Suppose an economy’s production possibilities are represented by the function Y = A K L where Y represents total output (i.e GDP), K is capital, L is labor, and A is total factor productivity (TFP) (aka efficiency or productivity parameter). Moreover, suppose that there is a fixed supply of capital equal to 10 and a fixed supply of labor equal to 2. TFP is equal to 1.

Set up the problem of a representative (aggregate firm) that maximizes profits taking as given a rental rate for capital (r) and a wage (w).

Calculate the equilibrium rental rate of capital and the equilibrium wage.

Suppose that there is a shift in labor supply and wages drop by approximately 50%. How large is the shift? What happens to the equilibrium rental rate of capital? Discuss your results.