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401_s09_hw4a

# 401_s09_hw4a - Eco 401 J Sandford spring 2009 Homework 4...

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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 Nadia’s 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 John’s shoe repair is c ( q ) = 100 + 10 q - q 2 + 1 3 q 3 , so that marginal cost is c 0 ( q ) = 10 - 2 q + q 2 . Shoe repair is a perfectly competitive industry. a. Suppose the price of shoes is \$80. Solve for John’s profit-maximizing quantity of shoes repaired. What is John’s profit in this case? The profit-maximizing quantity q solves 80 = 10 - 2 q + q 2 , or q = 9 . 43.

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401_s09_hw4a - Eco 401 J Sandford spring 2009 Homework 4...

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