1. Bob's electric bike has the following production function q = - L^2+ 20L where L is the number of employees working for Bob and the number of electronic bikes is given by q.

a. Calculate the Marginal Product of Labor (MPL) and the Average Product of Labor (APL).

b. For what values of L is the MPL > 0? For what values of L is the MPL diminishing?

2)

Suppose Bob's electric bike shop has the following production function: q = (L^X+ K^X)^1/Y.For what values of X and Y will Bob's production function exhibit constant returns to scale?

3)

Suppose Bob's electric bike shop has the following production function:= 15^0.25. Bob has $10000 to spend on the production of electric bikes. He pays his workers a wage of $10 and his capital costs are $50. If Bob wants to build as many bikes as he can with the $10000, how many employees and capital should Bob employ? How many e-bikes can Bob produce?

4)

Bob sells batteries for e-bikes. Bob's short-run cost function for e-bikes is

given byC(q) = q^2+ 25q + 144

a. If the market price is $75 per battery, how many batteries will Bob produce?

b. What is the price that will provide Bob zero profits?

c. If the price is below the level you found in part (b), will Bob shut down? If so,

explain. If not, below what price will she shut down?

5)

Suppose that Bob produces electric bikes in a competitive market. For simplicity, assume that there are no fixed costs to produce e-bikes. Illustrate two graphs side by side. On left- hand side graph, present the firm. On the right-hand side graph, present the corresponding market. For the firm draw a smooth U-shaped average cost curve and a corresponding marginal cost curve. For the market, draw a demand curve and short-run supply curve that provides positive economic profit for the firm. Illustrate those positive profits on the firm's graph. Also, show the long-run supply curve that would result.

6)

Suppose Bob is the sole producer of electric bikes and faces the following market demand: Q = 480 - 2p. Bob's cost function is given by C(Q) = Q^2 . What is the dead

weight loss resulting from Bob being a monopoly in this market?