Question

1. (50 marks) Answer the following questions on the basis of the table shown here. QB is type B or, and VMPBx and VMPBy are the industry values of the marginal products of this labor in producing x and y, the only two goods in the economy Explain why the VMPs in the table decline as more units of labor are employed If the supply price or opportunity cost of labor PL 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? Suppose PLis $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? Suppose PL 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 a. b. c. d. reallocation of labor? Suppose product x is sold in a perfectly competitive product market. Also ignore the e. VMPBy column and assume that the VMPBx 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.: 0s VMPa VMPBy Qs VMPBr VMPay Qs VMPBr VMPay 1 518 $23 1 $18 $23 1 $18 $23 2 15 19 2 15 19 2 15 19 3 12 15 3 12 15 3 12 15 4911 49 11 49 11 569 569 569 635 635 635

Answer 1

Given that: Table -1 shows the value of marginal product of labor in producing X and Y as follows: Table -1 23 18 19 15 12 15 a. According to the law of diminishing marginal returns, assuming the capital is constant at a certain level of production, if the firm use additional inputs, which will produce less and less additional output, so the marginal productivity of additional labor falls. Therefore, the value of the marginal product in the table -1 falls because as more units of labor are employed in the constant capital.

b. Suppose the opportunity cost of labor PL is S9, then the number of units of type B labor produces an output where the wage rate equal to the marginal product of the labor. According to table -1, the value of the marginal product of labor for producing good X equal to wage rate at the quantity of labor is 4 units and the value of the marginal product of labor for producing good Y equal to wage rate at the quantity of labor is 5 units. Therefore, the type B labor will produce 4 units of X and 5 units of Y Combined total value of two outputs: The combined value of two outputs can be calculated as follows Total productrMVM -(18 +15+12+9)+(23+19+15+11+9) -54+77 -131 Therefore, the combined value of two output is |131 units

ς. Suppose wage is $15 and presently 5 units of labor for good X and 2 units of labor for good Y. According to labor productivity condition, the labor will produce number of goods at the point where the wage rate equal to the value of the marginal product of labor. Since the wage is S15, 5 units of labor producing good X, the yalue of marginal product of labor is less than wage rate then it is an inefficient allocation In case of good Y, the number of labor is 2 units to producing output Y, in value ofmarginal product of labor is more than wage rate. Therefore, the labor allocation is inefficient in good Y also Suppose the wage rate is $15, the efficient allocation occur when the type of labor B produce 2 umits oflabor for good Xand 3 nits oflabor for good Y

d. Suppose wage is $25 and presently 3 units of labor producing good X and 6 units of labor for good Y. According to labor productivity condition, the labor will produce number of goods at the point where the wage rate equal to the value of the marginal product of labor Since the wage is $25, 5 units of labor producing good X, the value of marginal product of labor is less than wage rate then it is an inefficient allocation In case of good Y, the number of output producing is 6, yalue ofmarginal product oflabor is less than wage rate. Therefore, the labor allocation is inefficient in good Y also. Since the marginal product of labor in producing good X and Y is less than the wage rate, no labor would not produce good X and Y. Therefore, there is no efficient allocation when the wage rate is $25 Total production The total production if the wage rate is $25 can be calculated as follows Total production -yVMP+ VMP BF (18 1512) (23 +19+15 11+9+5) =45 +82 =127 Therefore, the total productivity is 127 units

Total wage: The total wage can be calculated as follows: Total wage- Number of units of labor x wage (6+3)x 25 225 Therefore, the total wage is $225 Gain in the total value of leisure, alternative outputs or home production is 98(225-127 units