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Unformatted text preview: Eco 401, J. Sandford, spring 2009 February 26, 2009 Homework 4 Answers Problem 1 Nadia likes spare ribs, R, and fired chicken, C. Her utility function is U = 10 R 2 C (1) Her marginal utilities are MU R = 20 RC and MU C = 10 R 2 . Her weekly income is $90, which she spends on only ribs and chicken. a. If she pays $10 for a slab of ribs and $5 for a chicken, what is her optimal consumption bundle? Show her budget line, indifference curve, and optimal bundle, e 1 in a diagram. C * = 6, R * = 6 b. Suppose the price of a chicken doubles to $10. How does her optimal consumption of chicken and ribs change? Show her new budget line and optimal bundle, e 2 , in your diagram. C * = 3, R * = 6 c. Solve for Nadias demand for chicken when the price of a chicken is p c , for any p c . C * = 30 p c Problem 2 The cost function for Johns shoe repair is c ( q ) = 100 + 10 q- q 2 + 1 3 q 3 , so that marginal cost is c ( q ) = 10- 2 q + q 2 . Shoe repair is a perfectly competitive industry. a. Suppose the price of shoes is $80. Solve for Johns profit-maximizing quantity of shoes repaired. What is Johns profit in this case?...
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