7 - Monopoly & Product Selection

Question 1

Given consumes value quality v(q,s) = qs, and production costs c(q) = q² per unit. What is the socially optimal production?

Answer 1

maximize social welfare: max {q} qs - q²

Question 2

Given consumes value quality v(q,s) = qs, and production costs c(q) = q² per unit. What is the monopolist’s profit?

Answer 2

qs - q²

Question 3

Given a share of x consumers values quality with 10q. A share of 1-x consumers values quality with 7q. What are the selling options and corresponding prices for a monopolist?

Answer 3

The monopolist could either sell to only the higher valuing consumers, then price = 10q and demand = x, or to all customers, then price = 7q and demand = 1.
It will depend on x which option brings the higher profit.

Question 4

Explain Klein-Leffler in monopolistic quality production

Answer 4

When producers can produce two qualities and the higher quality gives them a higher profit, there is a production distortion when the number of periods is finite: because in the last period, it is profitable to sell low quality, the consumers anticipate this. Going back to T-1, this is the exact same situation and the consumers can never trust that the producer is committed to producing high quality.