Answer to Question #230121 in Macroeconomics for beth

Question

the proportion of change in income on a citizen in the year 2019 and the year 2020 is 0.8. Assume that the income in 2019 is Ksh. 1,400,000 and in 2020 Ksh. 1,800,000. Calculate the steady rate of consump­tion the citizen could maintain for the rest of his or her life, given the present level of wealth and income now and in the future

Answer 1

Using Golden Rule:

At steady-state; change in income ($\Delta$Y) is equal change in Capital($\Delta$ K).

Therefore, from the case above between 2019 and 2020;

$\Delta$ Y = $\Delta$ K = (1,800,000 - 1,400,000) = 400,000

But this represent only 0.8 (80%) of the total capital invested implying that depreciation rate is (1 - 0.8) = 0.2 0 or (100% - 80%) = 20%

If 0.8(K) = 400000,

Therefore at 100 capital, income (Y) = (1$\times$ 400,000)/0.8 = 500,000

Capital depreciation ($\delta$K) will be (500,000 - 400,000) = 100,000,

At steady-state, consumption (C^*) is given by Income, f(k), minus depreciation, $\delta$K.

i.e C^* = f(K) - $\delta$K

$\therefore$ C^* = 400,000 - 100,000 = 300,000