Beth\'s Lawn Mowing Service is a small business and operates in a perfectly comp

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) =0.1 q^2 + 10_q + 50 and marginal cost (MC)=0.2_q + 10, where q=the number of acres Beth chooses to mow in a week. How many acres should Beth choose to mow in order to maximize profit if the prevailing market price of lawn mowing is $20 per acre Calculate Beth's maximum weekly profit. How many acres should Beth choose to mow if the market price of lawn mowing is $12 per acre Calculate the profit(loss) at this price level. Calculate the price at which Beth's company is making zero profit.

Explanation / Answer

a)   P=MC condition for competitive firm
MC = 0.2q+10
P =20
0.2q +10 =20
0.2q =10
q =10/0.2
=50
Profit = 50*20 -0.1(50)^2 -10(50) -50
=1000 -250 -500 -50
=200
b)   P=MC condition for competitive firm
MC = 0.2q+10
P =12
0.2q +10 =12
0.2q =2
q =2/0.2
=10
Profit = 10*12 -0.1(10)^2 -10(10) -50
=120 -10 -100 -50
= -40
c)   TR = 120 while it should be 160
10*P = 160
P = 160/10
P=16
  

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