(1) Given the market demand function

P+ Q² + Q 11

And the market supply function

2p-2Q²+Q - 4=0

Calculate the equilibrium price and quantity in the market.

(2) A monopolist's demand function is

P= 30- 0.75Q

And his average cost function is

AC - 30 =9+0.3Q

Q

(1) Find the Q which gives

a. Maximum revenue

b. Minimum average costs

c. Maximum profits

In each case check the second-order conditions(S. 0. C ).

(3) 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.

(4) Given the demand and supply function for three interdependent commodities

Q_D1 = 45 - 2P₁ +2P₂ - 2P₃

Q_{D2 =}16 ₊ 2P_{1 -} P₂+ 2P₃

Q_{D3 =} 30 - P₁ + 2P_2- P₃

Q_{S1 = -} 5 + 2P₁

Q_{S2 = -} 4 + 2P₂

Q_{S3 = -} 5 + P₃