Question

pls solve parts g,h,i, j

Suppose Country X's production function is given by F(K, A,N) = 206,05(A, N,905 where K, is the capital and A, N, is the effective worker. The evolution of the capital stock is given by K +1 = 0.74K, +1 where the depreciation rate is 26%. Additionally, the saving rate is 36%, the population growth rate is 4% and the technological growth rate is 10% (a) Derive and show that in the Solow growth model, the steady state capital per effective worker needs to satisfy: 0.40(KIAN) = 7.2(KIAN) (b) Calculate the steady-state capital per effective worker (KIAN)*, the steady-state output per effective worker (Y/AN), the steady-state consumption per effective worker (CIAN)". (c) Using graphs and your values from part (b), show the steady-state values of output per effective worker, capital per effective worker and consumption per effective worker. Suppose that country X permanently changes its saving rate to achieve the Golden rule of capital and output per effective worker. (d) Compute the saving rate that would maximize the steady-state consumption per effective worker. (e) Using graphs and your values from part (d) show the new steady-state values of output per effective worker, capital per effective worker and consumption per effective worker, and compare them to the old steady state values. (f) Consider the path from the old steady state to the new one. Compute the value of the output per effective worker and capital per effective worker in the first period after the change in the saving rate. (g) Compute the growth rate of capital per effective worker in the first period after the change. (h) Using a time series graph where time is on the horizontal axis and the growth rate of capital per effective worker is on the vertical axis, show the effect of the change in the saving rate on the growth rate of capital per effective worker. Using a time series graph where time is on the horizontal axis and Capital (in logs) is on the vertical axis, show the effect of an increase in the saving rate on capital (K). 0 Does the saving rate affect the growth rate of capital (K)? Briefly explain.

Answer 1

(g.) The growth rate of capital per effective effective worker is ZERO .

This is because with the help of satisfying equation the values are being converges . This can be decomposed by :- ( &y/&t ) / y = ( &y/&t)/y - gA , where & = delta and y = Y/N which is per capital output .

(h.) Here is the graph of time vs growth rate of capital per effective worker :-

0.0204 Effective o.oich cubital 0157 Grow the rate U 0.010+ llup ato.oost 0.0004 -0.005 soo 1000 1500 time (t)

(i.) Here is the graph of the of time vs capital and the effect of an increase in the saving rate on capital (k):-

- - - - - ---5 (in loge). (i capital - - - - - - - - -- Time

(j.) This things depends upon the saving rate . Higher the saving rate will affect the growth rate in the S-model but not permanently .

A higher saving rate may lead to a higher steady-state stock of capital and the higher level of output . And when the population growth increases then there will be low steady-state level of the per capital output .