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

Answer:

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

U ( c₁c₂ ) = $\frac{3}{2}$ ( c₁ )$^{\frac{2}{3} }$ + α $\frac{3}{2}$ ( c₂ )$^{\frac{2}{3} }$

Derive the budget constraint that the person faces

ANSWER : c1 + $\frac{c2}{1.04}$  = 35000 + $\frac{33990}{1.04}$

Explanation:

period 1 income ( y1 ) = $35000

period 2 income ( y2 ) = $33990

interest rate = 3% = 0.03

utility ( c1, c2 ) = $\frac{3}{2}$ ( c1 )$^{\frac{2}{3} }$ + α $\frac{3}{2}$ ( c2 )$^{\frac{2}{3} }$

Deriving The budget constraint that the person faces

saving ( s ) = y1 - c1

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

$\frac{c2}{( 1 + r )}$  =  y1 - c1  + $\frac{y2}{( 1 + r)}$

present value of consumption = present value of income

c1 + $\frac{c2}{1.04}$  = 35000 + $\frac{33990}{1.04}$

This is the derived equation