7. Given the data below on labor and output in the short run:

L Q

1 10

2 18

3 24

Suppose that the capital is fixed at K=4. If the rent R is $4 and the wage W is $8, then the total variable cost of producing 24 units is

Question

7. Given the data below on labor and output in the short run:

L             Q

1              10

2              18

3              24

Suppose that the capital is fixed at K=4. If the rent R is $4 and the wage W is $8, then the total variable cost of producing 24 units is

BlackTom AI · Accepted Answer

First, restating the given scenario helps focus on what drives costs in the short run. The data show a fixed capital stock of K = 4 and a wage rate W = 8, with labor L used to produce output Q. The total variable cost (TVC) in the short run is the cost of all variable inputs, which here are the wages paid to labor. Since capital is fixed, its cost (the rent R = 4) is a fixed cost, not part of TVC.

Option $16: This would imply a TVC of 2 units of labor times the wage (2 × 8 = 16). However, to produce 24 units, the data indicate L = 3, not L = 2. Therefore this value corresponds to the wrong level of labor and cannot represent TVC for 24 units.

Option $24: This equals 3 units of labor times the wage (3 × 8 = 24). From the table, producing 24 units uses L = 3. Since TVC = W × L and capital is fixed, this calculation correctly reflects the variable input cost at the reported output level.

Option $40: If one incorrectly used L = 5 (5 × 8), or added some fixed cost component to TVC, the result would be 40. But the table provides L values up to 3 for the given outputs, and there is no indication that more labor is employed beyond L = 3 for the Q = 24 case. Thus this value misattributes both the labor usage and the category of cost.

Option $48: This would correspond to 6 units of labor at wage 8 (6 × 8) or mixing an incorrect interpretation of fixed and variable costs. Again, the supplied data show L = 3 for Q = 24, so TVC cannot be 48 in this context.

In summary, the correct TVC for producing 24 units in this setup is determined by the wage rate times the labor used to generate 24 units, with capital costs fixed. The only option aligning with L = 3 and W = 8 is $24, while the other options misuse the labor quantity or misclassify fixed versus variable costs.

7. Given the data below on labor and output in the short run: L Q 1 10 2 18 3 24 Suppose that the capital is fixed at K=4. If the rent R is $4 and the wage W is $8, then the total variable cost of producing 24 units is 单项选择题

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