5. The traders' utilities are the following u'(x,,x,)= x}*x and u (x,,x,) = x"*x}². Their 2/31/3 1/31/2 initial endowments are a' = (10,10) and a² = (20,5). Traders come to a market and exchange commodities to maximize their utilities. Compute the price vector in equilibrium. Compare the utilities before and after the exchange.
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- Consider 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 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)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.
- Problem 5 Consider an exchange economy with two people: Will and Bob; and two goods: apples and bananas. Will's initial endowment is 10 apples and 5 bananas. Bob's initial endowment is 5 apples and 10 bananas. Will likes apples and hates bananas. Bob likes both apples and bananas. The preferences of both Will and Bob are strictly convex. (a) Draw an Edgeworth Box with apples on the horizontal axes. Put Will at the bottom left corner and Bob at the top right corner. Show the initial endowment and label it with W.Now,suppose N=3 with a market clearing interest rate. The first two agents are the same as earlier. The third agent has an endowment of 20 in the first period and consumes 15 in the second period. If the first two agents each consumed 21 units in the first period, how much did the third agent consume in the first period? Plz do fastConstructing an equilibrium Households live two periods and have prefernces U(c1)+βU(c2) where 0<β<1 and U is the utility function and satisfies our usual assumptions. There are N households in the economy. N1 of these have endowments y1 in the first period and no endowment in the second-these agents are called "Type 1". The remaining N2 have no endowment in the firs period and y2 in the second period- these agents are called "Type 2". Hencethe resources of the economy are N1y1 in the first period and N2y2 in the second, where N=N1+N2 Households have access to a credit market where the can borrow (s<0) or save s<0. The type 1 agent faces budget constraints y1=c11+s1 rs1=c21 where the consumption for the type i agent in period j is denoted cji. The type 2 agent faces budget constraints 0=c12+s2 y2+rs2=c22 The resource constraints are N1y1=N1c11+N2c12 N2y2=N11c21+N2c22 a) state the maximization problem solved by each type of agent and derive the fist order and second order…
- Households live two periods and have prefernces U(c1)+βU(c2) where 0<β<1 and U is the utility function and satisfies our usual assumptions. There are N households in the economy. N1 of these have endowments y1 in the first period and no endowment in the second-these agents are called "Type 1". The remaining N2 have no endowment in the firs period and y2 in the second period- these agents are called "Type 2". Hencethe resources of the economy are N1y1 in the first period and N2y2 in the second, where N=N1+N2 Households have access to a credit market where the can borrow (s<0) or save s<0. The type 1 agent faces budget constraints y1=c11+s1 rs1=c21 where the consumption for the type i agent in period j is denoted cji. The type 2 agent faces budget constraints 0=c12+s2 y2+rs2=c22 The resource constraints are N1y1=N1c11+N2c12 N2y2=N11c21+N2c22 a) state the maximization problem solved by each type of agent and derive the fist order and second order conditions. Derive the…If A has TIOLI power in an exchange, which of the following are true? a. Person A will capture most or all of the gains from trade. b. Person B will lose utility compared to their initial endowment. c. A Pareto-efficient outcome is assured. d. Person B could gain utility if they agree to A's offer.Which of the follwoing theoretical results is concerned with the relationship of factor endowments and the distribution of payoffs in an economy? Rybczynski Theorem Ricardian Equivalence Heckscher-Ohlin Theorem Stolper-Samuelson Theorem
- Dear tutor, please solve these True/False Questions. Thank You! 1. Any point on the contract curve is Pareto efficient regardless of the initial endowment. 2. When two people trade their initial endowments to a point on the contract curve, only the level of the endowments will determine the new allocation.In this problem, we want to think about the difficulties that governments face in agreeing to significantly reduce CO2 emissions in order to control climate change. In the context of climate change, what phenomenon does China’s utility function capture? What does this exercise tell us about the limitations of the first welfare theorem? What do you think is an important aspect of trade in reality which is not captured by this model? Provide detailed analysisConsider 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.