Refer to the following figure.The price of capital is $50 per unit: Which of the following combinations of capital and labor lies on the expansion path?
A)110K,120L
B)60K,120L
C)130K,200L
D)130K,175L

Question

Refer to the following figure.The price of capital is $50 per unit:  Which of the following combinations of capital and labor lies on the expansion path?
A)110K,120L 
B)60K,120L 
C)130K,200L 
D)130K,175L

Quizplus · Accepted Answer

The expansion path shows the optimal combinations of capital and labor for different levels of output. To find the expansion path, we need to find the combinations of K and L that produce the same level of output (isocost line) at different prices. In this case, the isocost line is $2500, which means that the total cost of producing a given level of output is $2500 regardless of the combination of K and L. 
Using the formula for total cost (TC = wL + rK), we can solve for L and K at different points on the isocost line:
At point A: 2500 = (20)L + (50)K, where L = 50 and K = 50, total output = 100
At point B: 2500 = (20)L + (50)K, where L = 120 and K = 60, total output = 180
At point C: 2500 = (20)L + (50)K, where L = 200 and K = 30, total output = 230
At point D: 2500 = (20)L + (50)K, where L = 175 and K = 65, total output = 240
We can see that point D (130K, 175L) is on the expansion path because it represents the optimal combination of K and L for a given level of output. As we move along the expansion path, we can see that the slope becomes steeper (more capital-intensive) because the price of capital is higher relative to the price of labor. Therefore, D is the best choice.

Refer to the Following Figure