Answer the following questions on the basis of the table shown here. Q_B is type B labor, and VMP_Bx and VMP_By are the industry values of the marginal products of this labor in producing x and y, the only two goods in the economy.
a. If the supply price or opportunity cost of labor P_L is $9, how many units of type B labor need to be used in producing x and y to achieve an efficient allocation of labor? What will be the combined total value of the two outputs?
b. Suppose P_L is $15 and that presently five units of labor are being allocated to producing x while two units are being allocated to y. Is this an efficient allocation of labor? Why or why not? If not, what is the efficient allocation of type B labor?
c. Suppose P_L is $25 and three units of labor are being allocated to producing x, while six units are being allocated to producing y. Explain why this is not an efficient allocation of labor. What is the efficient allocation of this type of labor? What gain in the total value of leisure, alternative outputs, or home production results from this reallocation of labor?
d. Suppose product x is sold in a perfectly competitive product market. Also ignore the VMP_By column and assume that the VMP_Bx schedule is representative of each firm hiring workers in a perfectly competitive labor market. If the market wage rate is $12, what will be each firm’s MWC? What will be their MRPs at their profit-maximizing level of employment? Explain why an efficient allocation of labor will occur in this industry.