$1)(50$ points$)$ Suppose the money demand function is:

$($M$/$P$)^$D $=800-5$r

where r is the interest rate, as a percentage. The money supply M is $2,000,$ and the price level P is fixed at $5.$

a$)$ What is the equilibrium interest rate? Interest rate is $8\%$

b$)$ What happens to the equilibrium interest rate if the supply of money is reduced from $2,000$ to $1,500?$ New equilibrium interest rate is $10\%$

c$)$ If the central bank wants the interest rate to be $4$ percent, what money supply should it set? Fed should set the nominal money supply to $3,000.$