1. Kaldor facts [50 points] Kaldor (1961) documented a set of stylized facts on the growth process of industrialized countries. We discussed these facts in lecture 2. Explain if and how the Solow-Swan model can rationalize each of these facts. You are allowed to focus on the steady state equilibrium of the model. Every statement needs to be supported with a mathematical equation. You can refer to the notes of lecture 5 and 6 for this. a. Output per worker Y/N grows at a rate that does not diminish. b. Physical capital per worker Kt/Nt grows over time at a constant rate. c. The ratio of physical capital to output K/Y, is constant. In the following exercise, you are allowed to assume that the production function F(K, AN) satisfies the Inada conditions. A firm chooses capital and labor to maximize its profits: max F(K, AN)-wit-r Kt Kt.Lt where we and r denote the wage and rental rate of capital, respectively. d. Derive the firm's first order conditions with respect to capital and labor. Interpret these equa- tions. e. Under constant returns to scale, we can write Fi(K, AN) = F (1) and F(Kt, AtNt) = F2 (1). Show that the rate of return to capital r is constant in the steady state equilibrium. f. Using the equality F (Kt, AtNt) = F2 (,,1), show that the wage rate w grows at the constant rate in the steady state equilibrium. g. Using your answers from 1c, le and 1f, show that the shares of labor and physical capital in national income, w+N/Yt and r Kt/Y are constant in the steady state equilbrium. A(Y/N) h. The last fact by Kaldor (1961) states that the growth rate of output per worker Y/N differs substantially across countries. Assuming that all countries are in their steady state equilibrium, what do we have to observe in the data to make the Solow-Swan model consistent with Kaldor's observation? Did you see any evidence for this in class?