Consider the consumption$-$savings problem for a two period asset choice

problem. The preferences of the consumer are u$($c$1)+$ u$($c$2)$ for $2(0$; $1)$ where

c$1$ is consumption and c$2$ is consumption tomorrow: Assume utility is u$($c$)$ is

strictly increasing, strictly concave, and continuously di$$erentiable$.$ There is a

single asset b that pays rate of return r on principle $($so if you invest b today,

you get b$(1+$ r$)$ tomorrow. Also, the consumer gets wage income of w$1>0$

today and w$20$ tomorrow.

a$.$ Write down the Marshallian demand problem for a consumer using $"$se$-$

quential budget constraits".

b$.$ Now, rewrite the Marshallian demand problem as a "single budget con$-$

straint" following ideas in class.

c$.$ What are the prices in this "single budget constraint" case.

d$.$ Draw a picture of the Marshallian choice problem for consumption to$-$

day and tomorrow. Explain if given endowments, and given preferences, your

Marshallian Consumer is a saver or a borrower.

e$.$ Now, can you develop a "Hicksian" demand problem for this consumer

when the budget constraint can be represented by a single budget constraint.

f$.$ Discuss the duality between the two representations of the consumer's choice problem.