1. A local pizza shop has hired a consultant to help it compete with national ch

Question

1. A local pizza shop has hired 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, the consultant finds that short-run total costs each day are given by:

STC = 10+q+0.1q²

A) Find the short-run marginal cost (SMC) function associated with this shop.

B)What is this price-taking firm's short-run supply curve?

C)Does this firm have a shutdown price? That is, what is the lowest price at which the firm will produce any pizza?

D)Find the short-run average cost (SAC) for this shop. Find the q where the SAC reaches minimum point. How would you verify this?

E) The consultant also claims that any price for pizza of less than $3 will cause the shop to lose money. Is this consultant correct? Explain.

F) 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.

Explanation / Answer

ans

a)STC = 10+q+0.1q²

SMC=dSTC/dq= 1+0.2q

b) this price-taking firm's short-run supply curve is the increasing part of its short run marginal cost curve above the minimum of its average variable cost

c) yes this firm will have shutdown point, if P< SAVC than firm will not produce and shut down. lowest price at which firm will produce iss when P=SAVC(short run average variable cost)

SAVC=(q+0.1q2)/q = 1+0.1q

d) SAC= STC/q =(10+q+0.1q²) /q= 10/q +1+0.1q

for minimum SAC

dSAC/dq=0

-10/q2 +0.1 =0

10/q2 =0.1

q2=100

q=10

for verification 2nd order condition

d2SAC/dq2= -20/q3 <0   so SAC is minimum at q=10

minimum SAC=10/q +1+0.1q = 1+1+0.1(10) = 3

at this point SAVC=1+0.1q= 1+1 =2

E) The consultant also claims that any price for pizza of less than $3 will cause the shop to lose money.

consultant is right as in this case P<minimum SAC= 3, so firm is loosing and not gaining

F) $ 2 price is low and not covering average cost but it is covering SAVC which is $2

so firm can continue production in short run. i don't agree with recommendation

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