For the following production functions, draw a graph of two isoquant curves with L on the horizontal axis and K on the vertical axis, corresponding to (,) = 10 and (, ) = 20. Label all relevant points.

a. (,) = min (3, 4)

b. (,) = 1/2

2. A firm is using 7 units of labor and 100 units of capital to produce 1000 units of goods. At these levels of inputs, the marginal product of labor is 5 and the marginal product of capital is 50. The cost of labor is $15 per unit and the cost of capital is $2 a unit. Is the firm minimizing its costs? If not explain how the firm could save on costs while still producing 1000 units.

3. Firm A and Firm B produce a homogenous good and compete via Bertrand competition. That is, they both post prices consumers see both prices and go to the firm with the lowest price. If the marginal cost of production is for Firm A and for Firm B, what will be the equilibrium price if < ?

4. The demand curve for a good has the form = with < 1, it has constant elasticity of demand. Suppose a monopolist with marginal cost equal to supplies the market with units of goods. Could the monoplist increase their profits, if so how? What does this imply about the equilibrium price and quantity?