Given a 2-digit sequence (which can start with 0), let us define a nudge as the operation of either increasing or decreasing one of the digits by $1, or changing a $0 to a $9 or a $9 to a $0. For example, we can nudge $19 to get $09, $29, $18, or $10. Suppose S is a set of 2-digit sequences such that it takes at least $3 nudges to transform any element of S into another element of S. Requried:
What is the maximum possible number of elements of S?

Assume that the following conditions exist: a. all banks are fully loaned up- there are no excess reserves, and desired excess reserves are always zero. b. the money multiplier is 5 .     c. the planned investment schedule is such that at a 4 percent rate of interest, investment =$1450 billion. at 5 percent, investment is $1420 billion. d. the investment multiplier is 3 . e.. the initial equilibrium level of real gdp is $12 trillion. f. the equilibrium rate of interest is 4 percent now the fed engages in contractionary monetary policy. it sells $1 billion worth of bonds, which reduces the money supply, which in turn raises the market rate of interest by 1 percentage point. calculate the decrease in money supply after fed's sale of bonds: $nothing billion.