Question

Consider a simple two-period model of intertemporal choice. Suppose that a person receives income $35,000 in period 1 and additional income $33,990 in period 2. The market interest rate at which the person can both borrow and save is 3%. Finally, the person’s intertemporal preferences are

Answer 1

Hello your question ls not complete here is the missing equation and question

U ( c₁c₂ ) =
`(3)/(2)` ( c₁ )
`^{(2)/(3) }` + α
`(3)/(2)` ( c₂ )
`^{(2)/(3) }`

Derive the budget constraint that the person faces

ANSWER : c1 +
`(c2)/(1.04)` = 35000 +
`(33990)/(1.04)`

Step-by-step explanation:

period 1 income ( y1 ) = $35000

period 2 income ( y2 ) = $33990

interest rate = 3% = 0.03

utility ( c1, c2 ) =
`(3)/(2)` ( c1 )
`^{(2)/(3) }` + α
`(3)/(2)` ( c2 )
`^{(2)/(3) }`

Deriving The budget constraint that the person faces

saving ( s ) = y1 - c1

c2 = ( 1 + r ) ( y1 - c1 ) + y2

`(c2)/(( 1 + r ))` = y1 - c1 +
`(y2)/(( 1 + r))`

present value of consumption = present value of income

c1 +
`(c2)/(1.04)` = 35000 +
`(33990)/(1.04)`

This is the derived equation