Question

1. Consider Dexter's intertempral choice (c1,2), where c is his consumption measured in $ for t 1,2. He has income of m 1000 and m2 1500 over those periods. His utility function is given by u(ci, c2-In(c) + δ ln(c2), where δ-0.9. (a) If he can borrow or save at the interest rate of 10% (r 0.1), then what is his optimal consumption bundle (ci,2)? b) If he would like to consume the same amount in each period, what should be r?

Answer 1

Process Used

In part (a) we first calculated the intertemporal budget constraint and then formed Legrange multiplier and then using first order conditions we calculated optimal value of c₁ and c₂

In part (b) we used same method used in (a) and instead of putting r = 0.9 we will put c₁ = c₂ and calculate r