PS5 - 100A - Econ 100A – Microeconomic Analysis Dept of...

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Unformatted text preview: Econ 100A – Microeconomic Analysis Dept. of Economics, UC Berkeley Prof. Santesteban Fall 2011 Problem Set 5 (Due Thursday, October 20, 11:10am. Please include your GSI and ID number at the top of the page.) 1. Suppose there are 100 identical firms in a perfectly competitive industry. Each firm has a short‐run total cost function of the form: C(q) = q3/300 + 0.2q2 + 4q + 10. a) Calculate the firm’s short‐run supply curve with q as a function of market price P. b) On the assumption that there are no interaction effects among costs of the firms in the industry, calculate the short‐run industry supply curve. c) Suppose market demand is given by Q=8000 – 200P. What will be the short‐run equilibrium price‐quantity combination? 2. The global propylene industry is perfectly competitive, and each producer has the long‐run margin cost function MC(q) = 40 ‐12q+q2. The corresponding LR average cost function is AC(q) = 40 ‐6q +q2/3. The market demand curve for propylene is Q(p) = 2200 – 100P. What is the LR equilibrium price in this industry, and at this price, how much would an individual firm produce? How many active producers are in the propylene market in a LR competitive equilibrium? 3. Problem 14.2 from the book. 4. A perfectly competitive industry has a large number of potential entrants. Each firm has an identical cost structure such that LR AC is minimized at an output of 20 units. The minimum average cost is $10/unit. Total market demand is given by: Q = 1500 – 50P. a) What is the industry’s LR supply function? b) What are the LR equilibrium price and output? What is the output of each firm? How many firms will be in the industry and what will be the profits of each firm? c) The SR total cost function associated with each firm’s LR equilibrium output is given by C(q) = 0.5q2 – 10q + 200. Calculate the SR average and marginal cost function. At what output level does the SR AC reach a minimum? d) Calculate the SR supply function for each firm and the industry SR supply function. e) Suppose now that the market demand shifts upward to Q =2000 – 50P. Using this new demand curve, answer part (b) for the very short run when firms cannot change their outputs. f) In the SR, use the industry SR supply curve to recalculate the answers to (b). g) What is the new LR equilibrium for the industry? ...
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