(5 pts) A local pizza shop has hired you as a consultant to help it compete with
ID: 1134357 • Letter: #
Question
(5 pts) A local pizza shop has hired you as a consultant to help it compete with national chains in the area. Because most business is handled by these national chains, the local shop operates as a price taker. Using historical data on costs, you find that short-run total costs each day are given by STC 10 q + 0.1q3, where q is daily pizza production. a. (1 pts) What is this pizza shop's short-run supply curve? (1 pts) If the market price is $15.00, what is the pizza shop's daily production quantity and profits? b. (1 pts) Suppose the pizza shop wants to know the lowest price such that it can break even (i.e., maintaining a net profit of zero). Please help the firm find this price. c. (2 pts) In the total costs, $10 are fixed costs that can't be changed in the short-run (e.g., rent of equipment), and q0.1q3 are variable costs (e.g., labor and raw materials). Currently, the price of pizza is low ($2.00) because one major chain is having a sale. As a consultant, would you recommend the pizza shop to continue operations? Would your answer change if the price of pizza stays at $2.00 in the long run? d.Explanation / Answer
STC = 10 + q + 0.1q3
(a) Short run supply curve is the marginal cost (MC) function.
MC = dSTC/dq = 1 + 0.3q2
Supply function: P = 1 + 0.3q2
(b) The firm equates price with its MC. So,
1 + 0.3q2 = 15
0.3q2 = 14
q2 = 46.67
q = 6.83
Taking number of pizzas as an integer, rounding off we get
q = 7
Revenue = Price x q = $15 x 7 = $105
STC ($) = 10 + 7 + (0.1 x 7 x 7 x 7) = 17 + 34.3 = 51.3
Profit ($) = Revenue - STC = 105 - 51.3 = 53.7
(c) In break-even, Price = MC = Average total cost (ATC)
ATC = STC/q = (10/q) + 1 + 0.1q2
Equating with MC,
(10/q) + 1 + 0.1q2 = 1 + 0.3q2
0.2q2 = 10/q
q3 = 10/0.2 = 50
q = 3.68
Taking number of pizzas as an integer, rounding off we get
q = 4
Break-even price = MC = 1 + (0.3 x 4 x 4) = 1 + 4.8 = 5.8
(d) Firm will shut down if price is less than Average variable cost (AVC).
AVC = TVC/q = 1 + 0.1q2
When q = 7 (current profit-maximizing output),
AVC = 1 + (0.1 x 7 x 7) = 1 + 4.9 = 5.9
Since current price is less than AVC at current output level ($2 < $5.9), firm will not continue operations. Since price is less than AVC, price is also les than ATC, leading to long run loss and firm will exit the market in long run.
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