Question

Assume a competitive market for computer hard drives. All firms in the market are identical each with cost function given by C(q) = 32 + 2q2 where q is measured in thousands of units per year. In this market, each firm will make zero profits when it produces _________ units.

Answer 1

A perfectly competitive firm makes zero economic profit in long run at following point;

i.e., P = MC = AC

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C = 32 + 2q²

MC = ΔC / Δq

=>MC = 2(2) q^2-1

=>MC = 4q

and

AC = C/q

=>AC = (32 + 2q²) / q

=>AC = (32/q) + 2q

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Set MC =AC

=> 4q = (32 / q) + 2q

=> 4q - 2q = (32 /q)

=> 2q = (32 / q)

=> q * q = (32 / 2)

=> q² = 16

=> (q²)^1/2 = (16)^1/2

=> q = 4

At q =4, the MC = AC

q is measured in thousands of units per year

In this market, each firm will make zero profits when it produces 4 thousands units.