Problem $2$

Consider a representative agent with CRRA utility. Her risk aversion is $=3$ and

the subjective discount factor is $=0\mathrm{.}98.$ The expected growth rate of the economy

is $2\%$ and the volatility is $1\mathrm{.}5\%.$

$($A$)$ What is the level of the risk$-$free rate in this economy?

$($B$)$ Determine the change in the risk$-$free rate if economic volatility increases to $2\%.$

What is the intuition?

$($C$)$ Compute the equity risk premium if the covariance between the market return

and consumption growth equals $0\mathrm{.}02.$