Beth’s Lawn Mowing Service is a small business and operates in a perfectly compe

Question

Beth’s Lawn Mowing Service is a small business and operates in a perfectly competitive market. The costs function for Beth’s company is given by: total cost (TC) =0.1q2 + 10q + 50 and marginal cost (MC)=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 prot if the prevailing market price of lawn mowing is $20 per acre? Calculate Beth’s maximum weekly prot.

b. How many acres should Beth choose to mow if the market price of lawn mowing is $12 per acre? Calculate the prot(loss) at this price level.

c. Calculate the price at which Beth’s company is making zero prot.

Explanation / Answer

a) MC= TC/ q = 0.2q+10

Set MC=P=20; q*=50.

Beth should choose to mow 50 acres to maximize profit if the price to mow is $20 per acre.

John’s maximum daily profit.   =Pq-TC=1000-800=200.

b) Beth should mow 34 acres to maximize profit if the price to mow is $12 per acre.

John’s maximum daily profit.   =Pq-TC=600-800=-200.(loss)

c) Price at which Beth’s company is making zero prot = 800/50 = $16.

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