The Gibson paradox, long observed by economists and named by John Maynard Keynes (1936), is a positive relationship between the interest rate and the price level. This paper explains the relationship by means of interest-rate, cost-push inflation. In the model: spending is driven in part by changes in the rate of interest and the central bank sets the interest rate using a policy rule based on the levels of output and inflation. A model shows that the cost-push effect of inflation, long known as Gibson's paradox, intensifies destabilizing forces and can be involved in the generation of cycles.