Final answer:
The value of the marginal product of labor is $2500 and the value of the marginal product of capital is $8000. The firm can improve by hiring more labor since VMP is less than the unit price of labor. Other factors should also be considered in real-life decision-making.
Step-by-step explanation:
In a perfectly competitive output market, the value of the marginal product (VMP) is calculated by multiplying the marginal product of labor (MPL) by the price of the output. In this case, MPL is given as 100 and the unit price of labor is $25, so VMP = MPL x PL = 100 x 25 = $2500. Similarly, the value of the marginal product of capital (VMPK) is calculated by multiplying the marginal product of capital (MPK) by the price of capital (PK). Given MPK = 200 and PK = $40, VMPK = MPK x PK = 200 x 40 = $8000.
The firm is not necessarily operating at its best because each input should be employed up to the point where the value of the marginal product equals the price of the input. In this case, the firm should hire more labor until VMP = PL and more capital until VMPK = PK. Since VMP = $2500 is less than PL = $25, the firm should hire more labor to reach its optimal level of employment.
It is important to note that while VMP helps determine the optimal levels of labor and capital, other factors such as cost, availability, and substitution possibilities should also be considered in real-life decision-making.