Consider again the profit-maximizing decision of Beth s Lawn Mowing Service from Problem Suppose Beth s greedy father decides to charge for the use of the family lawn mower.

a. If the lawn mower charge is set at $100 per week, how will this affect the acres of lawns Beth chooses to mow? What will her profits be?

b. Suppose instead that Beth s father requires her to pay 50 percent of weekly profits as a mower charge. How will this affect Beth s profit-maximizing decision?

c. If Beth s greedy father imposes a charge of $2 per acre for use of the family mower, how will this affect Beth s marginal cost function? How will it affect her profit-maximizing decision? What will her profits be now? How much will Beth s greedy father get?

d. Suppose finally that Beth s father collects his $2 per acre by collecting 10 percent of the revenues from each acre Beth mows. How will this affect Beth s profit-maximizing decision? Explain why you get the same result here as for part c.

Beth's Lawn Mowing Service is a small business that acts as a price taker (MR = P). The prevailing market price of lawn mowing is $20 per acre. Although Beth can use the family mower for free (but see Problem), she has other costs given by

Total cost = 0.1q2+ 10q + 50

Marginal cost = 0.2q + 10

where q = the number of acres Beth chooses to mow in a week.

a. How many acres should Beth choose to mow in order to maximize profit?

b. Calculate Beth's maximum weekly profit.

c. Graph these results and label Beth s supply curve.