1. A monopolist has an inverse demand curve given by p(y) = 12 y and a cost curve

given by c(y) = y^2

( show math)

a. What will be its profit-maximizing level of output and what price will the firm

charge? (1 mark)

b. Suppose the government decides to put a tax on this monopolist so that for each

unit it sells, it must pay the government $2. What will be its profit maximizing

output under this form of taxation? (1 mark)

2.Assume that the market demand curve for a good is Q(p) = 100 - 0.5p. (show math)

a. give an expression for the inverse demand curve (1 mark)

b. Assume that P=$50 and Q= 75 units. Find the price elasticity of demand and (1 mark)

provide a numerical interpretation for this elasticity.

3.Consider the cost function c(y) = 4y^2 + 16 (Show math)

a. Find the average cost function (1 mark)

b. Find the marginal cost function (1 mark)

c. Find the level of output that yields the minimum average cost of production (1 mark)

d. Find the average variable cost function (1 mark)

e. At what level of output does average variable cost equal marginal (1 mark)

cost?

4.A firm has a production function given by f(x1, x2, x3, x4) = mins{x1 + x2, x3 + 2x4}. Find

the cost function for this technology. (2 points)