117 Let the demand for money in the economy be given by 1500

(11.7) Let the demand for money in the economy be given by 150,000 - [Ination (%)] 3 . Calculate the amount of revenue raised through the ination tax for ination rates up to 50% (a spreadsheet would help!). What ination rate maximizes revenue?

Solution

Given that the demand for money = 150,000 - [Ination (%)^3]

inflation tax is given by = (inflation/100) x (150,000 – (% inflation)^3 = 1500 x inflation % - (inflation %)^4/100

For inflation rates 0% to 50%, we find the schedule of money demand and inflation tax. Find the optimum / revenue maximizing inflation tax by finding the derivative of the tax function and equating it equal to 0

1500 - 4*inflation%^3/100 = 0

150000/4 = inflation%^3

This gives the revenue maximizing inflation tax = 37500^1/3 = 33.47%.