Question

Inverse demand function is given as P=$100,000 - 52.5Qd, where Qd is the annual quantity demanded. development costs were substantial and marginal costs for a treatment are "just" $750 per treatment.

a) if you set a single price to maximize profits, what quantity will you supply annually? (hint: the marginal revenue function has the same y-axis intercept as the inverse demand function, but twice the slope. set MR=MC and solve for Q)

b) what is the price for treatment (hint: plug your quantity for a into the inverse demand function)

c) if the treatment was priced at the marginal cost, how many treatments would be provided per year?

d) what is the deadweight loss due to monopoly power in the market?

Answer 1

MR curve :

P = 100,000-(52.5*2)Q

P = 100,000 - 105Q

MC = 750

So at Monopoly eqm:

MR = MC

100,000-105Q = 750

Q*= 945.238

b)

P* = 100,000-52.5Q*

= $50,375

.c) at P = MC = 750

750 = 100,000 - 52.5Q

Q = (100,000-750)/52.5

= 1890.476

D) deadweight loss due to monopoly

= .5*(1890.476-945.238)*(50,375-750)

= $ 23,453,717.9