Question

In this scenario, assume that the paperclip industry has many buyers and sellers and no barriers to entry (perfectly competitive) and marginal cost is equal to average cost. There is a process innovation that reduces the cost of producing paperclips from $125 to $100. In other words, the process innovation is non-drastic. Demand for paperclips is equal to Q=100-2/3 P.

(i)Say the patentee provides the process innovation to these producers for free, what is the optimal quantity and the per period CS?

(ii) Say the patentee chooses to license the process innovation to the producers in the paperclip industry, charging a royalty. What is the optimal quantity, the per period CS, and the per period license revenues? Compare consumer surplus with case (i).

Answer 1

Q = 100 - (2/3)P

(2/3)P = 100 - Q

P = (300 - 3Q) / 2

P = 150 - 1.5Q

(i) In this case, competitive equilibrium is obtained by equating P with MC.

150 - 1.5Q = 100

1.5Q = 50

Q = 33.33

P = MC = $100

From demand function, when Q = 0, P = 150 (Reservation price)

CS = Area between demand curve & market price = (1/2) x $(150 - 100) x 33.33 = (1/2) x $50 x 33.33 = $1,666.67

(b) In this case, profit is maximized by equating Marginal revenue (MR) with MC.

Total revenue (TR) = P x Q = 150Q - 1.5Q²

MR = dTR/dQ = 150 - 3Q

150 - 3Q = 100

3Q = 50

Q = 16.67

P = 150 - (1.5 x 16.67) = 150 - 25 = $125

CS = (1/2) x $(150 - 125) x 16.67 = (1/2) x $25 x 16.67 = $208.375

Licence revenue = Decrease in MC x Q = $(125 - 100) x 16.67 = $25 x 16.67 = $416.75