1. (1.5 points) John\'s Lawn Mowing Service is a small business that acts as a p
ID: 1116809 • Letter: 1
Question
1. (1.5 points) John's Lawn Mowing Service is a small business that acts as a price-taker. The prevailing market price of lawn mowing work is p per acre. Total cost for him is given by c = 0.1r' + 10, + 50. where q is equal to the number of acres John chooses to cut in a day (a) what is John's profit function (q)? (b) Solve the profit maximization problem to derive John's supply curve p(). And graph the result. (c) If market price of lawn mowing is $20 per acre, how many acres should John choose to cut to maximize profit? Calculate John's maximum daily profit.Explanation / Answer
a) John's profit function is given by
TC=0.1q2+10q+50
MC=0.2q+10
John wil produce where MR=MC ,,,MR=p
0.2q+10=p
b)John's profit fucntion is given by
q2+10q+50
The supply function is given by the solution to the profit maximization problem
0=p-0.2q-10
qs(p)=5p-50
c)TC = 0.1q2+10q+50.
MC = 0.2 q + 10
MR = $20.
John will produce in the condition where MR = MC
therefore MC = 20
0.2 (50) + 10 = 20
Hence by subtituting q=50 ,we get the eqn equated that means
To maximize profits, John should cut 50 acres of lawn
John profit maximizing output should be lower than the market supply.He can make profit ony if he supplies the whole market .
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