Given a consumer with the utility function U $=$ C$^10\mathrm{.}5$C$^$

$20\mathrm{.}5,$ where consumption in

period $1$ is C$1$ and period $2$ C$2.$ The income in period $1$ M$1$ is $$30,000$ and in period $2$

M$2$ is $60,000.$ Interest rate r is $10\%.$

a$.$ Derive tangency condition for C$1*$ and C$2*,$ as a function of the interest rate r$.$

b$.$ Write down budget constraint

c$.$ Solve for optimal choice of C$1*$ and C$2*$

d$.$ Is the consumer a borrower or saver?