Suppose that total GDP in a country at a given year is given by the following production function:

Y=A(K)13(L)32

whererepresents labour productivity and all other variables are the same as in class. The introduction ofexpands the production model by allowing production to also depend on the human capital or productivity of the labour force. Assume that there are two countries with the same number of workers (L) and total factor productivity (A) but with different levels of labour productivity (). In particular, we are going to assume that the labour force in one country is twice as productive as the the labour force in the other country.

1. a(10 points) Calculate differences in GDP as a function of differences in the amount of physical capital,K, across countries. In a graph with GDP differences on the vertical axis and differences in physical capital on the horizontal axis, plot this function. In the same graph show what happens when labour productivity differences increase.
2. b(10 points) Assume now that these two countries also have the same level of capital,K. Assume that there is perfect competition and that capital and labour are paid their marginal products. Calculate the differences in real wages (w=WP) and in the real rental rate of capital (r=PR) across countries. Which of these countries pays its workers a higher real wage per unit of productivity (w)? Explain.
3. c(10 points) Assume that, in both countries,Lgrows at a constant rategL,Kgrows at a constant rategK,Agrows at a constant rategAandgrows at a constant rateg. Calculate the constant rate of growth of GDP,gY, and GDP per capita,gy.