Gamaleya Institute in Moscow claims to be first pharmaceutical company to have created a vaccine for Covid-19. Accordingly, the firm plans to sell its vaccine in two different markets: domestic and foreign. The corresponding demand functions are

P1 + 2Q1 = 100 (1)

2P2 + Q2 = 2a (2)

The total cost function is

TC = 500 + 10Q (3)

where

Equation 1 is the domestic market

Equation 2 is the foreign market

Q = Q1 + Q2

a is a positive constant.

(a) Determine, in terms of a, the prices needed to maximize profit

with price discrimination

without price discrimination.

(b) Show that the profit with price discrimination is always greater than the profit without discrimination, irrespective of the value of a.