Suppose the Production Function of Automobiles Is Given By $Q = K ^ { 1 / 4 } L ^ { 1 / 4 }$

Essay

Suppose the production function of automobiles is given by $Q = K ^ { 1 / 4 } L ^ { 1 / 4 }$ a.Show that the marginal product of any given quantity of labor increases as capital is increased.
b.Suppose Japanese and U.S.automakers produce on identical isoquants with this Cobb-Douglas production function and that labor costs are higher in Japan than in the United States.Do autoworkers in Japan have a higher marginal product than American autoworkers?
Explain carefully.
c.Now suppose Japanese automakers produce on a different isoquant from U.S.firms,but the prices of Japanese and American cars are identical.Do Japanese or American autoworkers have a higher marginal product?
Why?