Question

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?

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? Need a better answer.

Answer 1

Demand Equation => P = a - bQ

It has been provided that Q = 0 at P = $12.

=> 12 = a - 0

That is, a = 12

When Q = 8 at P = 8,

=> 8 = a - 8b

=> 8 = 12 - 8b

8b = 12 - 8

That is, b = 0.5

Therefore, the demand equation can be given as P = 12 - 0.5Q

P = 0 at Q = 12/0.5 = 24 (Horizontal intercept) & Q = 0 at P = 12 (Vertical intercept)

MR curve has the identical vertical intercept as the demand curve but the horizontal intercept is halved (24/2 = 12) Thus,

The equation of MR curve is P = 12 - Q.

Profit maximization requires MR = MC.

As provided by the question, the SRMC curve is intersecting the MC at Q = 8 which is profit-maximizing output level.

At Q = 8,

P = 12 - (0.5 * 8) = $8

Per unit profit = P - SRATC = 8 - 6 = $2

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

In following graph, MR intersects the MC curve at point E at a price P₀ ($8) and output level Q₀ (8). Profit equals area P₀ABC.

In following graph, at Q₀ = 8, SRATC = 8 + 2 = $10,

however, SRAVC = 8 - 2 = $6. Per unit loss turns out to be $2 as well as total loss equals P₀ABC = 8 * 2 = $16.

As Price > AVC, firm continues to produce in the short run.