Consider trade between two consumers (1 and 2) and two goods, X and Y. Suppose the total quantities of each good are 100 units. Each consumer has Cobb-Douglas preferences given by: U(X,Y) = XY Denoting by X1 the first consumer's consumption of X and by Y1 the first consumer's consumption of Y, the contract curve consists of all allocations where A. X1 = 0.5Y1 B. X1 = 2Y1 C. X1 = Y1 square D. X1 = Y1 %3D %3D
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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 fastIn an exchange economy, there are two people (Shadi and Nino) and two goods (x1 and x2). Their initial endowments are ωS = (2, 4) and ωN = (3, 6). Their utility is given by the following functions: US(x1,x2) = x12x23 and UN(x1,x2) = x1x24. Which of the following is the equation for the contract curve? Group of answer choices a. x2N = 96x1N / (15 + 4x1N) b. x2N = 47x1N / (8 + 4x1N) c. x2N = 91x1N / 5 d. x2N = 16x1N / (3 + x1N) e. x2N = 41x1N / (9 + x1N)
- 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.Consider an economy with 2 goods and 30 agents. There are 10 agentseach with the utility function u (x1; x2) = ln x1 + 2 ln x2 and endowments e = (3; 1).Also, the other 20 agents each have the utility function u (z1; z2) = 2 ln z1 + ln z2 andendowments e = (1; 2). Normalize p2 = 1. Calculate the Walrasian equilibrium pricep1*Suppose there are 3 agents i ∈{1, 2, 3} with preferences over 3 objects j ∈{a, b, c} as follows: 1 : c b a 2 : b c a 3 : b a c Consider the random allocation given by the following probability shares: Agent Good a b c 1 0.5 0 0.5 2 0.25 0.5 0.25 3 0.25 0.5 0.25 Is this allocation ordinally efficient? Is it ex-ante weakly envy-free? Be sure to explain how you arrived at your answer.
- In a pure exchange economy with two goods, G and H, the two traders have Cobb-Douglas utility functions. Suppose that Tony’s utility function is UT = GTHT and that Margaret’s utility function is UM = GM(HM)2. Between them, they own 100 units of G and 50 units of H. a. Please solve for their contract curve. b. Please solve for the demand functions for the two goods for both Tony and Margaret, assuming p is the competitive price of G, and the price of H is normalized to equal one.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.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.
- consider an exchange economy with 2 goods (1 and 2) and 2 consumer (A and B). a bundle with x units of good 1 and y units of good 2 is written as (x,y). consumer A has an endowment (4,0) and consumer B has an endowment (12,12). the 2 goods are perfect substitutes for each consumer. consider an allocation in which A receives (1,9) and B receives (15,3) if we can redistribute endowments suitably, it is possible to obtain this allocation as the outcome of a competitive equilibrium. is this true or false? explain carefullySuppose Mr. and Mrs. Ward agreed not to vote in tomorrow’s election. Would such an agreement improve utility? Would such an agreement be an equilibrium?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…