1 Simulating the Solow Model Consider the basic Solow Model. The production function is Y: = A(K:)* (L)' and the law of motion of capital is given by K;,; = (1 )K; + sY;. 1. What is the behavioral equation in this model and where does it enter in the law of motion? Rewrite the model in per capita terms and the law of motion as a function of capital per capita. That is, solve for 3 = f(k;), ko1 = g(k:) where small letters denote per capita variables. Solve for the steady state k*, and express technology A as a function of k*. Show that the law of motion of per capita capital can be rewritten as a ratio to the steady state level: kis1 - ke ke \\ = _(1_5}F+5(F) Set 6 = 0.05 and o = 0.3. Assume that the economy is initially at steady state, and half of its capital stock is suddenly destroyed (% =0.5). Use the equation from above to compute the number of years after which the economy will have returned to 95% of its steady state (when is %} >= 0.957). You can use formulas in Excel to do this. Solve for the income per capita relative to steady state in all periods. Compute the growth rate of income per capita. For how many years will the economy experience growth in income per capita higher than 0.9%7 Based on you answer, is this basic version of the Solow Model appropriate to explain growth patterns in the last century