Question

Consider a firm with total costs represented by TC=16+Q^2 and a corresponding marginal cost of 2Q (MC=2Q)

1). Graph the ATC and MC, be certain to label the lowest point of the ATC.

Consider that firm faces a price of 12$.

2). Find the optimal quantity.

3). Graph and find the total cost, total revenue, and any profit or loss at the optimal quantity.

Answer 1

Given, total cost, TC = 16 + Q^2 and MC = 2Q,

a) ATC = TC/Q = Q + 16/Q

Diagrammatically,

At the lowest point, MC = ATC

2Q = Q + 16/Q which gives Q = 4

At Q= 4, ATC = MC = 8

b) In equilibrium, MR = MC

TR = P.Q = 12Q

Thus, MR = dTR/dQ = 12

In equilibrium, 12 = 2Q which gives Q = 6

Ans. Optimal quantity = 6 units

c) Profit = TR - TC

= 12(Q) - (16 + Q^2)

Using Q = 6, we get:

TR = 12(6) = 72 and TC = 16 + (6)^2 = 52

Thus, profit = 72 - 52 = $20

Ans. Profit = $20