Ramsey-Cass-Koopmens (RCK) Model | Analysis

Ramsey-Cass-Koopmens (RCK) model is a neoclassical model which is dependant on economic growth developed by Frank P. Ramsey with significant extensions by Davis Cass and Tjaning Koopmans. It really is an extension of the Solow growth model whereby the new feature is that saving rate is not exogenously given. RCK model is also an alternative solution to the IS/ LM model for short run analysis. It combines some of the most basic macroeconomic mechanism in one model specifically consumptions/ keeping, investment and expansion. These mechanisms entail decision making. Hence, the RCK model is approximately intertemporal optimisation.

Diamond model can be an overlapping Era model (OLG) which has developed by North american Economist Peter A. Diamond (1965). The model extensions the original efforts of Allais (1945) and Samuelsan (1957) by including physical capital

The two models are similar yet different in some elements.

  1. Assumptions
Firstly, this exercise will concentrate on the assumptions in RCK model and Gemstone model whereby there are some similarities and distinctions. Both models are in line with basic neo-classical assumptions of properly competitive marketplaces whereby the aim of the firms is to increase profits and individual/ home is to maximize energy. Besides this two main assumption, the RCK and the Daimond have the same assumptions as below
  1. Same productions function with capital, knowledge and labour with regular returns to range. Y = F (Kt, AtLt)
  1. Capital is endogenous while knowledge and labour are exogenous
  2. Capital and end result are the same product. Thus, capital can be consumed
  3. No depreciation
  4. Household earned income as they had the firms
  5. Saving and intake are endogenous.
In the other point of view both models have different assumptions. Diamond model has the following assumptions
  1. Discrete time, two period model this means family members lives for two

periods namely working and pension.

  1. Population expansion- At rate n : Lt = (1+n)Lt1. This shows that in any period

t there Lt individuals and Lt1 indivuals in retirement.

  1. Labour resource and life span income- Each household supplies one unit of labour in period, earning income = Atwt 1. The lifetime income is divided between your two periods of life to cover consumption in each period.
  1. Savings. The household spends some of life-time income in period (1) on intake, C1t. The remainder (Atwt C1t) is kept to pay for ingestion in period (2), C2t+1.
  1. Lifetime utility- consumption for each period C1t and C2t+1, to maximize

lifetime utility

Ut = U (C1t, 1/1+П C2t+1)

  1. Production. Organizations choose capital Kt and labor Lt to maximize profits
according to the next production function
  1. Technology grows up at rate g : At = (1+g)At1.
The RCK model gets the following assumption
  1. Number of home- each household consists of lots of people and

that household size grows up at the speed n and all household last forever.

  1. Population size- Society size is denoted by L. When populace is

denoted at the starting place of the evaluation time 0, then it follows that how big is the populace at time t is.

  1. Consumption- ingestion per person is ct = Ct / L t
  1. Technology grows up at the regular rate g. Hence
  1. Capital Possession- homeowners own all the capital throughout the market and that

the firms rent the administrative centre from homes.

  1. Output - a single homogenous good that can be used for either

consumption or investment. Yt = Ct + It

  1. Convergence Dynamic

The next part of the paper will discuss on the dynamic of convergence in both models.


№ = 0





k* (0) k*MGRk

Figure 1: The RCK model Golden Guideline Equilibrium

The diagram above illustrates the progression way of c and k in the RCK model and its dynamic. Factors B and D converge to the equilibrium E at the intersection of the lines. On the other hand the other things are not feasible because the dynamics of this model will generate evolution paths that are not feasible. Point A produces a divergent journey, which shows the condition of k must maintain positivity. The path starting from Point B is also divergent and violates that the wealth is not used in sufficient way which resulting in increasing riches and reducing ingestion. Only Items B and D will generate paths that will converge effortlessly to the Modified Golden Rule equilibrium E. However, a essential point to please note for the RCK model would be that the starting point throughout the market is critical to ensure convergence. Its dynamics requires that the starting place to exactly on the saddle route denoted by details B and D. Other points and hence combinations of c and k off of the saddle path business lead to a divergence.

The dynamic of Stone Model can be illustrated in in body 2 and 3. There is a different on the dynamics of the Diamonds model compare to the RCK model. This is due to the assumption of your economy overlapping decades rather than an infinitely resided home. The dynamics of Stone model are determined by the Euler Formula k t +1 = Dk О± = f ( k t ). E shows the equilibrium point where at this time k * = k t = k t +1. The departed of the vertical k* lines, k t < k t +1 and therefore kt is growing until it converges to the equilibrium point. For the right k* collection, k t > k t and for that reason kt is lowering in until it converges to the equilibrium point. As illustrated in the diagram k is to the left of k* where k t < k t +1. Therefore, households will change the allocation of k in t and t+1 durations until it gets to in the balance. The course of the adjustment is to the right of k0 by increasing k in every t+1 period until equilibrium point E is come to. With the equilibrium point E, k will be fixed.

Figure 2 : The Dynamics of Diamond Model

k t +1 = f ( k t )

k t+1



k*1 k*2 kt

Figure 3 : The Stone Model (Non Cobb-Douglas Creation Function) A

The dynamics of convergence because of this model will depend on the form of the kt+1 function. The economy in body 3 will effortlessly converge to equilibrium point E1 at k1 when it starts with the condition kt < k1 or k1 < kt < k*2. However, it will diverge if it starts off with kt > k* You will find 2 equilibirium point E1 and E2. However, only E1 is secure while E2 is a knife-edge and unstable.

Figure 4: The Stone Model (Non Cobb-Douglas Development Function) B

The current economic climate as shown in the diagram above is only going to converge to the origin 0 regardless of its starting place. The RCK and Gem models will show similar characteristics upon getting their equilibrium details. In the equilibrium details, the overall economy will be on a well-balanced growth journey, where k and outcome per effective labour will grow at the pace of technical improvement g while GDP will expand at the put together labour and knowledge progress rates (n+g). The savings and utilization rates as a percentage of income will also continue to be constant.

  1. Ricardian Equivalence

There are two main ways to levy profits for a authorities, namely to taxes current generations or even to issue government arrears in the form of government bonds the interest and principal which needs to be paid later. The question then come up the particular macroeconomic outcomes of using these different tools are, and which tool is usually to be preferred from a normative point of view. The Ricardian Equivalence Hypothesis boasts that it makes no difference, that a switch in one instrument to the other does not change real allocations and prices in the economy. Ricardian equivalence retains under everything we previously called the natural borrowing limit, however, not under more stringent ones. The natural borrowing limit is the the one which lets households borrow up to the capitalized value of the endowment sequences. These results have counterparts in the overlapping years model, since that model is the same as an infinite horizon model with a no-borrowing constraint. Within the overlapping decades model, the no-borrowing constraint translates into a need that bequests be nonnegative. Thus, in the overlapping decades model, the domains of the Ricardian proposition is fixed, at least in accordance with the in_nite horizon model under the natural borrowing limit.

A natural starting point is the RCK model with lump-sum taxation, since this model avaoids all issues regarding market imperfections and heterogeneous homeowners. When the federal government imply taxes, the household's budget constraint will be the present value of its utilization cannot go beyond its initial riches and today's value of its after taxes labor income. Furthermore with no market imperfections, there is no reason behind the interest the household encounters at each time to differ from the one the federal government faces. The consequence of the irrelevance of the government's financing decisions is the famous Ricardian equivalence between credit debt and taxes. For instance if the government give some amount of bonds to each home at a time and likely to retire this debts at another time, this will require each home to be taxed. This coverage has two effects whereby household has acquired a secured asset which is the bond that has present value and also received a liability which is the near future tax responsibility that also has today's value. Therefore, the relationship does not signify the real 'net prosperity' to the household and this will not affect their use behaviour. Traditional financial models assume that a shift from tax to bond funding will increase the usage level. The Ricardian and traditional views of usage have completely different implications for many policy issues. For example, government often lower fees during recessions to increase consumption spending. However in the perceptive of Ricardian Equivalence, these work are failure.

One reason why Ricardian equivalence is never to be exavtly correct is because of turnover in the population. When new people are joining the economy, a few of the future taxes burden associated with a relationship issue is borne by those who are not alive when the bond is issued. Therefore, the bonds presents net wealth to those who find themselves currently living which will affects their behaviour. This likelihood is illustrated by the Gem overlapping-generations model

There is not a lot of Ricardian equivalence theorem for OLG economies. Any change in the timing of taxes that redistributes among years is in general not neutral in the Ricardian sense. If we insist on representative agents within one technology and solely sel. sh, two-period resided individuals, then in reality any change in the timing of taxes can. t be neutral unless it is targeted towards a specific technology, i. e. the taxes change is so that it decreases taxes for the presently young only and improves them for the old next period. Hence, with su cient generality we can say that Ricardian equivalence will not carry for OLG economies with strictly sel. sh individuals. Barro. s (1974) article. Are Federal Bonds Net Prosperity?. asks exactly offsetting the Ricardian question, specifically does an increase in government credit debt, . financed by future fees to pay the interest on your debt increase the online prosperity of the private sector? Barro discovered two main sources for why future taxes are not exactly arranging current tax slashes (increasing authorities deficits): a) finite lives of agents that lead to intergenerational redistribution the effect of a change in the timing of fees b) imperfect private capital market segments. Barro. s key consequence is the following: in OLG-models. niteness of lives will not invalidate Ricardian equivalence so long as current decades are connected to future years by a chain of functional intergenerational, altruistically enthusiastic transfers. These may be transfers from old to young via bequests or from young to old via interpersonal security programs.


Blanchard, O. J. and S. Fischer, 1989, Lecture on macroeconomics, The M. I. T. Presss, Cambridge

Barro, R. J. , 1974, Are federal bonds net riches?, Journal of Political Market, 82, 1095-1117.

Diamond, P. A. , 1965, National credit debt in a neoclassical expansion model, American Economic Review, 55, 1126-1150.

Romer, David (1996), Advanced Macroeconomics

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