A custodial company estimates that each cleaning job adds $25 to total costs. Th

Question

A custodial company estimates that each cleaning job adds $25 to total costs. The firm’s demand is given by the equation below. Estimated demand equation: Q = 55,000 – 1,000P She also calculates marginal revenue from this relationship. a. What is the optimal level of output? b. In order to sell the amount computed in part (a) above; at what price would the company have to offer its service? c. If fixed costs are $145,000, what is this firm’s total profit at the optimum price/output combination? (be SURE to show your work)

Explanation / Answer

Q = 55,000 – 1,000P

after simplification we get,

1000P = 55000 - Q

P = 55 - 0.001Q (Ths is the inverse demand function)

TR = P*Q = 55Q - 0.001Q^2 (The total revenue is the product of the price and quantity)

MR = dTR/dQ = 55 - 0.002Q

MC = 25

55 - 0.0002Q = 25

0.0002Q = 30

Q = 15000

P = 55 - 0.001*15000 = $40

C= 145000 + 25Q (Costs are sum total of fixed and variable costs)

Profits = TR-TC = 55Q - 0.001Q^2 - 145000 - 25Q

at Q = 15000, we replace Q= 15000 we will get

=55*15000-0.001*(15000)^(2)-145000-25*15000

Profits = 80000

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