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.