Both Markets are in Equilibrium There is Excess Demand in the Market for Good X = 2.4 There is Excess Demand in the Market for Good Y = 0.8 There is Excess Supply in the Market for Good Y = 1.6 There is Excess Supply in the Market for Good X = 1.6
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- Consider an economy with 2 goods and 2 identical agents, each of whom has the following utility function, u (x1; x2) = ln x1 + 2 ln x2. The aggregate endowments of the 2 goods are given by (1; 2). Suppose there is a social planner who cares about agents equally.(a) Set up the plannerís problem. Calculate the first-best outcome1.) 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.Let Utility Function be U = min {X, Y} As given Endowment of Good 1 and Good 2 is 100 and 200 respectively. Suppose that price of good x increases from 10 to 15 and price of good y is 10 , then Calculate Endowment Income effect
- Please draw its diagram Consider the following pure exchange economy with two consumers and two goods. Consumer 1 has utility given by U1 = min {4x1, 2x2} Consumer 2 has utility given by U2 = 2x1 + x2 The initial endowment has consumer 1 starting with 200 units of x1 and 200 units of x2. Consumer 2 starts with 300 units of x1 and 300 units of x2. Draw an Edgeworth box diagram for this initial endowment complete with the indifference curves for each individual.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 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*
- Chris and Dana live in an exchange economy with two goods: good Q and good R. Chris starts off with an endowment of 6 units of Q and 10 units of R. Dana starts off with an endowment of 8 units of Q and 8 units of R. Suppose that the price of good R is pR=1 and the price of good Q is pQ=2. a )At these prices, does the market clear? Yes or no? Explain your answer. b) What relationship must hold between the consumption of each agent and the price of the two goods at the market clearing equilibrium? Write the equationProblem 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.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.
- I need help with this homework problem. Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y) = (X^1/2)*(Y^1/2) UB(X,Y) = X + Y The initial endowments are: A: X = 8; Y = 3 B: X = 4; Y = 5 What is the marginal rate of substitution for consumer A at the initial allocation? What is the marginal rate of substitution for consumer B at the initial allocation? Is the initial allocation Pareto Efficient?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 carefullyConsider an economy with 2 goods and 2 identical agents, each of whom has the following utility function, u (x1; x2) = ln x1 + 2 ln x2. The aggregate endowments of the 2 goods are given by (1; 2). Suppose there is a social planner who cares about agents equally.(a) Set up the plannerís problem.(b) Calculate the first-best outcome 2. Consider an economy with 2 goods and 2 identical agents, each of whom has thefollowing utility function, 11(31, 3:2) = In 3:; + 2111332. The aggregate endowments ofthe 2 goods are given by (1, 2). Suppose there is a. social planner who cares aboutagents equally. (a) Set up the planner’s problem.(b) Calculate the first-best outcome (11.6., the social planner’s solution).