class we argued that if people could accumulate human as well as physical capital, the production function would look like the “AK” production function. • (a) If the production function is AK and the savings rate is constant at rate “s”, and the rates of depreciation and populati on growth are δ and n respectively, what would the growth rate of the economy be? • (b) What would be the macroeconomic

6.5 Exercises Exercise 6.1 (Technological Progress and Long-Run Growth). Consider a Solow economy with population growth and technological progress. The evolution of the capital stock per efficiency unit of labor, denoted k1, is given by the law of motion (1+n)(1+ g)kt+1 = (1 – 8)kt +of(kt). Capital per efficiency unit of labor is defined as k, = Kt/(LEt), where Kt denotes the stock of physical capital, L, denotes population, and E is a tech- nological factor. Population grows at the rate n and the technological factor grows at the rate g. The subscript t denotes time, measured in years. The parameters d E (0, 1) and o > 0 denote, respectively, the depreciation rate of capital and the savings rate. The function f(k;) represents the produc- tion technology. Specifically, let Y, denote output and yt = Yt/(LEt) denote output per efficiency unit of labor. Then yt = f(kt). Assume that f(kt) = /k. 1. Find the steady-state stock of capital per efficiency unit of labor, de- noted k*, as a…

I need help with parts (f) and (g) of question 2

1. Consider an economy that operates under competitive markets and meets the assumptions of the Solow model. The production function is given as follows: Y(t) = K (t) 0.3 (A(t)L(t)) ⁰.7 Assume a saving rate of 15%, labor force growth rate of 2% and depreciation rate of 5% and effectiveness of labor growth rate of 8%. a. Show that the production function exhibit constant return to scale? b. Derive the production function for output per capita. c. Derive the production function for output per effective unit of labor. d. Find equilibrium real wage as a function of capital per unit of effective labor and effectiveness of labor. e. Find equilibrium real rental price of capital as a function of capital per unit of effective labor and effectiveness of labor. f. Solve for steady state level of capital per unit of effective labor. g. Find steady state level of output per unit of effective labor. h. Find growth rate of output and output per worker on the balanced growth path. i. Which one would…