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Suppose that total GDP in a country at a given year is given by the following production function: Y = A(K) 1 3 (BL) 2 3 where [3 represents labour productivity and all other variables are the same as in class. The introduction of B expands 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 ([3). 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. 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. b (10 points) Assume that, in both countries, L grows at a constant rate gL, K grows at a constant rate gK, A grows at a constant rate gA and B grows at a constant rate gB. Calculate the constant rate of growth of GDP, gY , and GDP per capita, gy