Answer to Question #212599 in Microeconomics for Kirthy

Question

WOU Records decides to release an album by the group Cat and the Kittens. It produces the album with no fixed cost, but the total cost of downloading an album to a CD and paying Mary her royalty is RM6 per album. WOU Records can act as a single-price monopolist. Its marketing division finds that the demand schedule for the album is as shown in the accompanying table.

Price of album (RM) Quantity of album demanded

22 0

20 1000

18 2000

16 3000

14 4000

12 5000

10 6000

8 7000

(a) Calculate the total revenue and the marginal revenue per album.

[10 marks]

(b) The marginal cost of producing each album is constant at RM6. To maximize profit, determine the level of output and price it should charge for each album.

[15 marks]

(c) Cat renegotiates her contract and now demands a higher royalty per album. The marginal cost rises to be constant at RM14. To maximize profit, determine the level of output and price it should charge for each album.

[15 marks]

Answer 1

(a)Determination of Total revenue (TR), and Marginal Revenue (MR):

Total Revenue = Price (P) $\times$ Quantity (Q); Marginal Revenue (MR)= $\frac{Δ TR}{\Delta Q}$

P Q TR MR

22 0 0 0

20 1000 20000 20

18 2000 36000 16

16 3000 48000 12

14 4000 56000 8

12 5000 60000 4

10 6000 60000 0

8 7000 56000 -4

(b) Determination of the level of output and price that maximizes profit;

NOTE: Profits are maximized at the point where Marginal Revenue (MR) is slightly higher or equal to Marginal cost (MC)

Determination of TC and MC;

TC = 6 $\times$ Q, and MC = 6

P Q TR MR TC MC

22 0 0 0 0 0

20 1000 20000 20 6000 6

18 2000 36000 16 12000 6

16 3000 48000 12 18000 6

14 4000 56000 8 24000 6

12 5000 60000 4 30000 6

10 6000 60000 0 36000 6

8 7000 56000 -4 42000 6

From above table;

Profit is maximized at P = RM14, and corresponding output is 4000Units.

(c) Determination of the level of output and price that maximizes profit at MC of RM14

P Q TR MR TC MC

22 0 0 0 0 0

20 1000 20000 20 6000 14

18 2000 36000 16 12000 14

16 3000 48000 12 18000 14

14 4000 56000 8 24000 14

12 5000 60000 4 30000 14

10 6000 60000 0 36000 14

8 7000 56000 -4 42000 14

From above table;

Profit is maximized at P = RM18, and corresponding output is 2000Units.