Question

Hot air balloons are made in Nairobi by a number of perfectly competitive identically – sized firms, each with the following total cost function, TC = 4q² + 100q + 100. Market demand for hot air balloons is given by Q_D = 1000 – P, where Q_D represents total quantity demanded and P is the price per balloon.

1. What is the long run equilibrium price in this industry?
2. What is the equilibrium number of firms?
3. If this is a constant cost competitive industry, and demand decreases to Q_D = 775 – P, what are short run profit for a representative firm, and how many firms will exist in long run equilibrium?
4. Assuming this is an increasing cost competitive industry and demand still decreases to Q_D = 775 – P, but due to this, the balloon makers are able to negotiate at a lower rental rate on their factories so that fixed costs for the representative firm are now 64 (instead of 100). What is the long run equilibrium price, profit, and size of each representative firm (that is, how many balloons will each firm produce)?

Answer 1

Marginal cost (MC) = dTC/dq = 8q + 100

Average total cost (ATC) = TC/q = 4q + 100 + (100/q)

(a) In long run equilibrium, Price = MC = ATC.

8q + 100 = 4q + 100 + (100/q)

4q = 100/q

q² = 25

q = 5

P = MC = (8 x 5) +100 = 40 + 100 = 140

(b) QD = 1,000 - 140 = 860

Number of firms = QD/q = 860/5 = 172

(c) New QD = 775 - 140 = 635

New number of firms = 635/5 = 127

ATC = 4 x 5 + 100 + (100/5) = 20 + 100 + 20 = 140

Profit = q x (P - ATC) = 5 x (140 - 140) = 0

(d) Change in fixed cost will not change MC, but will change ATC.

New ATC = 4q + 100 + (64/q)

4q + 100 + (64/q) = 8q + 100

4q = 64/q

q² = 16

q = 4

P = MC = (8 x 4) + 100 = 32 + 100 = 132

QD = 775 - 132 = 643

Number of firms = QD/q = 643/4 = 161 (taking integer value only)

Profit in long run competitive equilibrium is zero.