We know the prices and payoffs for securities $1$ and $2$ and they are represented as follows:

Cash Flow in One Year

Weak Economy

Strong Econo

SO

$$175$

$$175$

SO

Security

$1$

$2$

Market Price Today

$$70$

$$90$

a$.$ What is the risk$-$free interest rate?

b$.$ Consider a risk$-$free security that has a payoff in one year of $$2,250.$

i$.$ How many units of each of securities $1$ and $2$ would be needed to replicate this risk$-$free security?

if$.$ Based on part b$.$i$),$ what is the market price today of this risk$-$free security? ill. Based on part a$),$ what is the market price today of this risk$-$free security?

c$.$ Consider a security that has a payoff in one year of $$2,250$ if the economy is weak and $$4,500$ if the economy is strong.

i$.$ How many units of each of securities $1$ and $2$ would be needed to replicate this security?

il$.$ Based on part c$.$i$),$ what is the market price today of this security?

d$.$ Consider a security that has a payoff in one year of $$4,500$ if the economy is weak and $$2,250$ if the economy is strong.

i$.$ How many units of each of securities $1$ and $2$ would be needed to replicate this security?

li$.$ Based on part d$.$i$),$ what is the market price today of this security?

e$.$ Explain the economic reasoning as to why the security in part c$)$ has a lower price than the security in part d$).$