Assume that a monopoly supplier of a good makes sales to customers located in different regions of the country. The following equations are demand functions for the good in each region:

Q₁= 1 P₁

Q₂= 0.5 P₂

where 1 and 2 index the two regions. Assume that production costs are zero.

a. Assuming that the monopolist must charge a uniform price to the two regions, calculate the profit-maximization uniform price and profit. What is consumer welfare as measured by consumer surplus? (show your work both graphically and mathematically)

b. Assume that the monopolist can engage in 3rd-degree price discrimination. Calculate the profit-maximizing price, quantity, and consumer welfare for each region. (show your work both graphically and mathematically)

c. Does 3rd-degree price discrimination increase or decrease consumer welfare? Which consumers gained and which lost?