Question

1. n number of firms operate in a perfectly competitive market in the long run. The marginal cost for each rm is MC = 30 − 16q + 3q 2 and the average cost is AC = 30 − 8q + q 2 . The market demand is QD = 4600 − 100P. Determine the individual supply by each rm, the market price, and the number of rms (n).

Answer 1

In long run Equilibrium, a firm operates at a point where AC= MC

Equating AC and MC

30–16q+3q2= 30–8q+q​​​​​​2

2q2–8q= 0

q(2q–8)= 0

Either q= 0 or q=4

Output will be Positive, Thus, q=4.

Output of a Single firm= 4 Units.

Marginal Cost at Price 4 units= 30–16×4+3(4)2= 14.

In long Run, in a perfectly competitive market, Marginal Cost= Average Cost= Price.

Thus, Price= 14.

Total Quantity in the market at a price of 14= 4600–100×14= 3200.

If total Number of firms in the market=n

Quantity Produced by each firm= 4 Units.

Thus, 4×n=3200

n= 800.

Number of firms= 800.

Market Price= 14.

Individual supply by firm= 4 Units.