Problem $1\mathrm{.}3.$ This problem shows how prices of some assets can be used to extract state

prices which can then be used to price other assets. The economic growth next year will be

high, medium, or low. There are four assets, A$,$ B$,$ C$,$ and D$,$ whose value $($cash flow$)$ in the

three states will be as follows:

The prices of the assets A$,$ B$,$ and C are $56\mathrm{.}40,56\mathrm{.}10,$ and $52\mathrm{.}20,$ respectively.

$($a$)$ What are the state prices of the three states $($high growth, medium growth, and low

growth$)?$

$($b$)$ What is the risk$-$free rate?

$($c$)$ What is the price of asset D$?$