Question

1. (10 pts). Assume that the per-worker production function is y, = 10.k'. Further, assume that the saving rate, s = 0.2, the depreciation rate, 8 = 0.4, and the population growth rate, n= 0. Calculate the following: (a) The steady-state values of the capital-labor ratio, k*, output per worker, y, and consumption, c. (b) The new steady-state values of the capital-labor ratio, output, and consumption (ki, yi, and Ci), if there is an increase in the saving rate, so that s 0.4. (c) Show your results from parts (a) and (b) on the same graph. Explain them briefly. What effects does an increase in the saving rate have on the economy? What happens to living standards when there is an increase in the saving rate?

Answer 1

yt = 10. k_{​​​​​​t}^​​​1/2 s=0.2. d= 0.4 n=0

A) As per the steady state condition, the depreciation of capital must offset the investment , therefore it is given as :

Investment = i=s. y(k) = Depreciation = dk

Now, 0.2× 10× k^1/2 = 0.4 × k

2 = 0.4×k^1/2   

5= k^{​​​​​1/2}

Hence, k*= 25.

y* = 10×5 = 50

c* = y* - s*k* = 50 - 0.2(25) = 50 - 5 = 25

B) If savings rate is increased to 0.4 then, again the above method can be used to calculate the variables :

6ya o.4x lo X JR o.yxk lox 1o 100 x JE 0.4 k 00- Co4() k yXlo 60 o .4 Sk o.k Lohun S 0,2 IO Jk 141 시4 EEE AH 16 Sk lo 204o Sk.6 16 16 Sk 6.4lol 40

C) As per the graph plotted above , as the savings rate in the economy increases, there is an increase in the level of investment that is required to offset depreciation , and hence the steady state is obtained at a higher level than before.

(40,100) 32 28 24 20 25,10) 10

An increase in the savings rate doesn't create a growth effect as the rate of growth of output will still be zero. It will indeed create a level effect which means that steady state will just be obtained at a higher level of Capital and output per capita but the rate of growth will remain the same.

There is an improvement in the standard of living because of the higher level of output as we move from one steady state to another but once it is achieved there's no growth of output and hence no improvement in standard of living afterwards.