilibrium? If so, describe it. If not, explain why notConsider a two-person exchange economy in which initial endowments for both individuals are such that (e1 = e1) = (1,1). Suppose the two individuals have the following indirect utility functions: V1 (x, y) = ln M1 - a ln Px - (1-a) ln Py V2 (x, y) = ln M2 -b ln Px - (1-b) ln Py Where Mi is the income level of person i and Px and Py are the prices for goods x and goods y, respectively. a) Calculate the market clearing prices.
- In a standard economic model, we generally assume the individual only cares about their own payoff. So, for example, utility of individual i is given by u = pi, where pi is the individual’s payoff. Suppose the individual is playing a dictator game with another partner j. How would you modify the utility function to explain the non-zero allocations to the partner that are typically observed?Economic agents for example consumers or firms often do things Economic agents (for example, consumers or firms) often do things that at first glance seem to be inconsistent with their self-interest. People tip at restaurants and when they are on vacation even if they have no intention to return to the same place. Firms, sometimes, install costly pollution abatement equipment voluntarily. How can these deviations from Nash predictions be explained? Economic agents for example consumers or firms often do thingsDemonstrate the concept of coordination failure by using the payoff matrix and prove that, Coordination failure among economic agents can lead to an inefficient outcome while the opposite can guide to an efficient outcome. Use any hypothetical scenario to justify your analysis.
- Bluth’s preferences for paper and houses can be expressed as Ub(p, h) = 2pb + hb, while Scott’s preferences can be expressed as Us(p, h) = ps + 2bs. Bluth begins with no paper and 10 houses, whereas Scott begins with 10 units of paper and no houses. 1. Is the starting endowment Pareto efficient? Justify your answer using an Edgeworth box? Determine whether each of the following price pairs is consistent with a competitive equilibrium. If yes, determine the resulting allocation of goods, sketching that equi- librium in your Edgeworth box. If not, explain why not (for what good is there a shortage, for what good is there a surplus?) pp =$3 and ph =$1 along with pp =$1 and ph =$1 Assume that the price of houses is $1. Given that price, determine the highest price pp that is consistent with a competitive equilibrium.For a certain company, the cost function for producing x items is C(x)=30x+200 and the revenue function for selling x items is R(x)=−0.5(x−110)2+6,050. The maximum capacity of the company is 170 items. The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit! 1. Assuming that the company sells all that it produces, what is the profit function? P(x)= ? 2. What is the domain of P(x)? 3. The company can choose to produce either 80 or 90 items. What is their profit for each case, and which level of production should they choose? Profit when producing 80 items=? Profit when producing 90 items=?For a certain company, the cost function for producing x items is C(x)=40x+150 and the revenue function for selling x items is R(x)=−0.5(x−90)^2+4,050. The maximum capacity of the company is 130 items. The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit! 1. Assuming that the company sells all that it produces, what is the profit function? P(x)= 2. What is the domain of P(x)? 3. The company can choose to produce either 50 or 60 items. What is their profit for each case, and which level of production should they choose? 4. Can you explain, from our model, why the company makes less profit when producing 10 more units?
- Consider a Bertrand (price choice) model where firms have identical costs. The equilibrium price is the same whether there are two or three firms in the market. (a) True. (b) False.According to the marginal decision rule, if marginal benefit: Group of answer choices A. exceeds marginal cost, an activity should be increased. B. is less than marginal cost, an activity should be increased. C. exceeds marginal cost, net benefit is maximized. D. is already equal to marginal cost, an activity should be increased.The standard assumption of self-interest implies that in the dictator games with $10 endowment, the dictator should share (A) $0; (B) $2; (C) $5; (D) $10.