Suppose there are two consumers, Az B. The utility functions of each consumer are given by kem xong U₂XX-X²² Therefore For consumer A: MU-2XY; MU, -X² For consumer B: MU-Y²: MU, -2XY The initial endowments are A:X-60: Y-150 B.X-45; Y-75 Suppose the price of Y, Py-1. Calculate the price of X, P, that will lead to a competitive equilibrium How much of each good does each consumer demand in equilibrium? Consumer A's demand for X: Consumer A's demand for Y Consumer 8's demand for X Consumer B's demand for Y ts) What is the marginal rate of substitution for consumer A at the competitive equilibrium
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- 1. Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y) = X*Y UB(X,Y) = X*Y3 Therefore: • For consumer A: MUX = Y; MUY = X • For consumer B: MUX = Y3; MUY = 3XY2 The initial endowments are: A: X = 10; Y = 6 B: X = 14; Y = 19 show all work a) Suppose the price PY = 1. Calculate the price of X, PX that will lead to a competitive equilibrium. b) How much of each good does each consumer demand in equilibrium? Consumer A’s Demand for X: Consumer A’s Demand for Y: Consumer B’s demand for X: Consumer B’s demand for Y: c)What is the marginal rate of substitution for consumer A at the competitive equilibrium?Zach's preferences are representable by the utility function u = 90.3927, where 9₁ and 92 denote his consumption of goods 1 and 2. (Answers to each of these questions are rounded, where required, to two decimal places.) Still assuming endowments of e₁ = 5 and e₂ = 9 and market prices p₁ = 20 and p2 = 30, what is the maximised value of Zach's utility? O Au= 6.74 O B. u = 5.39 O Cu = 5.65 O D.u = 7.56 O E. None of the above1. Suppose that the representative consumer has a utility function defined over consumption over two dates of the form U(C₁, C₂) = c₁²c₂². The general form of the slope of the indifference curve for the representative consumer is - C₂/C₁. Moreover, remember that c₁ = y₁ − S and C₂ = y₂ + s(1 + r). a. Assume that the representative consumer has an endowment of consumption goods in the two periods of y₁ = 20 and y₂ = 10. Assuming an interest rate r = 1, compute the equilibrium allocation and the implied savings. b. Suppose that, because of an attack of pessimism, the representative consumer assumes that future income will drop so that y₂ = 0. What happens to the savings s in the first period? c. In the previous part, the interest rate remained at 1. Now, consider the savings function, that is, the relationship between the real rate of interest and the amount saved. The equilibrium interest rate is then determined as a market price in the Saving-Investment diagram. Given the typical shape…
- Exercise 4 Consider an economy with two consumers, Alexia and Bart, who live two periods, t = 0 and t = 1. In each period they can consume one type of good and their preferences for consumption are given by U (co, ci) = c(ci)² _i = A, B. Alexia and Bart have the following endowment of good in each period M=1, M₁ = 1, MB = 2, MB = 2. In t = 0, Alexia and Bart can exchange a financial contract for the delivery of one unit of consumption good in t = 1 (a bond). Name p the price of the bond and b² the amount bought by agent i = =A, B. (a) Write down each agent's utility maximization and budget constraints assuming that he/she can trade the bond without restrictions. (b) Find each agent's optimal quantity b² as a function of the bond net return r. (c) Find the equilibrium value of r and the equilibrium demand/supply of each agent.Suppose Jimi has reference dependent preferences over guitars and money as in Tversky and Kahneman (1991). His utility functions are given below. Gains Gains 400 -2 -2 2 Guitars 2$ Losses Losses i-600 -2 What is the least amount of money Jimi is willing to accept to sell one of his guitars? (just enter a dollar amount, i.e., "10o0", not "$1000"Suppose the consumer's utility function is given by U(x,y) = X3/5y2/5, and the exogenous variables are given by M = 500, Px = 5, and Py = 4. Price of y changes to Py = 2. What is the income effect ony?O A.-14.53O B. +14.53O C. +24.21O D. +25.79O E. None of the above Note:- Please avoid using ChatGPT and refrain from providing handwritten solutions; otherwise, I will definitely give a downvote. Also, be mindful of plagiarism. Answer completely and accurate answer. Rest assured, you will receive an upvote if the answer is accurate.
- L 2nd attempt In a two-good market, a consumer starts with an initial endowment of (x1, x2) = (2.00, 3.00), while the market prices for these goods are given by (p1, p2) = (1.00, 8.00). The consumer has the following utility function: U = x0.540.46 1 Given this information, what will this consumer's final choice of quantity for each good be? X1 = x2 = ||2. General Equilibrium. consumers, each with the same Cobb-Douglas preferences except with differ- ent parameters. Consumer 1 has utility function u(x, x)= (x})"(x})!-«, while Consumer 2 has utility function u(x, x;) = (xP(x)-P. The endowment of good j owned by consumer i is denoted w. The price of good 1 is p, and the price of good 2 is 1. In the superscript, we denoted the consumer i = 1,2; in the subscript, we denote the good j= 1,2. Consider an exchange economy with two Write the maximisation problem faced by each consumer i = (a) 1,2, taking care to define the objective function and the budget constraint. Set up the Lagrangian and find the first order conditions. (b) For each consumer i = 1,2 , use the first-order conditions to determine the demand functions for each consumer i = 1,2 and for each good j = 1,2, in terms of the price p. (c) Find the aggregate demand for each good j = 1,2 and clear the markets for each good. Hence, show that the equilibrium price pi is given by the…A and yд are his = XBYB, Alberto's utility function is u(xA, YA) = min{A, YA}, where consumptions of goods and y. Bella's utility function is u(XB, YB) where x³ and yß are her consumptions of goods and y. Alberto's endowment is 5 units of x and no y. Bella's endowment is 11 units of y and no x. If x is the numeraire and p is the price of y in units of x, then in a competitive equilibrium ○ 11/5 = p 11/(p+1) +2.5 = 11 O min{5, 11}+11/2p=11 O min{5, 11}+5/2p=11 ○ 5/(p+1) +5.5 = 11
- q 14. suppose that MUx=10 and MUy=20. Furthur suppose that the consumer's budget constraint can be expressed as 20x+10y=400. For this consumer, the optimal amount of good x to buy would be.9. Consider an Edgeworth box economy with two consumers, whose utility func- tions and endowments are e' = (5,5) 2 = (5,5) In the following, use the normalization p2 = 1. (a) Find the competitive equilibrium price. (b) State the first fundamental theorem of welfare and verify that it holds in this economy. (e) Consider the allocation ã = (x',) = (2,3), (8, 7). Show whether this allo- cation can supported as an equilibrium with transfers. (d) State the second fundamental theorem of welfare, and briefly discuss whether the result in part (c) conform with or violate this theorem.3. Christina loves pizza and hates burger. Her utility function is U(p – b) = p – 6", where is the number of pizzas she consumes and b is the number of burgers she consumes. John likes both pizza and burger. His utility function is U(p, b) = p + 2\b Christina has an initial endowment of no pizzas and 8 burgers. John has an initial endowment of 16 pizzas and 8 burgers. a. Graph the initial endowment and label it E b. If Christina hates burgers and John likes them, how many burgers can Christina and John be consuming at a Pareto optimal allocation? What is John's marginal utility for pizzas and burgers? Mark the locus of Pareto optimal allocations of pizzas and burgers between Christina and John on the grapsh above.