Problem 1: The Solow Model [18 Points] Suppose that an economy has a labour force of 36 (L. = L = 36). Population growth is equal to zero (n=0), soL=36in all periods. Suppose also that this economy has a savings rate given by s (s = 10%), and a depreciation rate of 10% (& = 0.1). The economy's Total Factor Productivity (TFP), given by \"A\" is equal to 20. Finally, this economy has a production function given by: F(K, L) = AK?3L5 1. What is the equation for capital per capita next period (k:+1) as a function of capital per capita this period (k:)? [1 point] 2. What are the equations for GDP per capita next period (yw.1) and GDP per capita this period (yt) as a function of capital per capita this period (k:)? [2 points] 3. At what level of capital per capita (k:) is GDP growth equal to zero? [2 points] 4. |s your answer to Q3 the same as the Steady State level of capital per capita (k*) that we solved in lecture/tutorial by setting k+1 = kez [1 point] Now suppose that two countries, Economy A and Economy B, share the same values for s, A, n, L, and 4. 5. If Economy A begins with a level of capital of K:a = 3,600, and Economy B begins with a level of capital of Kis = 12,600. What is the percent change in GDP per capita that each Economy will experience? [Note these are capital (K:), not capital per capita (k)] [3 points] Suppose now that A begins at 2 (A = 2) for both economies, but is also growing at 5% per period for both economies. 6. Once again, if Economy A begins with a level of capital of Kia = 3,600, and Economy B begins with a level of capital of K = 12,600. What would be the percent change in GDP per capita that each Economy will experience now with this productivity growth? [3 points] 7. Are your answers to Q5 & Q6 consistent with the idea of Convergence? Explain your answer. [2 points] Finally, let's think about the example of China and the USA in the 2000s (A.C.E.). Suppose that the following things were true: China has a higher savings rate than the USA. China and the USA share the same production function, including the same TFP (A). China and the USA share the same population growth (n) and depreciation (4). China begins with a lower capital per capita than the USA (k:). Draw a figure that includes three lines, with k: on the x-axis and ki1 on the y-axis. Label each line accordingly and show the steady state for each country: [2 points] a. The 45 line. b. The k:+1 function for China. c. The kw1 function for the USA. Are these countries experiencing convergence? Why or why not? [2 points]