Question

4.2

2. Bucky is a firm that makes rocking horses, which is a perfectly competitive market. Bucky’s cost function is: C(q) = 12q2+40q+2450.
(a) Determine the firm’s short-run supply curve.
(b) The market price for rocking horses is p = 140. What is the firm’s optimal level of
output?
(c) What are firm profits from part b)?
(d) How would an increase in the rental rate affect your answer to part c)?
(e) What is the long-run market price and the long-run level of output?

Answer 1

Cost function is C(q) = 12q^2 + 40q + 2450. Firm operates in perfectly competitive market

a) Short run supply function is P = rising MC after minimum AVC

MC = dC/dq = 24q + 40.

Supply function is P = MC

24q + 40 = P

q = (P - 40)/24

This is  firm’s short-run supply curve.

b)  firm’s optimal level of output = (140 - 40)/24 = 4.167 units

c) Profit = Revenue - Cost = 140*4.167 - (12*(4.167^2) + 40*4.167 + 2450) = -2241.67

d) It will reduce profits because it is a part of fixed cost.

e) Long run price is P = LMC = LAC. Here AC = C/q = 12q + 40 + 2450/q. Then we have

24q + 40 = 12q + 40 + 2450/q

12q = 2450/q

q = 14.28

Long run price = 24*14.28 + 40 = $383