Question

Assume that labor (artist) and capital (robot) are perfect substitutes in producing an output (= painting) for a firm. Marginal product of labor (MP_L =AP_L ) is 15 paintings per day and the price of labor (P_L) is $20/day. The MP of capital (MP_K= AP_K ) is 20 paintings per day, and the rental rate of capital (P_K) for one day is $40. What is the maximum output (= paintings) producible with TC = $600?   

Answers:	a) 300 painting
	b) 450 paintings
	c) 500 paintings
	d) 600 paintings

Assume that labor (artist) and capital (robot) are perfect substitutes in producing an output (= painting) for a firm. Marginal product of labor (MP_L =AP_L ) is 20 paintings per day and the price of labor (P_L) is $40/day. The MP of capital (MP_K= AP_K ) is 15 paintings per day, and the rental rate of capital (P_K) for one day is $20. What is the minimum total cost needed to produce 1200 paintings?

Answers:	a) $600
	b) $1,200
	c) $1,600
	d) $2,400

Answer 1

1. b) 450 paintings
(MPL/PL = 15/20 = 0.75 and MPK/PK = 20/40 = 0.5 so only labor will be used as L and K are perfect substitutes and MPL/PL > MPK/PK. Total labor used = Total cost/PL = 600/20 = 30. Total output = Total labor used*MPL = 30*15 = 450)

2. c) $1,600
(MPL/PL = 20/40 = 0.5 and MPK/PK = 15/20 = 0.75 so only capital will be used as L and K are perfect substitutes and MPL/PL < MPK/PK. Total capital used to produce 1200 paintings = 1200/MPK = 1200/15 = 80. Total cost of K = PK*capital used = 20*80 = 1600)