A soot-spewing factory that produces steel windows is next to a laundry. Assume that the factory faces a prevailing market price of PX = $40. Its total cost function is C = X2,where X is window output. The laundry produces clean wash, which it hangs out to dry. The soot from the window factory smudges the wash, so the laundry has to clean it again. This increases the laundry's costs. In fact, the total cost function of the laundry is C = Y 2 + 0.05X, where Y is pounds of laundry washed. The demand curve faced by the laundry is perfectly elastic at a price at PY = $10 per pound.

1. (a)What outputs X and Y would maximize the sum of the profits of these two firms? Assume the two firms were run by the same management.
2. (b)What are competitive market outputs of X and Y ?
3. (c)What per-unit tax would we need to set on window production to obtain the outputs found in part a of this problem?