Analytical proof of Gibson's paradox - Osorio Vaccaro, Jorge Guillermo (2023)
The mainstream in macroeconomics and economic policy establishes an inverse relationship between the price level and the interest rate and income. To reduce inflation, an interest rate increase is used in order to depress consumption and investment, consequently reducing effective demand and inflationary pressures. If the unemployment rate is high, a reduction in the interest rate can be used to stimulate consumption and investment, which increases production and reduces unemployment. However, from the empirical work of A. H. Gibson (1922), it has been documented that in certain cases there is rather a positive relationship between the interest rate and the price level. This discovery was baptized by J. M. Keynes as the “Gibson Paradox”. This article makes an analytical demonstration of the conditions under which the Gibson Paradox can occur, which can be very useful to theoretically support future empirical work on the subject and the debate on the usefulness of monetary policy to achieve price stability.