Problem 1 Consider the Solow model with production function Y, = F (K ,, Lt ) = Ka(AL , ) 1 -a with A _ 1 and a = 0.3. ", ., and t are the levels of output, physical capital, and labor at time , respectively. The savings rate is = 0", with population growth rate and capital depreciation rate equal to ? = 0.03 and d = 0.05, , respectively. (i) Derive the production function in per-capita term "( :/;) as function of capital per capita (k, = K. /L.). (ii) Derive and describe the equation for t (the change in capital per capita over time). (iii) Sketch the Solow diagram in this economy and write the equations (actual and break-even investments). (iv) What are the steady-state growth rates of and Y? v) Derive the steady state values (when t = 0) of "t t Further, assume that the economy starts at ' = 0 with initial stock of labor o- what's the steady state value of t (hint: it depends on o and is time varying)? Is the steady state stable (illustrate this using the Solow diagram )? (vi) Suppose a politician argues that the savings rate is too high (and consumption is too low) and proposes that the savings rate should be permanently lowered to = 02. Analyze, using a diagram and in words, what should happen tot over time under this proposal. (vii) Another policitian disagrees with this policy change on the ground that the perma- nent decrease in ' would lead to lower level and growth rate of output per capita, both in the short run and long run. In the context of Solow model, do you agree with this statement? Why? Would your answer change if there is a positive technological progress ( grows at a constant rate)? Problem 2 Suppose an economy has a production function given by = ( AL,). Assume that L /L. = n = 0-05 and A, /A, = 9 = 0. . Further, assume that the savings rate is constant at s = 0.20 and the capital depreciates at the rate = 0.03 . (i) Derive output per effective labor,, = / Att, as a function of capital per effective labor, k, = KIA. L. (ii) Find the steady state (balanced growth path) values of and y