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5. Find a utility function representing Carol's preferences and find her cor- responding demands of dumplings and eggs as a function of her income mc and the prices of the two goods (which are again pp and pe).

5. Find a utility function representing Carol's preferences and find her cor- responding demands of dumplings and eggs as a function of her income mc and the prices of the two goods (which are again pp and pe).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 26EQ
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This problem set tells the story of four friends Alice, Bob, C'arol, who are consumers, and Fanny, who owns a firm. Alice, Bob and Carol have preferences over two goods, Dumplings and Eggs. Fanny's firm produces eggs. In what follows you should use m; for i = A, B, C to denote the income of each of the three consumers and p; for j = D, E to denote the prices of each of the two goods. Similarly, d; and e; denote the consumption of dumplings and eggs respectively by consumer i = A, B, C. Fanny uses two (non-fixed) inputs, called 1 and 2, to produce eggs; the price of these inputs is denoted by w; for j = 1,2.
Transcribed Image Text:This problem set tells the story of four friends Alice, Bob, C'arol, who are consumers, and Fanny, who owns a firm. Alice, Bob and Carol have preferences over two goods, Dumplings and Eggs. Fanny's firm produces eggs. In what follows you should use m; for i = A, B, C to denote the income of each of the three consumers and p; for j = D, E to denote the prices of each of the two goods. Similarly, d; and e; denote the consumption of dumplings and eggs respectively by consumer i = A, B, C. Fanny uses two (non-fixed) inputs, called 1 and 2, to produce eggs; the price of these inputs is denoted by w; for j = 1,2.
5. Find a utility function representing Carol's preferences and find her cor- responding demands of dumplings and eggs as a function of her income mc and the prices of the two goods (which are again pp and pE). 6. Fanny's firm is the only supplier of eggs in the region but she wants to be nice to her three friends, so she behaves as a perfectly competitive (i..e. price taker) firm. Her firm has the following technology: f(*1, #2) = (x1)04(x2)06, where x; for j = 1,2 is the amount of each input she uses. Assume that the price of input 1 is wi = 0.4(N + 1) and the price of input 2 is w2 = 0.6(N + 2). What is
Transcribed Image Text:5. Find a utility function representing Carol's preferences and find her cor- responding demands of dumplings and eggs as a function of her income mc and the prices of the two goods (which are again pp and pE). 6. Fanny's firm is the only supplier of eggs in the region but she wants to be nice to her three friends, so she behaves as a perfectly competitive (i..e. price taker) firm. Her firm has the following technology: f(*1, #2) = (x1)04(x2)06, where x; for j = 1,2 is the amount of each input she uses. Assume that the price of input 1 is wi = 0.4(N + 1) and the price of input 2 is w2 = 0.6(N + 2). What is
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