2 Assume that the Federal Reserve Board can control the growth rate of the U.S. money supply. Also assume that during a year in which the money supply grows by x%, the Gross Domestic Product (GDP) grows by Zx%, where Z is a known random variable. The government has decided it wants the GDP to grow by k% each year. (Too high a growth rate causes excessive inflation, and too low a growth rate causes high unemployment.) To model the government’s view, the government assesses a cost of (d  k)2 during a year in which the GDP grows by d%.
a Determine the growth rate of the money supply that should be set by the Federal Reserve Board if the goal is to minimize the expected cost to the government.
b Show that for a given value of E(Z), an increase in var Z will decrease the optimal growth rate of the money supply found in part (a). (Hint: Use the fact that var Z 
E(Z2) - E(Z)2.)