econ11_08_hw4_sol

econ11_08_hw4_sol - Eco11 Fall 2008 Simon Board Economics...

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Eco11, Fall 2008 Simon Board Economics 11: Solutions to Homework 4 December 4, 2008 Due date: Thursday 4th December. Instructions: You are required to write up your solution separately and independently, al- though you are encouraged to discuss and work in groups. Please write your name, student ID number, and the name of your TA on the front page of the assignment that you hand in. Also, please put boxes around your final answer to each part. 1. Deriving Supply Functions (a) A firm has cost function c ( q ) = q 2 for q < 2 = q 2 + q - 2 for q 2 Derive the firm’s supply curve, q * ( p ). (b) A firm has cost function c ( q ) = q 2 for q < 2 = q 2 - q + 2 for q 2 Derive the firm’s supply curve, q * ( p ). Solution (a) First suppose q < 2. The FOC is p = 2 q Hence q * ( p ) = p/ 2. This assumes that q < 2, and hence p < 4. Next suppose q 2. The FOC is p = 2 q + 1 1
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Eco11, Fall 2008 Simon Board Figure 1: Convex Cost Function. The black line shows the MC curve. The red line shows the supply curve. Hence q * ( p ) = ( p - 1) / 2. This assumes that q 2 and hence p 5. For p [4 , 5], the firm does not want to produce more than q = 2 at MC = 2 q + 1. It also does not want to produce less that q = 2 at MC = 2 q . Hence the firm will produce q = 2. See figure 1. (a) First suppose q < 2. The FOC is p = 2 q Hence q * ( p ) = p/ 2. This assumes that q < 2, and hence p < 4. Next suppose q 2. The FOC is p = 2 q - 1 Hence q * ( p ) = ( p + 1) / 2. This assumes that q 2 and hence p 3.
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