1. Consider the OLG model with the following specifications:

Let the utility of household i of cohort t be

u(ci

t(t); ci

t(t + 1)) =

q

ci

t(t) +

q

ci

t(t + 1)

where 0 < < 1.

Preferences are the same across individuals and across generations.

Also, let Y (t) = K(t)H(t)1:

The depreciation rate is 100%: = 1.

Questions

a Find the function G where

K(t + 1) = G(K(t)):

(Show your work.)

Additional specifications: Let us make the following assumptions:

There is no population growth: N(t + 1) = N(t) 8t.

Each young person in the economy works for hy = 10 hours, while each old person

works for ho = 5 hours:

hi

t =

hi

t(t); hi

t(t + 1)

= [hy; ho] = [10; 5]; 8(i; t):

Let = 0:8, = 0:5 and K(0) = 0:25.

b) Find K(1).

c) Calculate Y (1) using the income and expenditure approaches.

d) Suppose that due to the public health measures, the labor endowment of old

people h0 is increased starting from t = T. Using the model, discuss how this

change will affect the steady state wage w and consumption of young and old

workers cy and co. Explain why these changes occur.

1