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?
b. Now suppose the demand curve the firm faces is:Q = 3000 - 50 P. Is the firm going to achieve its profit goal? Explain.
c. If your to answer to (b) is "no", what would be the optimal markup ratio for this firm?

Explanation / Answer

A) TC = 6000 +10Q

where Q = 2000

6000 + (10*2000) = 26000

For target profit of 35000, revenue should be cost + profit

26000 +35000 = 61000

per car price should be 61000/2000 = 30.5

B) Profit / Cost

(35000/26000) *100 = 134.61%

C) Q = 3000 - 50P

3000 - (50*30.5) = 1475

Putting in TC, we get

6000 + 14750 = 20750 and

Revenue is 1475*30.5 = 44987.5

Profit is 44987.5 - 20750 = 24237.5

this number is well below target profit of 35000.

D) If we consider units serviced as 1475 then for a target profit of 35000

20750 + 35000 = 55750

per unit price should be 55750/1475 = 37.80

20750/1475 = 14.06

37.80 - 14.06 = 23.74

So, (23.74/13.06)*100 = 168.67%

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