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PS5_AK - Econ 110 Spring 2010 L1 L2 HW5 Solution A...

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Econ 110, Spring 2010, L1 & L2 HW5 Solution A. Chapter12, problem 2, [(12.2), (12.4)] 2. Pat’s Pizza Kitchen is a price taker. Its costs are in the table. a. Calculate Pat’s profit-maximizing output and economic profit if the market price is (i) $14 a pizza. (ii) $12 a pizza. (iii) $10 a pizza. (i) At $14 a pizza, Pat’s profit-maximizing output is 4 pizzas an hour and economic profit is $2 an hour. Pat’s maximizes its profit by producing the quantity at which marginal revenue equals marginal cost. In perfect competition, marginal revenue equals price, which is $14 a pizza. The marginal cost is the change in total cost when output is increased by 1 pizza an hour. The marginal cost of increasing output from 3 to 4 pizzas an hour is $13 ($54 minus $41). The marginal cost of increasing output from 4 to 5 pizzas an hour is $15 ($69 minus $54). So the marginal cost of the fourth pizza is half-way between $13 and $15, which is $14. Marginal cost equals marginal revenue when Pat produces 4 pizzas an hour. Economic profit equals total revenue minus total cost. Total revenue equals $56 ($14 multiplied by 4). Total cost is $54, so economic profit is $2. (ii) At $12 a pizza, Pat’s profit-maximizing output is 3 pizzas an hour and economic profit is $5. Pat’s maximizes its profit by producing the quantity at which marginal revenue equals marginal cost. Marginal revenue equals price, which is $12 a pizza. The marginal cost of increasing output from 2 to 3 pizzas an hour is $11 ($41 minus $30). The marginal cost of increasing output from 3 to 4 pizzas an hour is $13. So the marginal cost of the third pizza is half- way between $11 and $13, which is $12. Marginal cost equals marginal revenue when Pat produces 3 pizzas an hour. Economic profit equals total revenue minus total cost. Total revenue equals $36 ($12 multiplied by 3). Total cost is $41, so economic profit is $5. (iii) At $10 a pizza, Pat’s profit-maximizing output is 2 pizzas an hour and economic profit is $10. Pat’s maximizes its profit by producing the quantity at which marginal revenue equals marginal cost. Marginal revenue equals price, which is $10 a pizza. The marginal cost of increasing output from 1 to 2 pizzas an hour is $9 ($30 minus $21). The marginal cost of increasing output from 2 to 3 pizzas an hour is $11. So the marginal cost of the second pizza is half-way between $9 and $11, which is $10. Marginal cost equals marginal revenue when Pat produces 2 pizzas an hour. Economic profit equals total revenue minus total cost. Total revenue equals $20 ($10 multiplied by 2). Total cost is $30, so economic profit is $10. 1
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b. What is Pat’s shutdown point and what is Pat’s economic profit if it shuts down temporarily? The shutdown point is the price that equals minimum average variable cost. To calculate total variable cost, subtract total fixed cost ($10—when output is zero, total variable cost is $0, so total cost at zero output equals total fixed cost) from total cost. Average variable cost equals total variable cost divided by the quantity produced. The average variable cost of producing 2 pizzas is $10 a pizza. Average variable cost is a minimum when marginal cost equals average variable cost.
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