If a competitive firms cost function is C 2 3Q 4Q2 comput

If a competitive firm’s cost function is C = 2 + 3Q + 4Q2 compute the firm’s marginal cost function MC(Q) and the quantity Q0 that it will choose to produce when the price is P0 = 5. What quantity would the firm produce at prices less than P0 = 3?

Solution

(a) Marginal cost = dC / dQ = 3 + 8Q

(b) A competitive firm maximizes profits by equating MC with price.

3 + 8Q = 5

8Q = 2

Q = 2 / 8 = 0.25

(c) If P = 3, equating MC with P:

3 + 8Q = 3

8Q = 0

Q = 0

So, if price is less than 3, firm will produce zero output.