The Ideal Inflation Indexed Bond and Irving Fisher's Impatience Theory of Interest in an Overlapping Generations World

Irving Fisher long advocated inflation indexed bonds. I prove in the context of a multicommodity CAPM world that the best welfare improving bond pays the minimum money needed to achieve the same utility, and not the minimum needed to buy an ideal commodity bundle. Irving Fisher also developed and advocated the impatience theory of interest. But in OLG economies, the rate of interest is determined by population growth, not impatience. I reconcile this contradiction by proving that in stationary OLG economies with land, the interest rate at the unique steady state does depend on impatience. Indeed, the proposition that greater impatience creates higher interest rates holds more generally in OLG with land than in Fisher's two-period model.