Question

Suppose that the demand for stilts is given by Q=1500-50P and that the long-run total operating costs of each stilt making firm in a competitive industry are given by TC=50+10q+0.5q2 .

How many stilts are produced by each firm?

What is the long-run equilibrium price of stilts? What is the long-run equilibrium quantity of stilts produced in the market? How many firms will there be?

Answer 1

TC = 50 + 10q + 0.5q²

dTC/dq = MC = 10 + q

MC = 10 + q

AC = TC/q  

=   (50 + 10q + 0.5q² )/q  

= 50/q + 10 + 0.5q

In long run equilibrium

P = MC = AC  

MC = AC

10 + q = 50/q + 10 + 0.5q

10 - 10 + q - 0.5q = 50/q

0.5q = 50/q  

q/2 = 50/q

q² = 100

q = 10

So stilts produced by each firm is 10

MC = 10 + q  

= 10 + 10

= 20

P = MC

= 20

Thus,long run equilibrium price is 20

Q = 1500 - 50P

= 1500 - 50(20)

= 1500 - 1000

= 500

Long run equilibrium quantity is 500

Number of firms, n = Q/q

= 500/10

= 50