Consider Figure 11 $u\left(c_{1}, c_{2}\right)=\ln \left(c_{1}\right)+\delta \ln \left(c_{2}\right)$ And a Budget Constraint Given By

Essay

Consider Figure 11.1. Billy has a utility function given by $u\left(c_{1}, c_{2}\right)=\ln \left(c_{1}\right)+\delta \ln \left(c_{2}\right)$ and a budget constraint given by $c_{1}+c_{2} \leq 100$ . Where $c_{1}=$ hamburgers today and $c_{2}=$ hamburgers tomorrow, and $p_{1}=p_{2}=1$ .
a. What is the slope of Billy's indifference curve at any point $\left(c_{1}, c_{2}\right)$ ?
b. What is the slope of Billy's budget line?
c. At any optimal solution to Billy's utility maximization problem, it must be true that $\frac{c_{2}}{\delta c_{1}}=1$ .
d. Suppose Billy spends all of his income on hamburgers today and tomorrow. If $\delta=1$ , what percentage of his income is spent on hamburgers tomorrow?
e. If $\delta=.8$ , what percentage of his income is spent on hamburgers tomorrow?
f. In general, as $\delta$ decreases, hamburger consumption tomorrow increases.