Question

Assume the demand for a good that is a potential product innovation is predicted to be with certainty: Q=10-0.1P.

(a) If the production of the good is costless and the good is offered by the government (i.e. offered as a public good), what is the Consumer Surplus?

(b) Assuming a monopoly decides to invent the good, and maximizes short run profits, find the equilibrium. What is the monopoly profit? What is consumer surplus? What is DWL?

Answer 1

Assume the demand for a good that is a potential product innovation is predicted to be with certainty: Q=10-0.1P.

(a) If the production of the good is costless and the good is offered by the government (i.e. offered as a public good), what is the Consumer Surplus?

Price is 0. Hence Q = 10. Consumer surplus = 0.5*(Max price - current price)*qty = 0.5*(100 - 0)*10 = $500.

(b) Assuming a monopoly decides to invent the good, and maximizes short run profits, find the equilibrium. What is the monopoly profit? What is consumer surplus? What is DWL?

Monopoly finds that inverse demand is P = 100 - 10Q. MR = 100 - 20Q. Since MC = 0, MR = 0 and so Q = 100/20 = 5 units. P = 100 - 10*5 = $50

Profit = Revenue = $50*5 = $250

CS = 0.5*(100 - 50)*5 = $125. DWL = 0.5*(50 - 0)*(10 - 5) = $125.