Figure 18-5
The figure shows a particular profit-maximizing, competitive firm's value-of-marginal-product (VMP) curve. On the horizontal axis, L represents the number of workers. The time frame is daily.
-Refer to Figure 18-5. Suppose one point on the firm's production function is (L = 3, Q = 180), where L = number of workers and Q = quantity of output. If the firm sells its output for $5 per unit, then
A)a second point on the firm's production function is (L = 4, Q = 216).
B)the firm's production function exhibits the property of diminishing marginal product of labor.
C)the firm will maximize profit by hiring four workers if it pays workers $160 per day.
D)All of the above are correct.

Question

Figure 18-5
The figure shows a particular profit-maximizing, competitive firm's value-of-marginal-product (VMP) curve. On the horizontal axis, L represents the number of workers. The time frame is daily. 
-Refer to Figure 18-5. Suppose one point on the firm's production function is (L = 3, Q = 180), where L = number of workers and Q = quantity of output. If the firm sells its output for $5 per unit, then
A)a second point on the firm's production function is (L = 4, Q = 216). 
B)the firm's production function exhibits the property of diminishing marginal product of labor. 
C)the firm will maximize profit by hiring four workers if it pays workers $160 per day. 
D)All of the above are correct.

Quizplus · Accepted Answer

From the given point (L=3, Q=180), we can see that the VMP of the third worker is $60 (i.e. the change in output from the second to the third worker is 60 units and the firm sells each unit for $5). This implies that the firm will hire additional workers as long as their wage is below $60 per day. Therefore, the firm will hire a fourth worker if it pays workers $160 per day (i.e. $60 x 4 < $160). This also confirms choice C. Additionally, since the VMP curve is downward sloping, we know that the marginal product of labor is decreasing as more workers are hired, which confirms choice B. Finally, we can find the output corresponding to L=4 by noticing that the VMP of the fourth worker is $40 (i.e. the change in output from the third to the fourth worker is 40 units) and multiplying it by the price per unit ($40 x $5 = $200). Therefore, the firm's production function exhibits (L=4, Q=216), which confirms choice A.

Figure 18-5 The Figure Shows a Particular Profit-Maximizing, Competitive Firm's Value-Of-Marginal-Product (VMP)