Question

a-Draw a graph for a CwDP firm which faces a demand curve showing Q=0 at P=$12, and Q=8 at P=$8, a SRMC curve which interests MR at Q=8, and SRATC=$6 at Q=8. What level of output should this firm produce? At that output would the firm make a profit, or loss? How much per unit and in total?

b-Using the same information from the previous question, assume the SRATC changes so that at Q=8 the firm incurs a loss of $2/unit but P>AVC by $2. Redraw the graph and determine the firm’s profit or loss. Will the firm produce in the SR?

Answer 1

(a) Linear demand equation: P = a - bQ

When P = 12, Q = 0

12 = a - 0

a = 12

When P = 8, Q = 8

8 = a - 8b

8 = 12 - 8b

8b = 4

b = 0.5

Demand equation: P = 12 - 0.5Q

When Q = 0, P = 12 (Vertical intercept) & when P = 0, Q = 12/0.5 = 24 (Horizontal intercept).

MR curve will have same vertical intercept (= 12) but half the horizontal intercept (= 24/2 = 12) as demand curve. So

Equation of MR curve: P = 12 - Q

Profit is maximized when MR = MC. As per information, SRMC intersects MC when Q = 8. This is profit-maximizing output level. When Q = 8, from demand function,

P = 12 - (0.5 x 8) = 12 - 4 = $8

Unit profit = P - SRATC = $8 - $6 = $2

Total Profit = Q x (P - SRATC) = 8 x $(8 - 6) = 8 x $2 = $16

In following graph, D, MR, SMC and SRATC are demand, MR, short run marginal cost and short run average total cost curves. MR intersects MC at point E with price P0 (= $8) and output Q0 (= 8). Profit equals area P0ABC.

(b) In following graph, when Q0 = 8, SRATC = $8 + $2 = $10, but SRAVC = $8 - $2 = $6. There is per unit loss of $2 and total loss equal to area P0ABC = 8 x $2 = $16). But as Price > AVC, firm will continue to produce in short run.