An exchange economy has two goods (apples, bananas) and two types of agent (1, 2). The total endowment of this economy is 7 apples and 7 bananas. Both good are divisible goods, so that it is possible to consume fractions of each good (e.g. 4.2 bananas and apples). Each type 1 agent's preferences are represented by the utility functio U(xB,x) =200+x+x%, where x and x denote the agent's consumption of bananas an apples, respectively. Each type 2 agent's preferences are represented by the utility functio -20 + 3x + x, where x and x denote the agent's consumption of banana =

An exchange economy has two goods (apples, bananas) and two types of agent (1, 2). The total endowment of this economy is 7 apples and 7 bananas. Both good are divisible goods, so that it is possible to consume fractions of each good (e.g. 4.2 bananas and apples). Each type 1 agent's preferences are represented by the utility functio U(xB,x) =200+x+x%, where x and x denote the agent's consumption of bananas an apples, respectively. Each type 2 agent's preferences are represented by the utility functio -20 + 3x + x, where x and x denote the agent's consumption of banana =

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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2. Consider a consumer whose preference relation over the consumption set X = R can be repre- sented by the utility function: u (x1, x2, 13) = A (x1 – T1)ª (x2 – ã2)° (x3 – ã3)" - where A, a, B and y are all strictly positive. (a) Why can you assume A = 1 and a + B+y= 1 without loss of generality? Do so for the rest of the question. (b) Solve the UMP and derive the consumer's Walrasian demand. (c) Find the indirect utility function, the minimum expenditure function, and the Hicksian demand function.
1. Consider a consumer who consumes two goods. The utility function is given by u(x1, x₂) /2x1+1+√√√x₂, - where x > 0 denotes the amount of good i = the price of good 1 is 3, the price of good 2 is p2 > 0, and the income is 12. 1,2 consumed. Unless stated otherwise, (1) Calculate the marginal rate of substitution (measuring the value of good 1) at the consumption plan (x₁, x₂) = (3, 4). (2) Calculate the consumption plan that is optimal for the consumer. (3) Let v(p₂) denote the utility level at the optimal consumption plan. Calculate its derivative with respect to p2, i.e., v'(P2), at p2 = 3. (4) Suppose that p2 = 1 and the utility level is 10. Calculate the compensated demand for each good.
2- Suppose a consumer who consumes two goods, good 1 and good 2. We denote his consumption of good 1 by q1, and his consumption of good 2 by q2. Its preferences for good 1 and good 2 can be represented by the following utility function: U (Q1/ Q2) = 3 (Q1) 1/3 (Q2) 2/3 The marginal utility of good 1 is um1 = (Q2/Q1) 2/3 and the marginal utility of good 2 is um2 =2 (Q1/Q2) 1/3 Determine the quantity of good 2 q2 "in the shopping basket (q1 '; q2) = (32; q2 ) so as to find on the same indifference curve as the consumption basket (q1; q2) = (8; 64).
2. Consider an economy with two agents and two commodities. Consumers' preferences are represented by the following utility functions u₁(x,x) = (x²) ¹ (x²) ½ u₂(x², x²) = x² + x². Consumers' initial endowments are e² = (6,4). Note: You can normalize the price of one good to 1 at any point when solving this question. e¹ = (10,2) (a) Draw the Edgeworth box that represents this economy. Clearly indicate the size of the box (i.e. the maximal feasible amounts of good 1 and good 2). Show the location of the initial endowment and draw the indifference curve of each consumer that passes through the initial endowment.
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(c) If the preferences are concave, will the consumer ever consume both of the goods together?
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11) Stanley consumes only white and red wines and his utility function can be describedby U(R,W) = R0.40∙W0.60, where R is the number of bottles of red wine and W is the4number of bottles of white wine that he consumes per month. Suppose that his income is$500 and the price of a bottle of red wine $20 and the price of a bottle of white wine is$15. In this case, Stanley will purchase _____ bottles of red wine and _____ bottles ofwhite wine per month. Next, suppose that the price of red wine goes up to $35 per bottle.In this case, Stanley would consume ______ quantity of bottles of white wine comparedto the original situation.A) 10; 20; smallerB) 20; 10; smallerC) 10; 20; the sameD) 20; 10; the sameE) None of the above.
Refer to figure. Suppose the consumer is endowed with 10 units of orange and consumes 5 units of apple. The price of the apple decreases and at the new price the consumer consumes 9 units of apple. The change in the demand for apples due to the endowment effect is equal to Optionsa) 3b) 4c) 1d) none of these
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