You live in a world with two time periods. Your income is $100 in time period 1

Question

You live in a world with two time periods. Your income is $100 in time period 1 and $150 in period 2. (a) (15 points) If the interest rate is 0.03 (3%), draw your intertemporal budget constraint. (b) (10 points) If you value current consumption 1.5 as much as future consumption at all points (U = 1.5C1 + C2), what is your optimal consumption bundle? (c) (10 Points) Now suppose current and future consumption are perfect complements you can only enjoy current consumption if you consume it with two units of future consumption (U = min{2C1, C2}). What is your optimal consumption bundle?

Explanation / Answer

a) When income = 100 $ , let time be n
then A = P(1+r/100)^n
             = 100(1+.03)^n
    Let n = 25 years
A = 100* 1.03^ 25 = 209.3778
When income = 150 $ , then A = 150(1.03)^25 = 314.0667

b) C1 = 1.5 C2

U = 1.5 C1 + C2
   = 1.5 C2 + C2 = 2.5 C2
Optimal consumption bundle is 2.5 C2

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