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 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?

		a) $800
		b) $1,200
		c) $1,600
		d) $2,400
		e) $4,800

Answer 1

The correct answer is (c) $1600

Given L and K are perfect substitutes and hence Production function is given by:

Q = aL + bK

Here,

Hence Production function is given by:

Q = 20L + 15K

Hence It will use only L if P_L is lesser than (20/15)P_K and It will use only K if P_L > (20/15)P_K

Here P_L = 40 and P_K = 20 => (20/15)P_K = = 20*20/15 = 26.67 < P_L

Hence It will hire only K and Hence we want Q = 1200 and L = 0

=> 20L + 15K = 1200

=> 20*0 + 15K = 1200

=> K = 80.

Hencce He will hire only K = 80 and L = 0

Cost(C) = LP_L + KP_K = 0 + 80*20 = 1600

Hence minimum total cost needed to produce 1200 paintings is $1600

Hence, the correct answer is (c) $1600