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Some economists believe that the U.S. economy as a whole can be modeled with the following production function, called the Cobb-Douglas production function: a: II AXLE. where Y is the amount of output, K is the amount of capital. L is the amount of labor, and A is a parameter that measures the state of technology. For this production function, the marginal product of labor is: Suppose that the price of output (P) is $2, A is 3, K is 252,144, and L is 512. The labor market is competitive. so labor is paid the value of its marginal product. The amount of output produced (1') is , and the dollar value of output (P?) is $ The wage (W) is $ , and the real wage (g ) is . (Note: The wage is labor compensation measured in dollars, whereas the real wage is labor compensation measured in units of output.) What is the labor share (-13%)? (Note: The labor share is the fraction of the value of output that is paid to labor.) I -P-lu-' LAN Ni W' In each of the sllowing soenarios, calculate output (Y ), the wage (W), the real wage ( 1v: ), and the labor share ( $111: ). Real Labor Output Wage Wage Share Scenario (Y) (W) (2!W ) (15) Ination increases P from $2 to $4. $ ' Technological progress increasesA from 3 to 9. $ ' Capital accumulation increases K from 262,144 to $ ' 2.097.152. A plague decreases L from 512 to 64. $ ' Despite many changes in the U.S. economy over time, the labor share has been relatively stable. This observation ' consistent with the Cobb-Douglas production function. IS I IS NOT