By Michael D. Bordo, Barry Eichengreen
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Additional resources for A Retrospective on the Bretton Woods system
The overlapping generations model was developed by Allais (1947), Samuelson (1958), and Diamond (1965). The di¤erence between Ricardian and non-Ricardian models, notably for ﬁscal policy was studied by Barro (1974), who notably asked whether real bonds are net wealth. The cash-in-advance constraint is due to Clower (1967). In the original version the consumer had to carry cash from the previous period in order to consume. The timing we use (Helpman, 1981, Lucas, 1982), allows newborn agents to have positive consumption, a useful feature since the models we employ in this book will have newborn agents.
We know from equation (30) that there is such a Pigou e¤ect in the overlapping generations model. We know also from equations (33) and (36) that both the price determinacy and the liquidity e¤ect in the OLG model are due to the presence of W t in the central equilibrium equation (31). However, in the Ricardian model, we saw that although W t appears in budget constraints such as (5), it disappears in the consumption function (equation 10) or in the equilibrium equations (equation 12), and this leads to the bizarre properties of the Ricardian model.
Then the household always exactly satisﬁes the cash-inadvance constraint (2) so that mjt ¼ Pt cjt . 2 Dsþ1 Ps ðyjs À tjs Þ ð14Þ s¼t The Consumption Function Maximizing the utility function (1) subject to the intertemporal budget constraint (14) yields the ﬁrst-order conditions: Dsþ1 Psþ1 cjsþ1 ¼ bDs Ps cjs ð15Þ Pigou Reconstructed: The Weil Model 27 Combining these ﬁrst-order conditions and the intertemporal budget constraint (14) yields the following consumption function for a household j: " Dt Pt cjt ¼ ð1 À bÞ Dt ojt þ y X # Dsþ1 Ps ðyjs À tjs Þ ð16Þ s¼t Now insert into (16) the assumption above (equation 8) that yjs ¼ ys and tjs ¼ ts .