Consider the following model

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

asset.

 

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 , +

  1. 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).

  1. Under which condition the existence of Bubblecoin is rational?

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