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Q16. Suppose that the velocity of the monetary base is 20, real GDP grows 3% per year and inflation is 2%. (a) Calculate seignorage relative to GDP. AM %ANGDP 0.03 + 0.02 PY V 20 - = 0.0025 = 0.25% of GDP (b) Calculate seignorage relative to GDP if the real growth rate is instead 8% and velocity remains unchanged. AM %ANGDP 0.08 + 0.02 PY V = 0.005 = 0.5% of GDP 20 (c) Calculate seignorage relative to GDP if inflation is instead 7% and velocity remains unchanged. AM %ANGDP 0.03 + 0.07 PY V 20 = 0.005 = 0.5% of GDP (d) Would you expect velocity to be the same in cases (b) and (c) as in (a)? Consider both the short and the long run. In the short run it may be unchanged, but if people expect higher inflation, the nominal interest rate will increase and velocity will also increase, reducing the seignorage in case (c). (e) Is the result in (c) an over- or underestimation of the increase in seignorage? The assumption that velocity remains unchanged leads to an overestimation of the increase in seignorage received from an increase in inflation