Question

Suppose that population increases at a fixed rate n. For this model economy, verify that the horizontal intercept of the feasible set line is equal to y and the vertical intercept of the feasible set line is equal to ny.

Answer 1

In each period t,

N_t= Young individuals

N_t−1=Old individuals, alive in the economy.

For example, in period 1, there are N0 initial old individuals and N1 young individuals who were born at the beginning of period 1.

It is assumed:

• There is only one good in this economy which cannot be stored from one period to the next.
• Each individual receives an endowment of the consumption good in the first period of life. Thus, each individual receives no endowment in the second period of life.
• N_t= nN_t−1 for every period t, where n is a constant greater than 1 as the number of people born in any period is always n times the number born in the previous period.

Here,

y=Amount of endowment (only the young people are endowed with the consumption good at time t, which means here, Nt y=y)

c₁*= First-period consumption

c₂*= Second-period consumption

Golden Rule Allocation

The vertical intercept (ny) lies farther from the origin than does the horizontal intercept (y) as n > 1, if the two axes are scaled the same

Given the growth rate of the population is n, which implies there are n young people for each old person.

Therefore, if we divide the entire endowment of the young equally among the old, there will be ny goods for each old person.