7. Consider the model of illiquidity where individuals live for three periods. Each individual is endowed with y units of the consumption good when young and with nothing in the other two periods of life. Let Nt be the number of individuals in the generation born at t with Nt = nNt-1. There are two types of assets in the economy. (No inside money or private IOUS are available.) One asset is fiat money, with a fixed supply M. The other asset is capital. A unit of capital can be created from a unit of the consumption good in any period t and capital can be created in any amount. Two periods after it is created, a unit of capital produces X units of the consumption good and then disintegrates. Let X > n². Assume that the stock of money is distributed equally to the initial middle-aged and each initial old can produce Xko units of the consumption good in the first period. Now suppose that an individual's preference is given by U(C₁, C2, C3) = C1 C₂ C3. (a) Find the rate of return on fiat money. (b) Describe and explain how an individual finances his consumption in the second- period and third-period of life. (c) Write down the budget constraints faced by an individual when young, middle-aged and old. (d) Solve for the optimal stationary allocation of (c1, c₂, c) for all future generations.
7. Consider the model of illiquidity where individuals live for three periods. Each individual is endowed with y units of the consumption good when young and with nothing in the other two periods of life. Let Nt be the number of individuals in the generation born at t with Nt = nNt-1. There are two types of assets in the economy. (No inside money or private IOUS are available.) One asset is fiat money, with a fixed supply M. The other asset is capital. A unit of capital can be created from a unit of the consumption good in any period t and capital can be created in any amount. Two periods after it is created, a unit of capital produces X units of the consumption good and then disintegrates. Let X > n². Assume that the stock of money is distributed equally to the initial middle-aged and each initial old can produce Xko units of the consumption good in the first period. Now suppose that an individual's preference is given by U(C₁, C2, C3) = C1 C₂ C3. (a) Find the rate of return on fiat money. (b) Describe and explain how an individual finances his consumption in the second- period and third-period of life. (c) Write down the budget constraints faced by an individual when young, middle-aged and old. (d) Solve for the optimal stationary allocation of (c1, c₂, c) for all future generations.
Chapter17: Capital And Time
Section: Chapter Questions
Problem 17.1P
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Transcribed Image Text:7.
Consider the model of illiquidity where individuals live for three periods.
Each individual is endowed with y units of the consumption good when young and with
nothing in the other two periods of life. Let Nt be the number of individuals in the generation
born at t with N₁ = nNt-1. There are two types of assets in the economy. (No inside money
or private IOUS are available.) One asset is fiat money, with a fixed supply M. The other
asset is capital. A unit of capital can be created from a unit of the consumption good in any
period t and capital can be created in any amount. Two periods after it is created, a unit
of capital produces X units of the consumption good and then disintegrates. Let X > n².
Assume that the stock of money is distributed equally to the initial middle-aged and
each initial old can produce Xko units of the consumption good in the first period. Now
suppose that an individual's preference is given by
U(C₁, C2, C3) = C₁ C2 C3.
(a) Find the rate of return on fiat money.
(b) Describe and explain how an individual finances his consumption in the second-
period and third-period of life.
(c) Write down the budget constraints faced by an individual when young, middle-aged
and old.
(d) Solve for the optimal stationary allocation of (c1, c₂, c) for all future generations.
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