Answer to Question #294466 in Microeconomics for Amruth

Question

Johnny Rockabilly has just finished recording his latest CD. His record company’s marketing department determines that the demand for the CD is as follows:

PRICE

NUMBER OF CDS

$24

10,000

22

20,000

20

30,000

18

40,000

16

50,000

14

60,000

The company can produce the CD with no fixed cost and a variable cost of $5 per 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

Qn. a

To get the total revenue, $TR=P\times Q$

$Q=10,000:TR=10000\times24=240,000$

$Q=20,000:TR=20000\times22=440,000$

$Q=30,000:TR=30000\times20=600,000$

$Q=40,000:TR=10000\times18=720,000$

$Q=50,000:TR=10000\times16=800,000$

$Q=60,000:TR=10000\times14=840,000$

Marginal revenue $MR=\frac{\Delta Q}{\Delta P}$

${\Delta Q} = 10,000$

${\Delta P} =2$

$\therefore MR = \frac{10,000}{2} = 5000$

Qn. b

The quantity of CDs maximizing profit, can be obtained through tabulation of TC and TR, to get the profit, which highest value can be used to get quantity and price as below.

$Profit (\pi) = TR-TC$

$TC=VC \times Q_d$

$VC=5$

$@Q_d=10,000\ TR=240,00\ TC=50,000\$ $\pi=190,000$

$@Q_d=20,000\ TR=440,00\ TC=100,000$ $\pi=340,000$

$@Q_d=30,000\ TR=600,00\ TC=150,000$ $\pi=4500,000$

$@Q_d=40,000\ TR=720,00\ TC=200,000$ $\pi=520,000$

$@Q_d=50,000\ TR=800,00\ TC=250,000$ $\pi= \bold{550,000}$

$@Q_d=60,000\ TR=840,00\ TC=300,000$ $\pi=540,000$

from above, the maximum profit is noted to be 550,000. from that, we obtain the quantity and price.

$\pi = \$ 550,000$

$Q=50, 000$

$P= \$ 16$

Qn. c

$50,000 charging fee

At a profit of $ 550,000 with a quantity of 50,000 it is consistent that the 50,000 CDs produced will have a recording fee of $ 1 each. minimizing the cost.