Question one

Given the market demand function of

p + q² + = 11

And the market supply function of

2p ^_ + 2q² + q ^_ 4 = 0

Calculate the equilibrium price and quantity in the market.

Question two

The demand function of a profit maximizing monopolist is

p + 3q ^_ 30 = 0

And his total cost (TC) function is

TC = 2q² + 10q

If a tax of t per unit of quantity is imposed on the monopolist, calculate the maximum tax revenue obtainable by the government.