SupposetheproductionfunctionforacustomjewelrystoreisQ=0.5KL+2L,whereQ is the number of bracelets produced per day, K is the number of 3D printing machines, and L is the number of workers. Worker wages are $100/day, and each machine cost $50/day to run. The market price for a bracelet is $25.

(a) What is the marginal product of one additional worker? (Hint: your answer should be expressed in terms of units of capital, K.)

(b) What is the marginal product of one additional machine?

(c) Basedonyouranswersto(a)and(b),areworkersandmachinesperfectorimperfect substitutes? Justify your answer.

(d) Write the firm's long-run profit maximizing conditions. What are the profit maxi- mizing quantities of labor and capital? How many bracelets does the firm produce per day?

(e)Supposealaborshortagecausesworkerwagestoriseto$200/day.Themarketprice for a bracelet responds by increasing to $50. What are the new profit maximizing quantities of workers, machines, and bracelets?

(f) How did the profit maximizing quantity of labor change when the market wage increased? Use the concepts of scale and substitution effects to explain this result.