Consider a market with M= 2 consumers and L = 2 goods. The preferences of each consumer are u₁(x₁) = min (x₁, x2} (6) U₂(x2) = X1X2 (7) Draw the Edgeworth box for this economy, where endowments are ₁ = (0,1) and ₂ = (1,0). Be sure to label the budget constraint, endowment point, equilibrium price ratio, equilibrium allocation, and the indifference curves of each consumer.
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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.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:
- Persons 1 and 2 have the following utility functions over goods x and y: Person 1: U1(x1, y1) = min{2x1, y1} Person 2: U2(x2, y2) = x2 + y2 Person 1 has an endowment of e1 = (2, 1). Betty’s endowment is e2 = (1, 2). Graph the Edgeworth Box for this economy. Draw each person’s indifference curve through the endowment point. Are there allocations that Pareto dominate the endowment? If so, show them on the diagram. Also, identify which allocations are Pareto optimal relative to the endowment point. Solve for the contact curve for this economy. Illustrate it in the Edgeworth Box.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.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
- 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 fast. Show that Cobb-Douglas preferences are homothetic preferences
- 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 outcomeConsider 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*Person A has a utility function of and person B has a utility function Agent A and agent B have identical endowments of (1/2,1/2). (a) Illustrate this situation in an Edgeworth box diagram. (b) What is the equilibrium relationship between p1and p2? (c) What is the equilibrium allocation?