Following is a firm's expansion path.The price of capital is $5 per unit; the price of labor is $2 per unit. How much does the 10th unit of output add to long-run total cost?
A)zero
B)$3
C)$4
D)$40
E)none of the above

Question

Following is a firm's expansion path.The price of capital is $5 per unit; the price of labor is $2 per unit.  How much does the 10th unit of output add to long-run total cost?
A)zero 
B)$3 
C)$4 
D)$40 
E)none of the above

Quizplus · Accepted Answer

The expansion path shows the cost-minimizing combinations of inputs (capital and labor) required to produce different levels of output. The slope of the expansion path at any point is the ratio of the prices of the two inputs (in this case, 5/2 = 2.5).

To find the cost of producing the 10th unit of output, we need to look at the expansion path and find the point where output is 10. From the graph, we can see that this occurs at a capital-labor combination of (4,3).

To calculate the cost of producing the 10th unit, we need to add up the cost of the inputs required at this point. Using the given prices of capital and labor, we get:

Cost = (4 units of capital x $5/unit of capital) + (3 units of labor x $2/unit of labor) 
Cost = $20 + $6
Cost = $26

So the 10th unit of output adds $26 to long-run total cost. However, we are asked how much the 10th unit adds "to" total cost, which suggests that we should be looking for the marginal cost of production. The marginal cost is the additional cost of producing one more unit of output, which in this case is simply the difference between the cost of producing 10 units and the cost of producing 9 units.

To find the cost of producing 9 units, we can look at the expansion path again and find the point where output is 9. From the graph, we can see that this occurs at a capital-labor combination of (3,4).

Cost of producing 9 units = (3 units of capital x $5/unit of capital) + (4 units of labor x $2/unit of labor) 
Cost of producing 9 units = $15 + $8
Cost of producing 9 units = $23

So the marginal cost of producing the 10th unit is:

Marginal cost = Cost of producing 10 units - Cost of producing 9 units 
Marginal cost = $26 - $23
Marginal cost = $3

Therefore, the answer is (C) $4.

Following Is a Firm's Expansion Path