In: Economics
Kites are manufactured by identical firms in a perfectly competitive environment. Each firm’s long run average cost and marginal cost of production are given by: AC = Q + 100/Q and MC = 2Q where Q is the number of kites produced.
a) In long run equilibrium, how many kites will each firm produce? (2 pts)
b) What will the price of kites (P) be? (1 pt)
c) Suppose the demand for kites is given by formula Q = 8000 - 50*P. How many kites will be sold and how many firms will there be in kite industry? (2 pts)
Answer (a) - The firm has long run average cost function, AC = Q + 100/Q and MC = 2Q. A firm produces at minimum point of long run AC curve. We need to calculate first order condition and second order condition in order to find minimum AC cost.
First derivative of AC,
AC / Q = 1 - 100/Q2
2AC / Q2 = -200/Q3
Since second derivation has negative sign, therefore any value of 'Q' will negative result. The long run AC function will have minimum value when AC/Q = 0
1 - 100 /Q2 = 0
Or, 1 = 100 / Q2
Or, Q = 10 kites
The firm will have minimum cost of production when output will be 10 units.
Answer (b) - We know that perfectly competitive firms are price taker. The price will be equal to marginal cost. Place value of 'Q' into MC function,
MC = 2*10
MC = $20
This is market price in the long run
Answer (c) - The market demand curve is given Q = 8000 - 50P. Places value of 'P' into market demand equation.
Q = 8000 - 50 *20
Q = 8000 - 1000
Q = 7000 kites
Total demand for kites in the market is 7000 and a firm produces 10 kites in the long run. Total firms in the market,
Total firms in the market = 7000/10
Total firms in the market = 700 firms