Refer to the following graph.The price of capital r)is $20. At the optimal combination of inputs for producing 14,000 units of output,what is the marginal rate of technical substitution?
A)2.5
B)0.67
C)1.5
D)0.80
E)impossible to tell from the graph

Question

Refer to the following graph.The price of capital r)is $20.  At the optimal combination of inputs for producing 14,000 units of output,what is the marginal rate of technical substitution?
A)2.5 
B)0.67 
C)1.5 
D)0.80 
E)impossible to tell from the graph

Quizplus · Accepted Answer

The optimal combination of inputs for producing 14,000 units of output is where the isoquant (curve) is tangent to the isocost (line). At this point, the slope of the isoquant (MRTS) is equal to the slope of the isocost (-w/r). From the graph, the slope of the isocost is -20/40 = -0.5. At the same point, the MRTS is (dK/dL) = (ΔK/ΔL) = (40-20)/(25-10) = 2. Therefore, the marginal rate of technical substitution (MRTS) is equal to (-w/r) = -0.5. Solving for w/r, we get 0.5. Since MRTS = ΔK/ΔL, K/L is equal to the absolute value of MRTS. Therefore, K/L = 0.5. Solving for K/L, we get 1.5. Thus, the answer is C.

Refer to the Following Graph