Franco listens only to Symphonic music or Dolly Parton. Franco purchases 12 Symphonic music downloads and 24 downloads by Dolly Parton per month. He would forgo downloads by Dolly for the Symphonic downloads at the rate of 3:1 whenever he has more Dolly units than Symphonic ones. But he would forego only 1 unit by Dolly per Symphonic music unit when the opposite is true. If you somehow took away 18 of his Dolly tunes next month, how many Symphonic music tunes would he need to remain at the same satisfaction level? Be sure to show your work.

A custodial company estimates that each cleaning job adds \$20 to total costs. The firm’s demand is given by the equation below. Estimated demand equation: Q = 50,000 – 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 \$45,000, what is this firm’s total profit at the optimum price/output combination? (show your work)

Q.1. We have MRSsymphonic,dolly = 3/1 = change in symphonic / change in dolly

As he has now more of dolly tunes than symphonic, he will replace 1 tune of dolly with 3 tunes of symphonic.

As in replace of every dolly tunes, he takes 3 of symphonic tunes thus When we took 18 of dolly tunes, we have to provide him 18*3 = 54 tunes of symphonic to make him reside on same satisfaction level.

Q.2. inverse demand function : P = 50 – Q/1000

MC = 20

MR = dTR/dQ

and TR = P*Q = 50Q – Q2/1000

MR = 50 – Q/500

At optimal point MR = MC

thus 50 – Q/500 = 20

30 = Q/500

Q = 15,000 units. This is optimal level of output.

P = 50 – 15000/1000 = \$35 This is optimal price to be charged.

Total profit = TR – TC = P*Q – FC – VC = (35*15000) – 45000 – (20*15000) = \$1,80,000

Asked on February 15, 2018 in