-The marginal rate of technical substitution at point A is
A) less than 0.25.
B) less than 4.0.
C) greater than 0.25.
D) greater than 4.0.

Question

-The marginal rate of technical substitution at point A is
A) less than 0.25. 
B) less than 4.0. 
C) greater than 0.25. 
D) greater than 4.0.

Quizplus · Accepted Answer

The marginal rate of technical substitution (MRTS) is the rate at which one input can be substituted for another input without affecting the level of output.

At point A, the slope of the isoquant (the curve representing the same level of output) is steeper than the slope of the isocost line (the line representing the same total cost). This means that it is possible to substitute more of input 2 for input 1 while keeping the same level of output, which indicates a high MRTS.

To narrow down the options, we can calculate the MRTS at point A by taking the absolute value of the ratio of the marginal product of input 1 to the marginal product of input 2, evaluated at point A:

|MRTS| = |(dQ/dL1) / (dQ/dL2)|

Using the information given in the graph, we can estimate the marginal products as:

dQ/dL1 ≈ 36 - 20L1 + 0.5L2
dQ/dL2 ≈ 24 - 10L2 + 0.5L1

At point A, we have L1 = 1 and L2 = 3, so:

dQ/dL1 ≈ 16
dQ/dL2 ≈ 19

Therefore:

|MRTS| ≈ 16/19 ≈ 0.84

Since this value is greater than 0.25, but less than 4.0, the best choice is C.

-The Marginal Rate of Technical Substitution at Point a Is