Question

1. (10pts)The Classical Model: Cobb-Douglas Production Function:

(a) (6pts) Using calculus, demonstrate how the percentage of total income attributable to capital is equal to the exponent of capital in the Cobb-Douglas production function.  As you work through the proof, explain what each variable represents as if you were explaining this to a fellow student for the first time.

(b) (4pts) Using the following production function: Y=10K^0.25*L^0.75, suppose that capital (K) increases by 20%.

i)  (2pts) How much will total output increase in terms of percent? (Hint: Start with the equation for MPk and recall that MP_kcan be written as the ΔY/ΔK.)  

ii) (2pts) Explain in words what will happen to the rental price of capital and the real wage as a result of the increased amount of capital?

Answer 1