The Federal Reserve would want to use contractionary monetary policy primarily to fight inflation. Contractionary monetary policy involves decreasing the money supply and increasing interest rates, which can help reduce spending and investment, thereby slowing down inflationary pressures in the economy.
The other options, such as balancing the federal budget or moving the economy out of a recession, would typically not be associated with contractionary policy. Rather, expansionary monetary policy would be used to stimulate economic growth during a recession.