Question

A small monopoly manufacturer of widgets has a constant marginal cost of ​$15 . The demand for this​ firm's widgets is Q equals 105 minus 1 P . Given the above​ information, compute the social cost of this​ firm's monopoly power. The social cost is ​$ . ​ (Round your response to the nearest​ penny.)

Answer 1

In a monopoly market, there is only one seller but may buyers. The equilibrium condition is (MR = MC).

But as per the socially optimum equilibrium, it is (P = MC).

The difference is deadweight loss, which is also called social cost.

Computation:

Given demand, Q = 105 – 1P

By rearranging, P = 105 – Q …… price function

TR = P × Q = 105Q – Q^2

MR = Derivative of TR with respect to Q

        = {105Q^(1 – 1)} – {(1 × 2)Q^(2 – 1)}

        = 105 – 2Q

Given marginal cost (MC) = 15

Therefore, MR = MC

105 – 2Q = 15

2Q = 90

Q = 45

By putting this value in price function,

P = 105 – Q

   = 105 – 45

   = 60

Monopoly: Quantity (Q1) = 45 units; price (P1) = $60

Now, as per socially optimum level,

P = MC

105 – Q = 15

Q = 90

By putting this value in price function,

P = 105 – Q

   = 105 – 90

   = 15

Socially optimum: Quantity (Q2) = 90 units; price (P2) = $15

Social cost = 0.5 × Difference in price × Difference in quantity

                   = 0.5 × (Q2 – Q1) × (P1 – P2)

                   = 0.5 × (90 – 45) × (60 – 15)

                   = 0.5 × 45 × 45

                   = $1,012.50 (Answer)