Question

(6 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 4. STC- 10 + 2q + 0.1q', where q is daily pizza production. (1 pt) What is this pizza shop's short-run supply curve? (1 pt) If the market price is $6.00, what is the pizza shop's daily production quantity and profits? (2 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. (2 pts) In the total cost function, $10 represents fixed costs that can't be changed in the short-run (e.g., rent of equipment), and 2q 0.1q2 represents variable costs (e.g., labor and raw materials). Currently, the market price of pizza is reduced from $6.00 to $3.00 because one major chain is having a sale. As a consultant, would you recommend the pizza shop to continue operations in the short run? Would your answer change if the price of pizza stays at $3.00 in the long run? a. b. c. d.

Answer 1

(a)

Marginal cost (MC) = dSTC/dq = 2 + 0.2q

Firm's supply curve is its MC curve, so

Firm supply curve: P = 2 + 0.2q

(b)

Since firms equate market price with MC,

2 + 0.2q = 6

0.2q = 4

q = 20

P = $6

Revenue (R) = Pq = $6 x 20 = $120

STC ($) = 10 + (2 x 20) + (0.1 x 20 x 20) = 10 + 40 + 40 = 90

Profit ($) = R - STC = 120 - 90 = 30

(c)

When P = $3,

2 + 0.2q = 3

0.2q = 1

q = 5

Revenue = $3 x 5 = $15

Variable cost (VC) ($) = (2 x 5) + (0.1 x 5 x 5) = 10 + 2.5 = 12.5

Since revenue is higher than VC, the firm should continue operating in short run. However, in long run, Total cost will be $(12.5 + 10) = $22.5, which is higher than revenue and there will be a loss. So firm should exit the market in long run.