Topic 8 Assignment 5 . problems and Applica ions Q9 Some economists believe that the us. economy as a whole can be modeled with the following production function, called the Cobb-Douglas production function: i E. 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: H \"s" plat '21. Suppose that the price of output (P) is $2, A is 3, K is 1,000,000, and L IS 1,000. The labor market is competitive, so labclr is paid the value of its marginal product. The amount of output produced (Y) is , and the dollar value of output (PY) is S The wage (W) is $ , and the real wage () is t (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 (1319)? (Note: The iabor share Is the fraction of the value of output that Is paid to labor.) au an u m In each of the following scenarios, calculate output (Y), the Wage (W), the real wage (4'), and the labor share (gt). Rul Labor Output Wage Wage share scenario (1') (W) (ill) (W ination Increases r from $2 to $3. 3 ' \"a HR Tl\". Suppose that the prloe of output (P) ls 52, A ls 3, K ls 1,000,000, and L ls 1,000. The labor market is competitive, so labor is paid the value of its marginal product. The amount of output produced (Y) is , and the dollar value of output (FY) is E The wage (W) is $ , and the real wage ({5) is t (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 (1,7,5? (Note: The labor share Is the fraction of the value of output that Is paid to labor.) ad um N u ln each of the following scenarios, calculate output (Y), the wage (W), the real wage (1'3 ), and the labor share ($9 Real Labor output Wage Wage share Scenario (Y) (W) (ii) (-317) ination Increases P from $2 to 53. s _' Technological progress increases A from 3 to s 7 _' 9. Capital accumulation increases K from s _' 1,000,000 to 8,000,000. A plague decreases L from 1,000 to 125. s _' Despite many changes in the U51 economy over time, the labor share has been relatively stable. This observation V oonSistent with the CDbb-Duuglas production function. Save A Continue Continue without saving X