Question

Consider the following 2-period model U(C1,C2) = min{3C1,4C2}

C1 + S = Y1 – T1

C2 = Y2 – T2 + (1+r)S

Where

C1 : first period consumption

C2 : second period consumption

S : first period saving

Y1 = 20 : first period income

T1 = 5 : first period lump-sum tax

Y2 = 50 : second period income

T2 = 10 : second period lump-sum tax r = 0.05 : real interest rate

Find the optimal saving, S*

Answer 1

C₁ + S = Y₁ – T₁

C₂ = Y₂ – T₂ + (1+r)S

i.e   

Now, we have :

or,  

Now given U(C₁,C₂) = min{3C1,4C2} and the values of Y₁, Y₂ , T₁, T₂ and r ,

we can solve the value of C₁ and C_{2 by using the above relation in the previous equation.}

And then after deriving the value of C₁ and C₂ , we can obtain the value of S

( Here the value of S is negative, which is referred to as Dissaving)