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 maximum output (= paintings) producible with TC = $1200?   

		a) 600 painting
		b) 800 paintings
		c) 900 paintings
		d) 1000 paintings
		e) 1,200 paintings

Answer 1

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

F(K,L) = uL + vK

Here,

u = MPL = 20

v = MPK = 15

Hence Production function is given by:

F(K,L) = 20L + 15K

Hence According to cost minimizing criteria for perfect substitutes It will use only L, if P_L < (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 L = 0

Total Cost(TC) = LP_L + KP_K = and this cost must equals TC = 1200 and as discussed above that L = 0

=> LP_L + KP_K = 1200

=> 0*P_L + K*20 = 1200

Hence , Amount of K hired = 60 and amount of L hired = 0

Hence, F(K,L) = 20L + 15K => F(K,L) = 20*0 + 15*60 = 900 units

Hence, the maximum output = 900 paintings

Hence, the correct answer is (c) 900 paintings