# Answer to Question #49437 in Microeconomics for John

Question #49437

Consider a monopolist whose total cost function is TC = 40 + 4Q + Q2 and whose marginal cost function is MC = 4 + 2Q. The demand function for the firms good is P = 160 - 0.5Q. The firm optimizes by producing the level of output that maximizes profit or minimizes loss. If the firm uses a uniform pricing strategy, then rounded to the nearest dollar the deadweight loss that results is:

Expert's answer

TC = 40 + 4Q + Q2, MC = 4 + 2Q, P = 160 - 0.5Q

If the firm optimizes by producing the level of output that maximizes profit or minimizes loss, then output is produced at the point, where MR = MC:

MR = TR' = 160 - Q

160 - Q = 4 + 2Q

Q = 52 units

Level of P at MR = MC is P = 4 + 2*52 = $108

Price of the monopolist is Pm = 160 - 0.5*52 = $134

The price discremination output is at MC = D:

4 + 2Q = 160 - 0.5Q

Q = 62.4

If the firm uses a uniform pricing strategy, then rounded to the nearest dollar the deadweight loss that results is:

DWL = 0.5*(134 - 108)*(62.4 - 52) = 0.5*26*10.4 = $135.2

If the firm optimizes by producing the level of output that maximizes profit or minimizes loss, then output is produced at the point, where MR = MC:

MR = TR' = 160 - Q

160 - Q = 4 + 2Q

Q = 52 units

Level of P at MR = MC is P = 4 + 2*52 = $108

Price of the monopolist is Pm = 160 - 0.5*52 = $134

The price discremination output is at MC = D:

4 + 2Q = 160 - 0.5Q

Q = 62.4

If the firm uses a uniform pricing strategy, then rounded to the nearest dollar the deadweight loss that results is:

DWL = 0.5*(134 - 108)*(62.4 - 52) = 0.5*26*10.4 = $135.2

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