A local pizza shop has hired a consultant to help it compete with national chains in the area. Because these national chains handle most business, the local shop operates as a price taker. Using historical data on costs, the consultant finds that short-run total costs each day are given by STC = 10 + q + 0.1q2, where q is daily pizza production. The consultant also reports that short-run marginal costs are given by SMC = 1 + 0.2q.
a. What is this price-taking firm’s short-run supply curve?
b. Does this firm have a shutdown price? That is, what is the lowest price at which the firm will produce any pizza?
c. The pizza consultant calculates this shop’s short-run average costs as
SAC = 10/q + 1 + 0.1q
and claims that SAC reaches a minimum at q = 10. How would you verify this claim without using calculus?
d. The consultant also claims that any price for pizza of less than $3 will cause this shop to lose money. Is the consultant correct? Explain.
e. Currently the price of pizza is low ($2) because one major chain is having a sale. Because this price does not cover average costs, the consultant recommends that this shop cease operations until the sale is over. Would you agree with this recommendation? Explain.