Consider the Solow model with production function Y_t = F(K_t, L_t) = K^alpha_t (AL_t)^1 – alpha…

Problem 1 Consider the Solow model with production function with A 1 and a = 0.3. Y, Ke, and L, are the levels of output, physical capital, and labor at time t, respectively. The savings rate is s = 0.30, with <a href=population growth rate and capital depreciation rate equal to n= 0.03 and d= 0.05, respectively (i) Derive the production function in per-capita term -/Lt) as function of capital per capita (k- Kt/Lt) (ii) Derive and describe the equation for kt (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 yt and Yf? (v) Derive the steady state values (when kt 0) of k, yt. Further, assume that the economy starts at t = 0 with initial stock of labor Lo-whats the steady state value of Y (hint: it depends on Lo 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 s = 0.20. Analyze. using a diagram and in words, what should happen to kt over time under this proposal. (vii) Another policitian disagrees with this policy change on the ground that the perma- nent decrease in s 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 (At grows at a constant rate)? ” src=”https://files.transtutors.com/cdn/questions/transtutors006/images/transtutors006_a367f498-86b4-48c1-9e0b-d12acaca0bbf.png”>

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Consider the Solow model with production function Y_t = F(K_t, L_t) = K^alpha_t (AL_t)^1 – alpha with A = 1 and alpha = 0.3. Y_t, K_t, and L_t are the levels of output, physical capital, and labor at time t, respectively. The savings rate is s = 0.30. with population growth rate and capital depreciation rate equal to n = 0.03 and delta = 0.05, respectively. (i) Derive the production function in per-capita term (y_t = Y_t /L_t) as function of capital per capita (k_t = K_t/L_t). (ii) Derive and describe the equation for k_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 y_t and Y_t? (v) Derive the steady state values (when k_t notequalto 0) of k_t, y_t. Further, assume that the economy starts at t = 0 with initial stock of labor L_0 – what’s the steady state value of Y_t (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 s = 0.20. Analyze, using a diagram and in words, what should happen to k_t over time under this proposal. (vii) Another politician disagrees with this policy change on the ground that the permanent decrease in s 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 (A_t grows at a constant rate)?