Question

Section B (LONG QUESTIONS): Answer any THREE (3) of the following four ques tions. Each question is worth 25 marks for a total of 75 marks. B1. Solow (neoclassical) growth model: Consider the Solow (neoclassical) growth model seen in class where y denotes output per worker, k physical capital per worker, and A total factor productivity. Suppose that at any point in time the production function in per-worker terms is represented by where f(k) is increasing in k and there are diminishing returns to capital. Suppose that A is constant, labour N grows at rate n, the saving rate is s, and the rate of capital depreciation is d. (a) With the aid of a diagram, explain how the steady state capital stock per worker, k, i determined (b) So consumption per worker, ', assuming that total factor productivity, A, is 1, the saving rate, olve for the steady-state level of capital per worker k, output per worker, y, and s, is 0.4, the population growth, n, is 0.02, and the depreciation rate, d, is 0.08. (c) Suppose that there is a war that destroys half the capital stock, K, but leaves the labour force unchanged. Calculate the immediate impact of the war on capital per worker, output per worker, and consumption per worker. (d) Show graphically how the economy returns to the steady-state following the destruction of half the capital stock. (e) Suppose instead that the war destroys half the labour force (N) but leaves the capital stock unchanged. Assume that the economy was in the steady-state derived in part (b) before the war and the rate of population growth, n, returns to normal after the war. Calculate the immediate impact of the war on capital per worker, output per worker, and consumption per worker.

Answer 1

Note: According to HOMEWORKLIB POLICY only first four questions can be answered. Please post the other questions in separate post. The production function in per worker terms is represented by: Here, f(k) is increasing in k and there are diminishing returns to capital. Here A is constany N Labour n: population growth d: depreciation rate S: saving rate Steady state is defined by R=0 sf(k)= dk y*= f(**) The Solow model graph showing the savings line and the depreciation line. - Y-ik) Output per worker Capital per worker

Now the given information is: 4=1 n: population growth = 0.02(2%) d: depreciation rate = 0.08(8%) S: saving rate =0.4 Now the saving at golden rate steady state-level is: sy =(n+d')k SART = (n +d) 0.4x1x R2 = (0.02 +0.08)k 0.4 (0.02 +0.08) = 16 Thus, the steady-state capital per worker ** =16. Output per worker: =1x167 =1x4 =4 Consumption per worker at this level will be: C = y - sy = y(1-5) = 4(1-0.4) = 4x0.6 = 2.4

If the war destroys half the capital stock, K whereas the labour four remain unchanged the capital per worker will reduce. ! Y = AKL per unit output sy =(n+d)k S4 =(+d) 0.4*1*** = (0.02 +0.08) 02 (0.02 +0.08) Output per worker: =1x4 =1x2 2 Consumption per worker at this level will be: C=y-sy = y(1-5) = 2(1-0.4) = 2x0.6 =12 Thus, the immediate impact of the war on capital per worker, output per worker and consumption per worker is value of all these remain half.

d) Now the steady state will achieve at k*(New) which is less than the capital per worker before the destruction of half the capital stock. Thus, it will return to steady sate but at lower level of capital per workers shown in diagram below: Output per worker Y-f(k) y=f(k) sy k*(New) ** Capital per worker