Suppose the current one$-$year interest rate is $6\%.$ One year from now, you believe the economy

will start to slow and the one$-$year interest rate will fall to $5\%.$ In two years, you expect the

economy to be in the middle of a recession, causing the Federal Reserve to cut interest rates

drastically and the one$-$year interest rate to fall to $2\mathrm{.}5\%.$ The one$-$year interest rate will then rise

to $3\mathrm{.}5\%$ the following year and then return to $6\%$ the following year.

a$)$ If yof$1$ were certain regarding these future interest rate changes, what two$-$year interest

rate would be consistent with these expectations?

b$)$ What current term structure of interest rates, for terms of $1$ to $5$ years, would be

consistent with these expectations?

c$)$ How does the one$-$year interest rate compare to the five$-$year interest rate? Plot the yield$-$

curve: how would you call a yield$-$curve of this shape?

d$)$ What does this yield curve imply about the future of the economy? $($hint: why does the

relation between the $5-$year rate and one$-$year rate described in part c$)$ hold?$)$