Question

Consider the version of the OLG model where people live for three periods. Suppose there are 200 young people born each period. Each young person receives 200 goods, but nothing when middle-aged or when old. No one consumes when young.

Each young person has a chance of being either of the following types:

- The “Early” Type consumes in the first period after birth;

- The “Late” Type consumes in the second period after birth.

No person knows his own type when young. A person’s type is not directly observable by others. Assume that 10 percent of the people in each generation want to consume when middle-aged and the remainder want to consume when old.

There is a storage technology. For each unit of the consumption good put into storage in the current period, a person will receive one unit of consumption good next period. Storage can be done secretly.

In addition, capital is also available. For each unit of the consumption good that is invested in capital in period t, X = 1.25 units of the consumption good will be received at date t+2. If the person liquidates capital after one period, then only 0.8 units of the consumption good can be obtained at date t+1. Verifying that capital is not fake costs θ goods per unit of capital. We assume that θ > (X – 1).

IOUs and other contracts promising future payments are possible among members of the same generation but not between generations.

a. How many goods will the bank hold in the form of storage? How many in capital?

b. If there is no bank run, how many goods will middle-aged people consume? How many goods will an old person consume?

Answer 1