Question one

A monopolist's demand function is

P = 30 0 . 75q

And his average cost function (AC) takes the form

AC 30 = 9+ 0.3q

q

(i) Find the q which gives

a . Maximum revenue

b . Minimum average cost

c . Maximum profits

In each case check the second-order conditions (s. o . c).

Question two

Given the demand and supply function for three interdependent commodities

q_d1 = 45 2p₁ + 2p₂ 2p₃

q_{d2 =} 16+2p₁ p2 +2p₃

q_{d3 =} 30 p₁ + 2p₂ p₃

q_s1 = 5 + 2p₁

q_s2 = 4+2p₂

q_s3 = 5+p₃

Calculate the equilibrium prices and quantities of this three commodity market model