Suppose there a paper which sells paper to a book producer. Suppose that the boo

Question

Suppose there a paper which sells paper to a book producer. Suppose that the book producer makes books according to the production technology B = min(P.10C} where P is paper and C is a book cover. A book cover costs b = $5 for the book producer, paper is purchased in a monopoly market from the paper mill at a price p(P) and the marginal cost of a piece of paper is m = $1. Lastly, books are sold in a perfectly competitive market with demand Pa (B) = 500-B 1. What is the price of paper, the quantity of paper and the quantity of books produced in the market? What are the profits for each firm? To solve this problem, we break up into key parts. First we want to solve for the inverse demand that the monopolist faces. We know that we can back out the inverse demand p(P) from the downstream firms profit maximizing condition: P = 500-B = MC(B) Since our production technology is Leontief, we get the book producer makes books using P = 10C as the optimal ratio for producing books One way to interpret this is that for each book cover C they need 10 pages (or for one book they need 1 page and a book cover). Thus the marginal cost for a book is MC(B) = p(P) + .5. Thus we have: 500-B = p(P) + .5 499.5-B = 499.5-P = p(P) With the inverse demand for paper, we get the paper producers problem which is: max (499.5-P)P-1 P = 498.5P-P2 498.5-2P = 0 P-249.25 & p(P) = 250.25 The profits for paper mill are = 62125.5625. For the quantity of books, we know that there will be P = 249.25 = B which means there will be C = 24.925. Thus the profits for the book producer are = 240.75(249.25)-250.25(249.25)-5(24.925) =-2492.5

Explanation / Answer

The profit function of the paper mill producer is given as,

profit = (499.5-P)P-1P

Maximizing with respect to P, we get P* = 249.25

thus, profit*=(499.5-249.5)249.25 - 249.25 = 62125.5625.

Hope this helps! Revert in case of any doubts.

Thanks!

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.