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.
[...] Cass, D “Optimum Growth in an Aggregate Model of Capital Accumulation,” Review of Economic Studies 32 (July): 233-240. Hubbard, R. and Judd, K. L “Liquidity Constraints, Fiscal Policy, and Consumption,” Brookings Papers on Economic Activity, no 50. Koopmans, T. C the Concept of Optimal Economic Growth,” in The Economic Approach to Development Planning. Amsterdam: Elsevier. O'Driscoll, G. P Ricardian Nonequivalence Theorem,” Journal of Political Economy 85 (February): 207-210. Poterba, J. and Summers, L. H “Finite Lifetimes and the Effects of Budget Deficits on National Saving,” Journal of Monetary Economics 20 (September): 369-391. [...]
[...] Conclusion We have seen many reasons why Ricardian equivalence may not give the most accurate approximation in the real world. The entry of new households, liquidity constraints, the fact that taxes are non-lump sum and individual's short-termist behavior are the main limitations of Ricardian equivalence, however, due to the simplicity of the result, it remains a useful concept in economics. 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. [...]
[...] Ramsey Model With Government So far, we have only looked at the Ramsey model without adding government into any of the equations. This is obviously somewhat unrealistic, so we now extend the model to include a government sector. Once again, there are some new assumptions, which need to be stated before continuing. Firstly, the Government buys output at rate G(t). Government purchases are assumed not to affect the utility households derive from private consumption, nor do they affect future production. [...]
[...] Barro tested his findings by constructing estimates of the temporary component of military spending then regresses the long-term interest rate on this estimate. He found that evidence from the United Kingdom supports his predictions, however, the theory does not hold so well out with the UK. The United States for example, seems to have lower interest rates during wars, and hence the theory does not provide us with a good description of how real interest rates respond to changes in government purchases. [...]
[...] Outline of the Ramsey Model (Without Government) To begin with, an outline of the Ramsey model without government will be given, and at a later stage government will be added. Looking at the household, we can express the household utility function as: Here, is the discount rate, is the number of members in the household and is the instantaneous utility function which gives each member of the household's utility at a given point in time. It also shows that utility depends on consumption. [...]
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