1. A firm has a proprietary technology and demand for the technology is given by

Question

1. A firm has a proprietary technology and demand for the technology is given by Q 5-4P, where Qp is the quantity demanded for the licenses of the technology per year and P is the price of the licenses. Please answer the following questions. To maximize profits, how much should the firm charge for each license of the technology? Calculate (per-year) consumer surplus, producer surplus and deadweight loss (if there is any) Suppose according to the intellectual property law, patents expire after 20 years. The interest rate is 4%. Calculate the private value of the patent. What is the total deadweight loss of the patent over its life? What is the total consumer surplus generated by the patent over its life (including the time after the patent expires) What is the social value of the patent? Someone suggests the government purchase the patent from the firm. How much does the government need to pay the firm for the patent? What are the benefits of doing so? What does Michael Kremer (1998) suggest the government to do in this case? a. b. c. d. e. f. g. h.

Explanation / Answer

QD = 5 - 4P

4P = 5 - QD

P = 1.25 - 0.25QD

(a) With a patent, marginal cost (MC) is zero. The firm will maximize profit by equating Marginal revenue (MR) and MC.

Total revenue (TR) = P x QD = 1.25QD - 0.25QD2

MR = dTR/dQD = 1.25 - 0.5QD

Equating with MC,

1.25 - 0.5QD = 0

0.5QD = 1.25

QD = 2.5

P = 1.25 - (0.25 x 2.5) = 1.25 - 0.625 = 0.625

(b)

From demand function, when QD = 0, P = 1.25 (Reservation price)

Consumer surplus (CS) = Area between demand curve and market price

= (1/2) x (1.25 - 0.625) x 2.5 = 1.25 x 0.625 = 0.78125

Producer surplus (PS) = Area between market price and MC curve

= $(0.625 - 0) x 2.5 = $0.625 x 2.5 = $1.5625

Efficient outcome is when P = MC:

1.25 - 0.25QD = 0

0.25QD = 1.25

QD = 5

P = MC = 0

Deadweight loss (DWL) = (1/2) x Difference in price x Difference in quantity

= (1/2) x $(0.625 - 0) x (5 - 2.5) = (1/2) x $0.625 x 2.5 = $0.78125

(c) Private value over lifetime ($) = Price x P/A(4%, 20) = 0.625 x 13.5903** = 8.49

(d) Total deadweight loss ($) = DWL x P/A(4%, 20) = 0.78125 x 13.5903** = 10.62

**From P/A factor table

NOTE: As per Chegg Answering policy, first 4 parts have been answered.

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