# intertemporal utility maximisation

Adam's consumption period 1 and 2 are denoted by $c_1$ and $c_2$ respectively. His utility function is $U(c_1,c_2)=4c_1^{0.5} + c_2$ Ben earns an income of \$3 in period 1 and \$3 in period 2, regardless of the level of inflation. a. Suppose there is no inflation and the interest rate is 5%. How much will Ben consume in each period? b. Now suppose that inflation rate rise to 100%. How much will Adam consume in each period now?

For part a, I took $c_2= -1.05c_1 + 6.15$ as the budget line and equated it to MRS of his utility function. I managed to obtain $c_1 = 3.63$ and $c_2= 2.341$.

However, I am unsure of how to do part b as I obtain a negative answer for $c_2$ after doing the same steps as part a. The only differenece was that I took into account inflation for part b.

• let m1 =3 , m2 = 3 c2 = m2 + (1+0.05)/(1+1) * (m1 -c1) c2= -0.525c1 + 4.575 Equating MRS and slope of budget line, 2c1^(-0.5) = 0.525 , c1 = 14.51 , c2 = -3.04 – skukkzky Sep 11 '18 at 15:14

Note that there is probably an implicit constraint that $c_2$ cannot be lower than 0, so the answer would be $c_1 = \$6, c_0 = \$0$.