Question

The monetary base is $1,500, the currency to deposit ratio = 2 and the reserve to deposit ratio = 0.1. The central bank wants to reduce money supply by 10% without changing the monetary base. What reserve ratio should the central bank set?

Answer 1

Ans. Current monetary base, H = $1500

Currency to deposit ratio, c = 2

Required reserve to deposit ratio, r = 0.1

Money multiplier, m = (1+c)/(c+r) = (1+2)/2+0.10) = 1.428

Money supply, M = m*H = $2142.86

New money supply, M’ = (1-0.10)*M = $1928.57

For fix monetary base, new multiplier, m’ = M’/H =  1.2857

New multiplier, m’ = (1+c)/(c+r’) = 3/(2+r’) = 1.2857

=> r’ = 0.33333 or 33.33%

Therefore, central bank should set required reserve ratio as 33.33%

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