Problem
John's Lawn Mowing Service is a small business that acts as a price taker. The prevailing market price of lawn mowing is $20 per acre. Although John can use the family mower for free, he has other costs given by
TC = 0.1 Q2 + 10 Q + 50
and
MC = 0.2 Q + 10,
where Q = the number of acres John has chosen to mow in a week.
a) How many acres should John choose to mow in order to maximize profits?
b) Calculate John's maximum weekly profit.
Suppose John's father decides to charge John for the use of the family lawn mower.
c) If the lawn mower fee is set at $100 per week, what will be
- the profit-maximizing number of acres John chooses to mow?
- John's profits?
d) Suppose next that John's father removes the $100 weekly fee and instead imposes a charge of $2 per acre for the use of the family mower, what will be
- John's marginal cost function?
- the profit-maximizing number of acres John chooses to mow?
- John's profits?
e) The $2 per-acre charge remains in place, and the government is thinking of instituting a subsidy for John's business. Two plans are under consideration: (1) a flat grant of $200 per week to John; and (2) a grant of $4 per acre mowed.
- Which of the two plans will John prefer?
- What would be the cost of plan (2) to government?
f) Suppose now that the subsidy - either plan (1) or plan (2) applies to all lawn mowing service businesses. Without reference to specific numbers, use a diagram showing the long-run impact of the subsidy
- on the market price of lawn mowing
- on the amount of lawn mowing in total and per firm.