The Ramsey-Cass-Koopmans model

Résumé du document

The Ramsey-Cass-Koopmans model is an economic model resembling the Solow model. The purpose of this paper is to outline the model with government, and assess the effects of government spending being tax or bond financed. We will see a result stating that it does not matter whether government spending is tax or bond financed. The Ramsey model is a micro-founded model – where the dynamics of economic aggregates are determined by decisions at a microeconomic level. The growth rates of population and technology are constant, and capital stock evolves through the interaction between households and firms in a competitive market. Savings rate therefore, is no longer exogenous and does not have to be constant. Before outlining the model however, the assumptions used need to be outlined for both firms and households.

Firstly, we assume there are a large number of identical firms, all trying to maximize profit. Each firm has access to the production function Y = F(K, AL), where K is capital and AL is effective labor. The firms operate in a competitive factor market, i.e. they hire workers and rent capital in a perfectly competitive market, and sell output in a perfectly competitive market. Technology (A) is given, and this grows at rate g. Also, because the firms are owned by households, any profits a firm gains are accrued in a household.

Extraits

[...] For example, traditional economic models state that a shift from tax to bond finance increases consumption, and so the United State's huge budget deficits will be increasing consumption and hence reducing capital accumulation and growth. If Ricardian equivalence holds however, this is not the case, and cutting taxes will make no difference. References Aiyagari, S. and Gertler, M Backing of Government Bonds and Monetarism,” Journal of Monetary Economics (July): 19-44. Barro, R. J Government Bonds Net Wealth?” Journal of Political Economy 82 (November/December): 1095-1117. Barro, R. [...]

[...] Also, more realistically, bonds are usually paid back by individuals who were alive at the time of issue. Lifetimes are long so an increase in wealth due to a bond issue only actually represents a small impact on consumption. It seems that even with the entry of new households, Ricardian equivalence is still a good approximation. Ricardian equivalence is closely related to the permanent-income hypothesis, and it is argued that if the permanent-income hypothesis fails, then so will the Ricardian equivalence result. [...]

[...] J “Government Spending, Interest Rates, Prices and Budget Deficits in the United Kingdom, 1701-1918,” Journal of Monetary Economics 20 (September): 221-247. Barro, R. J “Macroeconomics, 4th Edition. New York: Wiley. Barsky, R. Mankiw, N. and Zeldes, S. P “Ricardian Consumers with Keynesian Propensities,” American Economic Review 76 (September): 676-691. Cass, D “Optimum Growth in an Aggregate Model of Capital Accumulation,” Review of Economic Studies 32 (July): 233-240. Hubbard, R. [...]

[...] Taxes do not enter into a household's preferences and hence taxation does not affect consumption. Also, households acquire a bond as an asset but also acquire the future tax burden associated with the bond. The household simply saves the bond and the interest the bond accrues in order to pay the future taxes needed to pay the bond back. Only the quantity of government purchases, not the division of financing between taxes and bonds affect the economy. There are some reasons however, why the Ricardian equivalence result may not hold. [...]

[...] The arrows in the above diagram show the direction of motion of consumption. When k is greater than f'(k) is less than , and so is negative. Similarly, when k is less than is positive. Hence consumption is rising if k [...]