Question

Assume that the paperclip industry is a monopoly and marginal cost is equal to average cost. The average and marginal cost of paper clip production is 125, and the interest rate is 10 %. Demand for paperclips is equal to Q=100-2/3 P. What is the optimal quantity, per period CS, and per period license revenues?

Answer 1

Solution :- The profit-maximizing rule for monopoly firm / monopoly industry is equating marginal revenue (MR) and marginal cost (MC) for the firm / industry.

Q = 100 - 2 / 3 P (Demand equation)

2 / 3 P = 100 - Q  

Dividng the above equation by 2 / 3.

P = 150 - 1.50 Q (Inverse demand equation)

Marginal revenue (MR) = 150 - 3Q (The slope of marginal revenue function is that of twice of the slope of inverse demand function).

Marginal cost (MC) = $ 125.

Equating Marginal revenue (MR) and Marginal cost (MC),

150 - 3Q = 125

150 - 125 = 3Q

25 = 3Q

Q = 25 / 3

Q = 8.33 Units.

P = 150 - 1.50 * 8.33

P = 150 - 12.50 (approx)

P = $ 137.50.

Consumer surplus (CS) per period = 0.50 * Base * Height.

= 0.50 * (150 - 137.50) * 25 / 3 (Quantity of 8.33 units can also be written as 25 / 3).

= 0.50 * 12.50 * 25 / 3

= $ 52.08 (approx).

Per period license revenue = Price (P) * Quantity (Q)

= 137.50 * 25 / 3   (Quantity of 8.33 units can also be written as 25 / 3).

= $ 1145.83 (approx).

Conclusion :-

Optimal quantity (Q)	8.33 units (approx).
Per period consumer surplus (CS)	$ 52.08 (approx).
Per period license revenues (Total revenue)	$ 1145.83 (approx).