This function exhibits decreasing retums to scale.For example,if L is 2 and K is 2 then q is 13.66.IfL is 4 and K is 4 thenq is 24. When the inputs are doubled output will less than double The marginal product of labor is decreasing and the marginal product of capital is constant.For any given value of L,when K is increased by 1 unit,q will go up by 4 units,which is a constant number.To see that the marginal product of labor is decreasing,fix K=1 and choose values for L.If L=1 then q=8,if L=2 then q=9.65, -13.The marginal product ofthe se Marginal product of labor is diminishing. 9.The produetion function for the personal computers of DISK,Ine.,is given by q=10KasLas,where q is the number ofcomputers produced per day,K is hours of machine time,and Lis hours of labor input.DISK's competitor,FLOPPY,Inc.,is using the production function g=10K0.6Lo4. a.If both companies use the same amounts of capital and labor,which will generate more output? Let Q be the output of DISK.Inc.g2.be the output of FLOPPY.Inc.and Xbe the same equal amounts ofeapital and labor for the two firms.to thei production functions, g=100.5X05=100.5+0.5=10X and =10604=10X0.6+00=10K Because g =g both firms generate the same output with the same inputs Note that if the two firms both sed the same amount of capital and the amount of labor,but the amount of capital was not equal to the amount of labor then the two firms woul not produce the same level of output.In fact,if K>L then q>q. b.Assume that capital is limited to 9 machine hours but labor is unlimited in supply.In which company is the marginal product of labor greater? Explain. 0Todetermine the production function with thehigh marginal productivity of labor,consider the following table: MPr MPL Firm】 Firm2 Firm 2 0 00 0.00 1 30.00 30.00 37.37 37.37 2 42.43 12.43 49.31 1194 3 51.96 93 58.00 8.69 This function exhibits decreasing returns to scale. For example, if L is 2 and K is 2 then q is 13.66. If L is 4 and K is 4 then q is 24. When the inputs are doubled, output will less than double. The marginal product of labor is decreasing and the marginal product of capital is constant. For any given value of L, when K is increased by 1 unit, q will go up by 4 units, which is a constant number. To see that the marginal product of labor is decreasing, fix K=1 and choose values for L. If L=1 then q=8, if L=2 then q=9.65, and if L=3 then q=10.93. The marginal product of the second unit of labor is 9.65-8=1.65 and the marginal product of the third unit of labor is 10.93-9.65=1.28. Marginal product of labor is diminishing. 9. The production function for the personal computers of DISK, Inc., is given by q = 10K0.5L0.5, where q is the number of computers produced per day, K is hours of machine time, and L is hours of labor input. DISK’s competitor, FLOPPY, Inc., is using the production function q = 10K0.6L0.4. a. If both companies use the same amounts of capital and labor, which will generate more output? Let Q be the output of DISK, Inc., q2 , be the output of FLOPPY, Inc., and X be the same equal amounts of capital and labor for the two firms. Then, according to their production functions, q = 10X0.5X0.5 = 10X(0.5 + 0.5) = 10X and q2 = 10X0.6X0.4 = 10X(0.6 + 0.4) = 10X. Because q = q2 , both firms generate the same output with the same inputs. Note that if the two firms both used the same amount of capital and the same amount of labor, but the amount of capital was not equal to the amount of labor, then the two firms would not produce the same level of output. In fact, if K>L then q2>q. b. Assume that capital is limited to 9 machine hours but labor is unlimited in supply. In which company is the marginal product of labor greater? Explain. With capital limited to 9 machine units, the production functions become q = 30L0.5 and q2 = 37.372L0.4. To determine the production function with the highest marginal productivity of labor, consider the following table: L q Firm 1 MPL Firm 1 q Firm 2 MPL Firm 2 0 0.0 _ 0.00 _ 1 30.00 30.00 37.37 37.37 2 42.43 12.43 49.31 11.94 3 51.96 9.53 58.00 8.69