Question
In: Economics
A publisher in a competitive market faces the following cost schedule for publishing a novel by...
A publisher in a competitive market faces the following cost schedule for publishing a novel by one of its authors: the author is paid a $3,000,000 up-front signing bonus to write the book (it is not refundable). The going market price for a hardcover book is $32 per copy. Where Q is the number of books printed and AVC is the average variable cost of producing books at a given Q.
|
AVC |
Q |
|
$0.00 |
0 |
|
$10.000 |
100,000 |
|
$10.666 |
150,000 |
|
$11.326 |
200,000 |
|
$11.993 |
250,000 |
|
$12.660 |
300,000 |
|
$13.327 |
350,000 |
|
$13.994 |
400,000 |
|
$14.661 |
450,000 |
|
$15.328 |
500,000 |
|
$15.995 |
550,000 |
|
$16.662 |
600,000 |
|
$17.329 |
650,000 |
|
$17.996 |
700,000 |
|
$18.663 |
750,000 |
|
$19.330 |
800,000 |
|
$19.997 |
850,000 |
|
$20.664 |
900,000 |
|
$21.331 |
950,000 |
|
$21.998 |
1,000,000 |
|
$22.665 |
1,050,000 |
- Compute total revenue, total cost and profit at each quantity.
- Compute marginal revenue. How does marginal revenue compare to price? Explain.
- Compute marginal cost.
- Is there a quantity where marginal revenue and marginal cost cross? What does this signify? What is the quantity?
- What quantity would a competitive profit maximizing publisher choose?
- If the author were paid $4 million instead of $3 million to write the book, how would this affect the publisher’s decision on what quantity to sell and its profits?
Solutions
Expert Solution
*We are supposed to do only four subparts to a question. For solution to other parts please post as a separate question.
| AVC | Q | TFC | Price | Total Revenue | Total Cost | Profit | Marginal Revenue | Marginal Cost |
| $ - | 0 | $ 30,00,000.00 | $ 30,00,000.00 | |||||
| $ 10.00 | 1,00,000 | $ 30,00,000.00 | 32 | 3200000 | $ 40,00,000.00 | $ -8,00,000.00 | $32.00 | $10.00 |
| $ 10.67 | 1,50,000 | $ 30,00,000.00 | 32 | 4800000 | $ 45,99,900.00 | $ 2,00,100.00 | $32.00 | $12.00 |
| $ 11.33 | 2,00,000 | $ 30,00,000.00 | 32 | 6400000 | $ 52,65,200.00 | $ 11,34,800.00 | $32.00 | $13.31 |
| $ 11.99 | 2,50,000 | $ 30,00,000.00 | 32 | 8000000 | $ 59,98,250.00 | $ 20,01,750.00 | $32.00 | $14.66 |
| $ 12.66 | 3,00,000 | $ 30,00,000.00 | 32 | 9600000 | $ 67,98,000.00 | $ 28,02,000.00 | $32.00 | $16.00 |
| $ 13.27 | 3,50,000 | $ 30,00,000.00 | 32 | 11200000 | $ 76,44,500.00 | $ 35,55,500.00 | $32.00 | $16.93 |
| $ 13.99 | 4,00,000 | $ 30,00,000.00 | 32 | 12800000 | $ 85,97,600.00 | $ 42,02,400.00 | $32.00 | $19.06 |
| $ 14.66 | 4,50,000 | $ 30,00,000.00 | 32 | 14400000 | $ 95,97,450.00 | $ 48,02,550.00 | $32.00 | $20.00 |
| $ 15.33 | 5,00,000 | $ 30,00,000.00 | 32 | 16000000 | $ 1,06,64,000.00 | $ 53,36,000.00 | $32.00 | $21.33 |
| $ 16.00 | 5,50,000 | $ 30,00,000.00 | 32 | 17600000 | $ 1,17,97,250.00 | $ 58,02,750.00 | $32.00 | $22.67 |
| $ 16.66 | 6,00,000 | $ 30,00,000.00 | 32 | 19200000 | $ 1,29,97,200.00 | $ 62,02,800.00 | $32.00 | $24.00 |
| $ 17.33 | 6,50,000 | $ 30,00,000.00 | 32 | 20800000 | $ 1,42,63,850.00 | $ 65,36,150.00 | $32.00 | $25.33 |
| $ 18.00 | 7,00,000 | $ 30,00,000.00 | 32 | 22400000 | $ 1,55,97,200.00 | $ 68,02,800.00 | $32.00 | $26.67 |
| $ 18.66 | 7,50,000 | $ 30,00,000.00 | 32 | 24000000 | $ 1,69,97,250.00 | $ 70,02,750.00 | $32.00 | $28.00 |
| $ 19.33 | 8,00,000 | $ 30,00,000.00 | 32 | 25600000 | $ 1,84,64,000.00 | $ 71,36,000.00 | $32.00 | $29.34 |
| $ 20.00 | 8,50,000 | $ 30,00,000.00 | 32 | 27200000 | $ 1,99,97,450.00 | $ 72,02,550.00 | $32.00 | $30.67 |
| $ 20.66 | 9,00,000 | $ 30,00,000.00 | 32 | 28800000 | $ 2,15,97,600.00 | $ 72,02,400.00 | $32.00 | $32.00 |
| $ 21.33 | 9,50,000 | $ 30,00,000.00 | 32 | 30400000 | $ 2,32,64,450.00 | $ 71,35,550.00 | $32.00 | $33.34 |
| $ 22.00 | 10,00,000 | $ 30,00,000.00 | 32 | 32000000 | $ 2,49,98,000.00 | $ 70,02,000.00 | $32.00 | $34.67 |
| $ 22.67 | 10,50,000 | $ 30,00,000.00 | 32 | 33600000 | $ 2,67,98,250.00 | $ 68,01,750.00 | $32.00 | $36.01 |
| a) Total Revenue = Price *Quantity | ||||||||
| Total Cost = TFC+ AVC*Quantity | ||||||||
| Profit =Total Revenue -Total Cost | ||||||||
| b) Marginal Revenue = ΔTR/ΔQ | ||||||||
| Marginal revenue is equal to price. This implies the market structure is perfect competition. | ||||||||
| c) Marginal Cost = ΔTC/ΔQ | ||||||||
| d) Yes, the marginal revenue and the marginal cost cross at Q = 900,000 | ||||||||
| This signify that profit is at maximum level. | ||||||||
| e) The profit maximizing publisher will choose Q = 900000. | ||||||||
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