Consider a pure exchange economy with two goods k = 1,2 and two households = A, B. Consider the endowments eA = (10, 2) and eg = (2, 10) for households A and B, respectively. Assume the utility functions as the following: 1/3 2/3 UA(TA1, TA2) = 3x A1 + 5xA2 and uB(xB1,TB2) %3D
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Find the marginal rate of substitution for Household A.
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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.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 outcomeIf the initial distribution of two goods between two people is Pareto optimal, which of the following statements is TRUE? A. It is possible to reallocate the goods between the two people so as to increase the utility of both people. B. It is possible to reallocate the goods between the two people so as to increase the utility of one person without decreasing the utility of the other. C. It is possible to reallocate the goods between the two people so as to increase the utility of one person, but only at the expense of the other person. D. It is impossible to reallocate the goods between the two people so as to increase either person's utility. E. None of the above
- 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 effectBluth’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.Q16 Pareto optimality refers to the maximum efficient allocation of economic resources such that there is no way that one's wealth another person worse off: this statement is choices - irrelevant -conditionally true -always true -always false
- 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.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 a pure exchange economy, where each consumer has preferences described by a Cobb-Douglas utility function. Both consumers have exactly the same endowment. In such an economy, an equitable distribution of goods (where each individual consumes exactly half of each good) is a Walrasian equilibrium allocation. a. always for any consumers' preferences b.only if consumers' preferences are exactly the same c. never d. non of the above
- Answer both question (a) and (b) below. (a) State theWeak Axiom of Revealed Preference (WARP). (b) In a two-good model, suppose a consumer always chooses the midpoint of the budget line given any (p1; p2; I), does the demand function satisfy WARP? Why? (HINT: Graphs can be helpful to answer the question.)Suppose the utility function for Njeru is given by U = f(X1, X2) = X10.25 X20.75. Given that the price of commodity X1 is Kshs. 10 per unit and that of community X2 is Kshs. 15 per unit. Using Lagrangian multiplier technique determine units of the two commodities Njeru will buy given an income of Kshs. 40,000 in order to maximize his utility.Consider a pure exchange economy, where each consumer has preferences described by a Cobb-Douglas utility function. Both consumers have exactly the same endowment. In such an economy, an equitable distribution of goods (where each individual consumes exactly half of each good) is a Walrasian equilibrium allocation? a. always, for any consumers' preferences b. only if consumers' preferences are exactly the same c. Never d. None of the above