Consider a two-good, two-agent general equilibrium model represented by an Edgeworth box. Consumer 1 has preferences represented by a utility function U(r, y) = ry. In a competitive equilibrium this consumer receives a bundle (2,y) = (2, 4). What is a price pair for æ and y that satisfies the competitive equilibrium? %3D O P1,Py = 2 O P. = 2,P, 4
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- A husband and wife would produce incomes Yh and Yw in their fallback situations. The utility each derives in any circumstance is just equal to his or her consumption expenditure in that circumstance. In their fallback situations, their consumption expenditure levels are just equal to their incomes. Thus their fallback levels of utility are Yh and Yw. If they cooperate, they produce Z>Yh + Yw. They engage in Nash cooperative bargaining to determine how to allocate Z across the consumption of the husband, Ch, and consumption of the wife, Cw, subject to the budget constraint that Ch + Cw = Z. Under any bargained allocation, the two would derive utilities of Ch and Cw. a) The surplus associated with cooperation is S = Z − Yh − Yw. Show that each spouse consumes his or her fallback income plus half the surplus in the Nash cooperative bargaining solution. Please do fast ASAP fast please.A husband and wife would produce incomes Yh and Yw in their fallback situations. The utility each derives in any circumstance is just equal to his or her consumption expenditure in that circumstance. In their fallback situations, their consumption expenditure levels are just equal to their incomes. Thus their fallback levels of utility are Yh and Yw. If they cooperate, they produce Z>Yh + Yw. They engage in Nash cooperative bargaining to determine how to allocate Z across the consumption of the husband, Ch, and consumption of the wife, Cw, subject to the budget constraint that Ch + Cw = Z. Under any bargained allocation, the two would derive utilities of Ch and Cw. What do Ch and Cw equal if Yh = Yw (but this quantity is not equal to zero)? Please do fast ASAP fastFor 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.
- A Gain from Trade occurs when a unit is sold for a price greater than the unit of the good is worth to a seller and, simultaneously, bought for a price less than the good is worth to a buyer. Consider the first 2 units of the good that would be sold in this market (the vertical red line on the graph). Which answer choices are correct? If Kai and Mint sold one unit each to Gob and Yam at a price of $6, the trade would be mutually beneficial. At a price of $6, Gob would benefit by $3 because she is paying $6 for a unit of the good which is worth $9 to her. At a price of $6, Kai would benefit by $4 because she is getting $6 for a unit of the good which is worth $2 to her. For the first 2 units of the good there is potential gain from trade of $7 for each of the 2 units. For the first 2 units of the good sold the difference between the value to buyer and seller is $9 each. This means there is a potential gain from trade of $9 per unit. If the first 2 units of the…The market-clearing equations of a general equilibrium model with two markets are given as in1/(w/p)2 = 96 =aw/pwhere a > 0 is some fixed parameter. Under what condition(s) on ? does there exist a general equilibrium?1.) In an endowment economy with market exchange, let two consumers have preferences given by the utility function U^{h}=(x_{1}^{h})^{a}*(x_{2}^{h})^{1-a}for consumer h (1,2) with endowments given by\omega _{1}^{1}=6, \omega _{2}^{1}=4, \omega_{1}^{2}=4, and \omega_{2}^{2}=6. a.) Calculate the consumers' demand functions. b. Selecting good 2 as the measure of value (i.e. p2=1) and with alpha=1/4, find the equilibrium price of good 1 which implies equilibrium levels of consumption of both goods for both consumers. c. Demonstrate whether both consumers' indifference curves are tangential at the equilibrium. Demonstrate whether both consumers' indifference curves are tangential at the initial endowment.
- Consider the following simplified bargaining game. Players 1 and 2 have preferences over two goods, x and y. Player 1 is endowed with one unit of good x and none of good y, while Player 2 is endowed with one unit of y and none of good x. Player i has utility function: min{xi, yi} where xi is i's consumption of x and yi his consumption of y. The "bargaining" works as follows. Each player simultaneously hands any (nonnegative) quantity of the good he possesses (up to his entire endowment) to the other player. (a) Write this as a game in normal form. (b) Find all pure strategy equilibria of this game. (c) Does this game have a dominant strategy equilibrium? If so, what is it? If not, why not? Please show all work. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.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.Suppose that consumer I has the utility function u(x,y) = x + 2y and consumer II has the utility function u(x,y) = min{x, 2y}. Consumer I initially has 12 units of y and zero units of x, while consumer II has 12 units of x and zero units of y. It is correct to state that, in competitive equilibrium, the agents' consumption basket will be:
- Suppose the household’s preferences are given the following forms: u(c)=log(c), v(l)=log(l), that ß=2/3, and that the production functions are given by: F1(L)=L1/2 and F2(K)=K1/2. a) What are the equilibrium conditions? Derive them. b) What are the quilibrium quantities?Give typing answer with explanation and conclusion Consider an exchange economy consisting of two people, A and B, endowed with two goods, 1 and 2. Person A is initially endowed with ωA = (0,10) and person B is initially endowed with ωB = (11,0). They have identical preferences, which are given by U^A(x1,x2) = U^B(x1,x2) = x1^2*x2. Suppose that p2 =1. Under the competitive equilibrium, what is p1? Round answers to two decimal places.Consider two consumers (1; 2), each with income M to allocate between two goods. Good 1 provides 1 unit of consumption to its purchaser and units of consumption to the other consumer. Each consumer i, i = 1; 2, has the utility function is consumption of good 1 and is consumption of good 2. a. Provide an interpretation of α. b. Suppose that good 2 is a private good. Find the Nash equilibrium levels of consumption when both goods have a price of 1. c. By maximizing the sum of utilities, show that the equilibrium is Pareto-ancient if α = 0 but incident for all other values of α. d. Now suppose that good 2 also provides 1 unit of consumption to its purchaser and a, 0 ≤ α ≤ 1, units of consumption to the other consumer. For the same preferences, find the Nash equilibrium and show that it is ancient for all values of α. e. Explain the conclusion in part d.