Question

1. Consider the case of The Electric Company which produces electricity in New York State. The average monthly demand curve for the firm can be represented by P=65-Q where Q represents the quantity of electricity produced, in megawatt-hours (mwh) and P is measured in cents. Their marginal costs can be represented by MC=5+0.5*Q. Please provide graphs to accompany your analysis.

b. In the case above, is this profit-maximizing outcome efficient?  If not, calculate any deadweight loss.  

Answer 1

Answer : b) Given,

P = 65 - Q

TR (Total Revenue) = P * Q = (65 - Q) * Q

=> TR = 65Q - Q^2

MR (Marginal Revenue) = TR / Q

=> MR = 65 - 2Q

MC = 5 + 0.5Q [Given]

Here at equilibrium condition, MR = MC.

=> 65 - 2Q = 5 + 0.5Q

=> 65 - 5 = 0.5Q + 2Q

=> 60 = 2.5Q

=> Q = 60 / 2.5

=> Q = 24

Now, P = 65 - 24

=> P = 41

Therefore, the inefficient output level is, Q = 24 and price is, P = $41.

This profit maximizing output is not efficient. Because the efficient outcome occur when P = MC.

=> 65 - Q = 5 + 0.5Q

=> 65 - 5 = 0.5Q + Q

=> 60 = 1.5Q

=> Q = 60 / 1.5

=> Q = 40

Now P = 65 - 40

=> P = 15

Therefore, efficient output level is, Q = 40 and price is, P = $15.

Deadweight loss = 0.5 * P * Q

=> Deadweight loss = 0.5 * (41- 15) * (40 - 24)

=> Deadweight loss = 0.5 * 26 * 16

=> Deadweight loss = 208

Therefore, here the deadweight loss is $208.

These results are showing by the following picture's diagram.