Question

Johnny Rockabilly has just finished recording his latest CD. His record company's marketing department determines that the demand for the \(\mathrm{CD}\) is as follows:

$$ \begin{array}{cc} \text { Price } & \text { Number of CDs } \\ \hline \$ 24 & 10,000 \\ 22 & 20,000 \\ 20 & 30,000 \\ 18 & 40,000 \\ 16 & 50,000 \\ 14 & 60,000 \end{array} $$

The company can produce the CD with no fixed cost and a variable cost of \(\$ 5\) per \(\mathrm{CD}\).

a. Find total revenue for quantity equal to \(10,000,20,000\), and so on. What is the marginal revenue for each 10,000 increase in the quantity sold?

b. What quantity of CDs would maximize profit? What would the price be? What would the profit be?

c. If you were Johnny's agent, what recording fee would you advise Johnny to demand from the record company? Why?

Answer 1

a) Find total revenue for quantity equal to:
10,000: Revenue=Price*Quantity Revenue=10,000*$24=$240,000
20,000: 20,000*$22=$440,000
30,000: 30,000*$20=$600,000
40,000: 40,000*$18=$720,000
50,000: 50,000*$16=$800,000
60,000: 60,000*$14=$840,000

Marginal Revenue at:
20,000: Revenue @ 20,000-Revenue @ 10,000=Marginal Revenue $440,000-$240,000=$200,000
30,000: $600,000-$440,000=$160,000
40,000: $720,000-$600,000=$120,000
50,000: $800,000-$720,000=$80,000
60,000: $840,000-$800,000=$40,000

b) Find profit at each price level. Profit=Revenue-Cost. We have already found Revenue at each level, so we will find Cost, then profit.
10,000: Cost=10,000*$5=$50,000
20,000: Cost=20,000*$5=$100,000
30,000: Cost=30,000*$5=$150,000
40,000: Cost=40,000*$5=$200,000
50,000: Cost=50,000*$5=$250,000
60,000: Cost=60,000*$5=$300,000

10,000: Profit=Revenue-Cost Profit=$240,000-$50,000=$190,000
20,000: Profit=$440,000-$100,000=$340,000
30,000: Profit=$600,000-$150,000=$450,000
40,000: Profit=$720,000-$200,000=$520,000
50,000: Profit=$800,000-$250,000=$550,000
60,000: Profit=-$840,000-$300,000=$540,000

The quantity of CD's that would maximize profit is 50,000 CD's. The price at 50,000 is $16. The profit is $550,000.