An auto-service establishment has estimated its monthly cost function as follows

Question

An auto-service establishment has estimated its monthly cost function as follows:
TC = 6000 + 10 Q
where Q is the number of cars it services each months and TC represents its total cost. The firm is targeting 35,000 net monthly profit servicing 2000 cars.
a. What price should the firm charge to realize the targeted profit?
b. What would be its (cost-based) markup ratio?
c. Now suppose the demand curve the firm faces is:Q = 3000 - 50 P. Is the firm going to achieve its profit goal? Explain.
d. If your to answer to (c) is "no", what would be the optimal markup ratio for this firm?

Explanation / Answer

1.TC=6000+10*Q

Q=2000

Profit=Price*Q-TC=P*2000-(6000+10*2000)=35000

=>2000P-(26000)=35000

=>2000P=61000

=>P=30.5

b)TC=26000

Markup ratio=TC/Q=26000/2000=13

C)Q=3000-50P

Profit=PQ-TC=P(3000-50P)-6000-10(3000-50P)

=3500P-50P^2-36000

Profitmax at dPr/dP=0

=>3500-100P=0

=>P=35

Profitmax=3500*35-50*35^2-36000=25250 at Q=3000-50*35=1250

as profitmax<desired profit ,the firm is not going to achive its goal

D)Optimal markup is P=35,Q=1250

MR=(6000+12500)/1250=14.8

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