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1(b)A soot-spewing factory that produces steel windows is next to a laundry. We will assume that the factory faces a prevailing market price of P= $40. Its cost function is C= X", where X is window output, so the factory's marginal cost is MC= 2X. The laundry produces clean wash, which it hangs out to dry. The soot from the window factory smudges the wash, so that the laundry has to clean it again. This increases the laundry's cost. In fact, the cost function of the Laundry is C=Y" + 0.05X, where Y is pounds of laundry washed. The demand curve faced by the laundry is perfectly horizontal at a price of $10 per pound. a. What outputs X and Y would maximize the sum of the profits of these two firms? b. Will those outputs be set by a competitive market? C. What per-unit tax would we need to set on window production to obtain the outputs found in Part a of this problem?

1(b)A soot-spewing factory that produces steel windows is next to a laundry. We will assume that the factory faces a prevailing market price of P= $40. Its cost function is C= X", where X is window output, so the factory's marginal cost is MC= 2X. The laundry produces clean wash, which it hangs out to dry. The soot from the window factory smudges the wash, so that the laundry has to clean it again. This increases the laundry's cost. In fact, the cost function of the Laundry is C=Y" + 0.05X, where Y is pounds of laundry washed. The demand curve faced by the laundry is perfectly horizontal at a price of $10 per pound. a. What outputs X and Y would maximize the sum of the profits of these two firms? b. Will those outputs be set by a competitive market? C. What per-unit tax would we need to set on window production to obtain the outputs found in Part a of this problem?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1(b)A soot-spewing factory that produces steel windows is next to a laundry. We will assume that the factory faces a prevailing market price of P= $40. Its cost function is C= X', where X is window output, so the factory's marginal cost is MC= 2X. The laundry produces clean wash, which it hangs out to dry. The soot from the window factory smudges the wash, so that the laundry has to clean it again. This increases the laundry's cost. In fact, the cost function of the Laundry is C=Y" + 0.05X, where Y is pounds of laundry washed. The demand curve faced by the laundry is perfectly horizontal at a price of $10 per pound. a. What outputs X and Y would maximize the sum of the profits of these two firms? b. Will those outputs be set by a competitive market? C. What per-unit tax would we need to set on window production to obtain the outputs found in Part a of this problem?
Transcribed Image Text:1(b)A soot-spewing factory that produces steel windows is next to a laundry. We will assume that the factory faces a prevailing market price of P= $40. Its cost function is C= X', where X is window output, so the factory's marginal cost is MC= 2X. The laundry produces clean wash, which it hangs out to dry. The soot from the window factory smudges the wash, so that the laundry has to clean it again. This increases the laundry's cost. In fact, the cost function of the Laundry is C=Y" + 0.05X, where Y is pounds of laundry washed. The demand curve faced by the laundry is perfectly horizontal at a price of $10 per pound. a. What outputs X and Y would maximize the sum of the profits of these two firms? b. Will those outputs be set by a competitive market? C. What per-unit tax would we need to set on window production to obtain the outputs found in Part a of this problem?
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