Question 4

The Downstream Sunglass Company has a monopoly on sunglasses. The inverse demand for sunglasses is given by:

PD = 60 QD

The firm needs to 1 unit of tinted glass for every pair of sunglasses it produces. It has a marginal cost is equal to the price of the input (tinted lenses):

MC1 = PL

(a) Write down the marginal revenue function (MR1) for the downstream firm.

(b) Write down the downstream firm's profit maximizing quantity of sunglasses, as a function of PL.

This function tells you the downstream firm's demand for tinted glass.

The Upstream Lens Company has a monopoly on the manufacture of tinted lenses. It also has a constant marginal cost:

MC2 = 2

This company only sells to one customer: Downstream Sunglass Company.

(c) Based on the downstream firm's demand, write down the marginal revenue function (MR2) for the upstream firm.

(d) Solve for profit-maximizing price of tinted class PL that the upstream firm will charge.