Question

2. Assume that the information below describes the economy of Country A. First, assume that Country A has a production function equal to Y = F(K,L) = K L (where Y = output, K = capital, L = Labor) Second, assume that the economy of Country A conforms to the assumptions and conditions discussed in Chapter 8, where the population growth and the depreciation of capital occur at the rates provided below, and this economy's savings rate is equal to the value below as well. S=0.25 8= 0.1 s=savings rate 8 = depreciation rate n=population growth rate n = 0.1 (10 pts) a. Find this economy's steady state level of k (capital per worker) and then report the numerical value of these variables (below) when Country A is operating at its steady state. • output per worker (V) investment per worker (i) consumption per worker (c) . . FO

Please use the equations provided to solve for all parts of question A. Please be detailed, and use the formulas provided, and show all steps with the formulas. I need to understand and see the work with the solutions for each part so that I can understand how you got the solution. Thank you so much! Correct answers will get a thumbs up!

Answer 1

It is given that, y = F(K, 2) = where Youtput, K= capital and L = Labor Dividing both sides by L, we get Y Uk. I 1/2 1/2 L L - Here y (K) 1/2 y = k112 21/2 where y = output per worker k = capital per worker. f(K) = (K) 1/2 In Solow model, r = ct where, c = consumption per worker i= investment per worker. Also, i = sY Plugging we get Y =C+SY c=Y-SY = (1-5) Y=cti

Date In steady state, change in capital - labor Here AR = Investment -depriciation - population dilution ratio is zero Cie OR=0) AR = i-SR=nR cats population growth (OR=o) 0 = i-SR-nk i = (otn) k 2 sy = 8 tn) kl (i=SV) Steady state condition

Y = (R)/2 In this sum, Given s=0.25 Savings rate depriciation rate n = 0.1 population growth rate putting the values in steady-state condition, We get sY = (stn) k =) 0.25(k)/2 = (0.1 to 1)R k 0.25 (R) 1/2 > 0.2 (k) 1/2 1-25 k =(1-25) ² Squaring both sides) => R=1861.5625 - Steady state Level of capital Steady state output > Y= (k)/2 per worker Y = (1.5625)/ > y = 1.25 Steady state investment - i-sh per worker (0.25) x(1.25) i ~ =) i = 0.3125 1 Steady state consumption > c=(1-5) per worker > C = (1-0-25) x(125) 1=0.9375