Ramsey-Cass-Koopmens (RCK) Model | Analysis

Ramsey-Cass-Koopmens (RCK) Model | Analysis Ramsey-Cass-Koopmens (RCK) model is a neoclassical model which is based on economic growth developed by Frank P. Ramsey with significant extensions by Davis Cass and Tjaning Koopmans. It 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 to the IS/ LM model for short run analysis. It combines some of the most basic macroeconomic mechanism in one model namely consumptions/ saving, investment and growth. These mechanisms involve decision making. Hence, the RCK model is about intertemporal optimisation. Diamond model is an overlapping Generation model (OLG) which has developed by American Economist Peter A. Diamond (1965). The model extensions the original contributions of Allais (1945) and Samuelsan (1957) by including physical capital The two models are similar yet different in some elements. Assumptions Firstly, this exercise will focus on the assumptions in RCK model and Diamond model whereby there are some similarities and differences. Both models are in line with basic neo-classical assumptions of perfectly competitive markets whereby the objective of the firms is to maximize profits and individual/ household is to maximize utility. Besides this two main assumption, the RCK and the Daimond have the same assumptions as below: Same productions function with capital, knowledge and labour with constant returns to scale. Y = F (Kt, AtLt) Capital is endogenous while knowledge and labour are exogenous Capital and output are the same commodity. Thus, capital can be consumed No depreciation Household earned profits as they owned the firms Saving and consumption are endogenous. In the other perspective both models have different assumptions. Diamond model has the following assumptions: Discrete time, two period model which means the household lives for two periods namely working and retirement. Population growth- At rate n : Lt = (1+n)Lt−1. This shows that in any period t there Lt individuals and Lt−1 indivuals in retirement. Labour supply and lifetime income- Each household supplies one unit of labour in period, earning income = Atwt Ãâ€" 1. The lifetime income is divided between the two periods of life to pay for consumption in each period. Savings. The household spends a portion of lifetime income in period (1) on consumption, C1t. The remainder (Atwt − C1t) is saved to pay for consumption in period (2), C2t+1. Lifetime utility- consumption for each period C1t and C2t+1, to maximize lifetime utility Ut = U (C1t, 1/1+Ï  C2t+1) Production. Firms choose capital Kt and labor Lt to maximize profits according to the following production function: Technology grows at rate g : At = (1+g)At−1. The RCK model has the following assumption: Number of household- each household consists of a number of adults and that household size grows at the rate n and all household last forever. Population size- Population size is denoted by L. When population is denoted at the starting point of the analysis time 0, then it follows that the size of the population at time t is . Consumption- consumption per person is ct = Ct / L t Technology grows at the constant rate g. Hence Capital Ownership- households own all the capital in the economy and that the firms rent the capital from households. Output a single homogenous good that can be used for either consumption or investment. Yt = Ct + It Convergence Dynamic The next part of this paper will discuss on the dynamic of convergence in both models. Figure 1: The RCK model Golden Rule Equilibrium The diagram above illustrates the evolution path of c and k in the RCK model and its dynamic. Points B and D converge to the equilibrium E at the intersection of the lines. Meanwhile the other points are not feasible because the dynamics of this model will generate evolution paths that are not feasible. Point A generates a divergent path, which shows the condition of k must be positive. The path starting from Point B is also divergent and violates that the wealth is not consumed in sufficient way which leading to increasing wealth and reducing consumption. Only Points B and D will generate paths that will converge smoothly to the Modified Golden Rule equilibrium E. However, a pertinent point to note for the RCK model is that the starting point in the economy is critical to ensure convergence. Its dynamics requires that the starting point to exactly on the saddle path denoted by points B and D . Any other points and hence combinations of c and k off the saddle path lead to a divergenc e. The dynamic of Diamond Model can be illustrated in in figure 2 and 3. There is a different on the dynamics of the Diamond model compare to the RCK model. This is due to the assumption of an economy overlapping generations instead of an infinitely lived household. The dynamics of Diamond model are determined by the Euler Equation k t +1 = Dk ÃŽ ± = f ( k t ). E shows the equilibrium point where at this point k * = k t = k t +1. The left of the vertical k* line, k t k t and therefore kt is decreasing in until it converges to the equilibrium point. As illustrated in the diagram k is to the left of k* where k t Figure 2 : The Dynamics of Diamond Model Figure 3 : The Diamond Model (Non Cobb-Douglas Production Function) A The dynamics of convergence for this model depends on the shape of the kt+1 function. The economy in figure 3 will smoothly converge to equilibrium point E1 at k1 when it starts with the condition kt k* There are 2 equilibirium point E1 and E2. However, only E1 is stable while E2 is a knife-edge and unstable. Figure 4: The Diamond Model (Non Cobb-Douglas Production Function) B The economy as shown in the diagram above will only converge to the origin 0 regardless of its starting point. The RCK and Diamond models will exhibit similar characteristics upon reaching their equilibrium points. At the equilibrium points, the economy will be on a balanced growth path, where k and output per effective labour will grow at the rate of technical progress g while GDP will grow at the combined labour and knowledge growth rates (n+g). The savings and consumption rates as a proportion of income will also remain constant. Ricardian Equivalence There are two principal ways to levy revenues for a government, namely to tax current generations or to issue government debt in the form of government bonds the interest and principal of which has to be paid later. The question then arise what the macroeconomic consequences of using these different instruments are, and which instrument is to be preferred from a normative point of view. The Ricardian Equivalence Hypothesis claims that it makes no difference, that a switch from one instrument to the other does not change real allocations and prices in the economy. Ricardian equivalence holds under what we earlier called the natural borrowing limit, but not under more stringent ones. The natural borrowing limit is the one that lets households borrow up to the capitalized value of their endowment sequences. These results have counterparts in the overlapping generations model, since that model is equivalent to an infinite horizon model with a no-borrowing constraint. In the overlapping g enerations model, the no-borrowing constraint translates into a requirement that bequests be nonnegative. Thus, in the overlapping generations model, the domain of the Ricardian proposition is restricted, at least relative to 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 complications involving market imperfections and heterogeneous households. When the government imply taxes, the household’s budget constraint will be the present value of its consumption cannot exceed its initial wealth and the present value of its after tax labor income.In addition with no market imperfections, there is no reason for the interest rate the household faces at each point in time to differ from the one the government faces. The result of the irrelevance of the government’s financing decisions is the famous Ricardian equivalence between debt and taxes. For example if the government give some amount of bonds to each household at a time and planning to retire this debt at a later time, this will require each household to be taxed. This policy has two effects whereby household has acquired an asset which is the bond that has present value and also acquired a liabilit y which is the future tax obligation that also has the present value. Therefore, the bond does not represent the actual ‘net wealth’ to the household and this will not affect their consumption behaviour. Traditional economic models assume that a shift from tax to bond finance will increase the consumption level. The Ricardian and traditional views of consumption have very different implications for many policy issues. For instance, government often cut taxes during recessions to increase consumption spending. But in the perceptive of Ricardian Equivalence, these efforts are failure. One reason why Ricardian equivalence is not to be exavtly correct is because of turnover in the population. When new people are entering the economy, some of the future tax burden associated with a bond issue is borne by individuals who are not alive when the bond is issued. Therefore, the bonds represents net wealth to those who are currently living and this will affects their behaviour. This possibility is illustrated by the Diamond overlapping-generations model There is very limited Ricardian equivalence theorem for OLG economies. Any change in the timing of taxes that redistributes among generations is in general not neutral in the Ricardian sense. If we insist on representative agents within one generation and purely sel.sh, two-period lived individuals, then in fact any change in the timing of taxes can.t be neutral unless it is targeted towards a particular generation, i.e. the tax change is such that it decreases taxes for the currently young only and increases them for the old next period. Hence, with su ¢ cient generality we can say that Ricardian equivalence does not hold for OLG economies with purely sel.sh individuals. Barro.s (1974) article .Are Government Bonds Net Wealth?. asks exactly offsetting the Ricardian question, namely does an increase in government debt, .financed by future taxes to pay the interest on the debt increase the net wealth of the private sector? Barro identified two main sources for why future taxes are n ot exactly setting current tax cuts (increasing government deficits): a) finite lives of agents that lead to intergenerational redistribution caused by a change in the timing of taxes b) imperfect private capital markets. Barro.s key result is the following: in OLG-models .niteness of lives does not invalidate Ricardian equivalence as long as current generations are connected to future generations by a chain of operational intergenerational, altruistically motivated transfers. These may be transfers from old to young via bequests or from young to old via social security programs. REFERENCES Blanchard, O.J. and S. Fischer, 1989, Lecture on macroeconomics, The M.I.T.  Presss, Cambridge   Barro, R.J., 1974, Are government bonds net wealth?, Journal of Political Economy,  82, 1095-1117. Diamond, P.A., 1965, National debt in a neoclassical growth model, American  Economic Review, 55, 1126-1150. Romer, David (1996), Advanced Macroeconomics Euthanasia: The Right To Die Euthanasia: The Right To Die Euthanasia is the intentional killing of a human being either because he/she has requested for it or when the person being killed hasnt made any request at all. This topic has always brought about so much controversy amongst people in most countries. Everyone in this world has his own experience with death. At least you have witnessed someone die or you have lost a friend or a family member and because of this, death has instilled so much fear in us. You will hear people saying I want a good death. There is no doubt in every man that at one point he will have to die because this is a biological fact. Many people especially the elderly who are approaching the end times of their lives will always say I have lived a good life and now am ready to go. Some who are going through so much problems in their lives will say Am tired of living and now I want to die. According to Harris (2003), all this are very common statements we here in life. This essay is going to address the importance of e uthanasia to both the victims and the family members. The audience readers to which this essay is meant for are the faith groups which may include the Christians, Jewish, Muslim and other religious groups who consider life to be given by God and therefore say only God should take it away. There are two types of euthanasia that we should look into i.e. passive and active euthanasia. The difference between these two is that in passive euthanasia, the patient dies on his own in the sense that the doctor does not do anything to the patient. He simply neglects him or stops giving him the medication that could have helped him remain alive. On the other hand active euthanasia is where by the doctors performs some action to bring to an end the life of the patients. In most cases it might involve giving a very powerful injection. All the same it still remains to the euthanasia. A doctor who does not give a throat cancer patient medication and lets him die of cancer is no better than that who gives him a strong injection and makes him die. Either way both doctors will have saved the patient the agony of having to live with so much pain in their lives and then die in the long run (Hermsen and Henj 517) Most terminally ill patients normally undergo so much pain that they cannot sometimes bear. In addition they also experience very poor life that they feel not human or feel God has neglected them. It is very frustrating for someone to experience such intractable pain and yet he was a healthy human being a few days a go. This is the reason why most of them voluntarily decide to request the doctor to end their lives. In some instances the doctor is in a better position to understand whether the patient will live or not. According to Franjo (1980), if the patient is going to die in the long run, then there is no need of keeping him in hospital for a few more days and incur so much expense because he is going to die either way. Even when the doctor does not end the life of such a patient, the body is finally going to give in. the pain these people undergo is so intense that ending their life may even give them peace because there is nothing they are enjoying by remaining alive. Even though everyone has a right to life of which the state is supposed to ensure that it is realized, it does not have the right to deny people their wish to die given such circumstances. Suicide is a legal matter that is applicable to all and is punishable by law. However a terminally ill person in hospital may not be in a position to exercise such an option either because of the physical or mental limitations. At such a point, the doctor may be in a good position to understand what is good for the patient. Even though most religious people may argue that the doctor is a human being and is capable of telling lies, there is no point in a doctor lying about someones life because he does not benefit in any way. According to Harris (2003), it is important to note that doctors do not have any personal gain in ending the patients life; they are only involved in instances where the patients life is of no benefit to him any more or when the patient has become a very huge burden to the fami ly or will become a huge burden with time. Many faith groups believe that its Gods will for terminally ill patients to undergo pain and suffering and they consider this a divine learning opportunity or a purification opportunity. This is a misguided way of thinking. There is no way god can allow his follower to undergo so much pain just because he wants the patient to grow strong in faith. In fact the bible says Gods has good plans for humanity. Plans that will give him a better future. Following this statement, there is no chance that the God will make a patient go through such painful experience. As a matter of fact, Jesus Christ suffered on our behalf and that is enough (Franjo 1980 ) At this point in time, there is a growing restriction in medical funding. This has led to doctors and family members having to result to very expensive treatments for patients who are terminally ill so that they can at least extent their days of living. If the patient does not want to continue living like that, then it is only fair that we grand them their wish and allow them to die. According to Hermsen Henj (2002), The amount of money that could be used in such expensive treatment can be diverted into other areas with insufficient funding such as infant care and pre-natal care (p. 519). This way the money will help save a lot of lives and also help in improving the lives of many more people other than spending the whole amount on one person who will die either way. Imagine a family spending five hundred thousand dollars on a patient to be kept alive on machines in he cannot survive without the life supporting machine. This will drain the family every single cent in their accounts but the bottom line is, the patients will die either way. It would be therefore wise for them to end the patients life and use the money for other purposes. Many people might also argue that terminally ill patients can be relieved off the pain they experience through proper management. It is true that the doctors who handle such patients must have undergone proper training and therefore capable of handling extreme medical cases like the terminally ill. According to Zdenkowski (1996), the problem is that not everyone can find access to the adequate pain management facilities and medication. So many Americans do not have health coverage. It therefore becomes very difficult and ex[pensive for them to take care of terminally ill patients considering the amount of money required. This as led to may people selling off their assets just to foot the bills of friends and relatives who end up dying after causing so much inconvenience to friends and relatives. To avoid such problems, it would be better if doctors agree to the wishes of the patients an d end their lives. Just like every person has the right to life, he also has autonomy over the same life. It is therefore upon him to decide whether or not to end it especially when his quality of life is not even in existence. He can also seek assistance from other people who might be taking care of him to do so. In any case a person in such a state is virtually dead. according to Mohita Chibber (2007), the main reason why people exist on this earth is to enjoy life and socialize with one another for mutual development of the community. If a person is always on the bed in a room somewhere, there is nothing he is enjoying on earth. Actually he is in fact suffering. Ending his life will doing him so much favor because sometimes the experience of terminal illness is so painful that a victim will see life as a burden he cannot continue living with. The only solution that will relieve him of and intolerable pain and suffering is death. Keeping euthanasia illegal like it is in the present time is even more hurtful for the patients. It is very disheartening to see animals being treated better than human beings because the law considers it illegal to keep a suffering animal alive while for human beings, it does not mind how much suffering they undergo. If the main purpose for existence of the law is to take care of the citizens, then euthanasia should be legalized so that terminally ill patients can be relieved from the never ending pain they undergo. With proper structures and responsibility, euthanasia can be very helpful in the health sector. Together with permission from the patient, organs from a victim can be preserved and donated to other patients who are really in need of them for survival. Furthermore these bodies could be used by medical experts to advance research in medical science to ensure that future generations are in a better position to deal with such problems whenever they occur (Zdenkowski 1996). The major issue with euthanasia is therefore whether it will bring more benefit when the person is dead than keeping him alive. It does not make sense to waste away someones life in a hospital bed in a state than can no longer be recognized as human being. In most cases terminally ill people are just like puppets who are controlled in every thing they do. They can not exist on themselves. For those who have been in critical states that can be considered next to death understands the pain one goes through. This is why no one would wish to spend the rest of his life on machines and pipes all over his body in every opening in the name of survival. Such person should not even be considered a human being because ideally he is no less than a machine (Mohita Chibber 2007). Although Euthanasia might have some disadvantages to both victims and the family members , the fact still remains that it is all about following the victims wish and because he is the one who understands the kind of pain he is going through, then it is only fear that the doctor grants him his wish. Annotated Bibliography Franjo, Cardinal Seper. Declaration on Euthanasia, the sacred congregation for the doctrine of the faith. May 5, 1980. April 6, 2010. http://www.cin.org/vatcong/euthanas.html Franco article focuses on the dignity a person possesses and the importance of his life. It also describes what the Christian understand by the suffering and pain they undergo whenever they are sick. Man should therefore accept the power of death the way it comes because at one point we shall all die. However those in the medical field should take good care of the patients. Harris John. Concent and end of life decisions. Journal of medical ethics. Feb. 2003. EBSCO Host. April 6, 2010 http://jme.bmj.com/content/29/1/10.full Harris discusses about the importance of consent in putting an end to someones life. The concept of autonomy is talked about where he insists that the victim has a right of deciding whether to end his life or not. According to Haris treatment of a person who has refused to get medication is a violation of his right and therefore should be avoided. If the victim is going to die either way, then there is no problem in ending hid life Hermsen, Maaike A, NA Henj A M.J. Euthanasia in Palliative care journals. Journal of pain and symptom management. 2002. Vol. 23 No. 6 517-522 These authors say palliative care has become a very intristing issue for most countries in the world since the 1980s. We have both those people who are for euthanasia and those who are against it. According to them we have those people who say dying is a part of life that is inevitable and therefore there is nothing wrong in ending terminally ill patients life. However we also have those who say we have to respect life and let it take its course without interference Mohita Chibber Aman. Euthanasia and Human rights legal service India.com. 22 Nov. 2007. 6 April 2010. Mohita and Chibber say there are a lot of people we come across in hospitals who totally depend on machines and medication for survival. The question has always been whether the best option is to end the victims life or continue sustaining his life with machines and medication The law in various countries varies when it comes to exercising the right to life in such instances but the fundamental issue is that every person has the autonomy to choose whether to live or die Zdenkowski, George. Human rights and euthanasia. Australia human rights commission. 1996 Retrieved on April 6, 2010 from http://www.hreoc.gov.au/human_rights/euthanasia/index.html According to Zdenkowski, euthanasia is a very controversial issue that has been in existence for quite sometime. We should therefore concentrate on reconciling the competing issues that exist between respect to life and the desire of a victim to die when suffering. Every human being has a right to life which should be respected and the violation of this is punishable by law. The doctors should also respect the patients right to life.