Question

Suppose a closed economy has a consumption-output ratio of 0.8. Total output is 1 Billion in 2018 and the capital stock equals 5 Billion. It's depreciation rate and population growth rate are both equal to 2%. What is true in 2019?

  

income will have grown

   

consumption will take an even larger share of output

   

we do not have enough information to calculate changes from 2018 to 2019

   

the capital stock must be smaller than in 2018

Answer 1

We have the following information,

c/y=0.8

c=0.8y

c=(1-0.2)y {c=(1-s)y}

hence, saving rate, s = 0.2

now, y= 1 billion and capital stock k is 5 billion

change is capital is k'= investment - population growth - depreciation of capital

k' = sy- (n+d)k where n is population growth rate which is 0.02

  where d is the depreciation rate which is 0.02

k' =0.2(1) - (0.02+0.02)5

k' = 0.2 - 0.2

k' = 0 hence, it's a situation of steady state means, total capital reduction is equal to total investment. So no change  in capital in 2019.

But, it does not mean that income will not change.

Income will increase as, population grows with same capital increases. Then, economic activities also increase.

Hence, income will increase.

As about consumption please carefully notice it's a share of income so that will not increase because they need a same or higher saving rate to maintain steady state.