Consider the following model.
Agents live for two periods. Generation t is born and “Young” at time t. Generation t is “Old” at time t + 1. The population born at time t is La
Each young person is endowed with one unit of labor and saves a constant fraction
1 — ;z of his or her wage •• The old person does not work and consumes all their
savings. Population grows at a rate n.
The production function is Yr — AK L1*‘
In addition to physical capital K, there is a financial asset called Bubblecoin. Bubblecoin does not pay any dividends and thus has no intrinsic value. The total number of Bubblecoins at date t is Be and it grows at rate Q
Bi+i = Bi I l + ‹:f)
We try to construct a trajectory of the economy such that Bubblecoin are valued. Let $ be the price of one Bubblecoin at date f. Let • be the real interest rate between f – l and f. Young can save in terms of physical capital and financial
Show the consumption when young c , of a consumer born at f as a function of
kmb. e.« =nd •• –
2 Show the consumption of the above person when old c , +
- What are competitive equilibrium values of r and
4. Show/Justify that one must have
(I — p)w N — Km+ + q B
(Use economic intuition and you only need 1 or 2 sentences).
5 From the above equation and think about when consumers would hold Bubblecoin, conclude that for Bubblecoin to be valued in equilibrium it must be that their growth rate satisfies
1 + n
‘ 1 + r — 1
(Hint: Introducing growth rates into the equations. It might be helpful if you remember some knowledge from the Solow model).
- Under which condition the existence of Bubblecoin is rational?