I see no reason, unless you are saving on purpose (e.g., for retirement). 

Yes, for retirement, or bequest (in a same way as in joy-of-giving models), or social motives (as the continual seek for wealth accumulation in the Capitalist spirit literature). I explain in more details the justifications in the paper. I also try to expose results and implications rigorously.

Hi

Please find your answer in the following link:

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&ved=0CDQQFjAD&url=http%3A%2F%2Fwww.sfu.ca%2F~bkrauth%2Fecon808%2F808_lec1.pdf&ei=qy1zVIySM8_jaIPtgrAM&usg=AFQjCNG0uJimBDAA39_zQ8bhXfSUmErdrQ&bvm=bv.80185997,d.d2s&cad=rja

Good and also tricky question. Firstly, why do you want to take into account savings in your utility ? Economically, it is the bequest which has a positive effect on welfare then savings. If a guy has 1 billion dollars and will die soonly ? So, to my point of view, philosophically, if the savings become  bequest and transferred to future generations, there can be a utility. Also, at the paper, s_t is the bequest and not the savings.

So, I don't really see the reason behind to put savings in the utility function. But if we put savings in the utility function, I think there are any other stuff to discuss.

Just a brain storm. If savings are considered as a good in the utility function, like U(C,S) (C -> consumption, S -> savings). If we are on a non-seperable utility form, the elasticity of marginal utility of consumption with respect to savings would be something non-zero.

So, economically, is there any reason that marginal utility of consumption increases/decreases with savings ? (constant case is valid for seperable utility function, because the derivative of marginal utility of consumption acc. to savings will be 0.)

If there is, I think it is necessary to justify. Why the elasticity is increasing/decreasing or constant ?

Dear all,

In the paper I wrote on the subject, I extend the Ramsey Growth model by including the saving flow in the Utility function. In that context precisely, this can be motivated in different ways:

1) The Ramsey Growth model is an altruistic model that involves successive generations. Assuming the recursive definition from Barro (1974), where a representative generation lives only at time (t), the bequest corresponds to the part of the lifetime income saved. This bequest received by the next generation at (t+1) might be consumed or invested. In the paper, for the sake of simplicity, I consider that all the amount is reinvested to investigate implications of this assumption. This idea constitutes therefore one possible justification to include savings in Utility (ie. bequest reinvested).

2) Some authors have considered social motives for wealth accumulation (capitalist spirit, status..). Notable works follow Zou (1994) where the Utility function includes the absolute amount of wealth (or capital) as an argument. Others like Corneo and Jeanne (2001) have included the relative amount of wealth instead. I propose in this paper to include the "variation" or the growing of wealth in Utility (hence, savings in that context), as an alternative way to capture the continual seek for wealth accumulation (for those social motives).

You can get more details about the justifications and implications of this assumption in the paper by following this link:

http://mpra.ub.uni-muenchen.de/59751/1/MPRA_paper_59751.pdf

Models of accumulation and growth, most likely. As I explained above, the Ramsey model is perhaps the most obvious case where savings in Utility can make sense, according to what has already been done in the literature. It is worth reading the paper in the link. I have submitted it to the AER. The idea that savings never provide Utility is misleading and prevents from discovering interesting results, as shown in that paper.

I think that yes.

While the paper is under review for an official publication, I encourage you to share and discuss the paper with colleagues. Once you agree that savings can enter Utility (actually the motivations I give above are already widely admitted in the literature), the remaining is just technical. A good math reference is Schattler and Ledzewiczs (2012). For instance, I personnally obtained some help from Heinz Schattler to solve the problem (a detailed resolution is exposed in appendix)

Mathematical results show that weaknesses of the standard Ramsey model can be overcome; they show also that the extension motivated by Zou (1994) can be generalized. Finally, it could be that the standard Ramsey model is not the "right" optimized version of the Solow model.

Incorporating Saving and Consumption in the same utility function is like the treatment of Intertemporal Budget constraint where individuals spread incomes over life-cycle by maximizing present and PDV of Future consumption. S = Y--C = I. Thus, incorporating both in same period sounds a bit counter-intuitive. I am not sure. Thanks.

Yes. That 's exactly the problem : it sounds counter-intuitive. However, it sounds counter-intuitive only at first glance. I explain, both in my previous answers above and in the paper linked below, that because of this reason, we accidently missed important results and properties in Macroeconomic Dynamics.

Excluding savings from the Utility function has been a misleading conventionnal rule followed by all researchers apparently (nobody has never investigated this issue; perhaps, it did not seem necessary..). The claim that savings can never enter the Utility function is a pre-conceived idea. This assumption has never been rigorously discussed and justified. I encourage you all to read the clarifications I give above, and the paper linked below:

http://mpra.ub.uni-muenchen.de/59751/1/MPRA_paper_59751.pdf

I encourage you to share and discuss the paper with colleagues, while it is under review for a publication. It is important to clarify this misunderstanding and to start working from now on a new and more appropriate dynamic structure.Thanks

I have received 2 best paper Awards since. And a Professor attending my presentation at a Conference said during the discussion that this research paper could lead one to a Nobel Prize. 

I am not so convinced by this reformulation. Already the consumption decision (as it is a control variable) is made indirectly on savings. Implicitly, your utility is at optimum with some precised level of savings. (Y=C+I)

You can see also this one by looking at the capital constraint Kdot on your model. In this constraint, there is already the role of savings.

Dear Can, savings in the standard model is indeed already controlled (indirectly) but motivated only by the interest rate motive and the time preference rate; ie. you defer current consumption based on the interest rate (or capital productivity) and on the time preference rate. However, in that model of accumulation, other motivations for saving should be  included explicitely (I am not the first Economist talking about that).

The time preference rate is originally a dsicounter of future Utility and not future consumption, which means therefore a discounter of futur pleasure, feelings or incomes. It is not a mathematical problem and this is why it might be complicated. The standard model is a restrictive (or too fictitious) version of the Neoclassical growth model, and certainly not the right optimized version of the Solow model. In the Solow model, the individual saves independtly from the interest rate, and hence potentially for several reasons. This individual could have a saving rate of 50% or more, if he likes saving (no matter what reasons are!). You will never be able to get this rate  in the standard Ramsey model. Adjusting the time preference rate will not allow you to reach such solutions. Yan can even not adjust it so as to get the highest futur level of consumption..

The only way to reconcile the model with this standard exogenous version (and to extend the steady-state solution set of capital per capita on both sides) is to include savings explicitely. What I find to be mistake is to consider that savings should never enter Utility.

Your opinion is shared by many Economists, and this is what gives this paper its importance.

Thank you.

Dear Atef, discounting consumption and discounting utility are some other subjects and irrelevant with our discussion I think. The debate on this is not new and always continuing. (you can look at some Christian Gollier's papers)

the fact that people save exogenously in the solow model is one of the possible critics of the model, I have no problem with this idea.

There is some conceptual issue on what you are doing with putting the savings in the utility function. People save for some reason. Savings are not by itself providing utility but  via bequests to children from their parents and also for retirement.  As you know, this kind of ideas are always present in OLG models with alturistic agents.

I think savings by itself is even providing desutility for agent, especially for some short term (if we think that agents are so impatient with a huge discount rate) because there is a cost of opportunity to not consume. This cost is higher for impatient agents.

As you are speaking about a "flow" of savings and not "stock" of savings and as we are in a usual time-additive growth model, the utility of agent is seperable temporally and so, at each date, savings by itself as you consider in the utility function will provide a desutility.

As a nutshell, I think you must focus on these kind of conceptual issues for motivating why you are inserting savings to your utility function.

Dear Can, thank you.

I am not sure if I have understood all your comments. If you read the two parts (A and B) of my first section, in which I treat motivations in details concerning savings in Utility, and including perhaps the technical subjects you raise, you will see what I tried to explain shortly.

You may be right about a possible debate on the fact that savings could or not provide Utility, or disutility. But this is a matter of "preferences and tastes" we suppose. We may not have to set a general rule about that. It might be possible in specific contexts that people appreciate saving rather than consuming (in the specific context of the dynastic Ramsey model). Leaving aside the extreme case of miserliness, I explain in that the flow of saving may enter the Utility function:

- it avoids anxiety: with a growing household at rate n, with depreciation of capital, people might obtain comfort from saving (this is to be viewed in the sense of anticipatory feelings, => there are some interesting papers in this literature)

- it formalizes the capitalist spirit, in a slightly different way from Zou (1994). The continual desire of wealth accumulation for its own sake (power, prestige, notoriety, status...)

- savings in Utility could be viewed in this context as a gift to heirs (savings are given for capital renovation or accumulation to the next generation). This seems a beautiful way to characterize solidarity accross generations.

The paper is titled "Utility from bequeathing savings or Utility from accumulating in the Ramsey model"

Now, when I talk about the time preference discounting future feelings or incomes, instead of future consumption, it is because I would to dissociate love of wealth accumulation (no matter what reasons are: miserliness, gifts, status..) from patience. Is miserliness opposed to impatience for example? Is generosity towards heirs oposed to impatience? I think that those notions should be separate in that specific model.

I will take a look at what you advised me. Thanks again.

Also, I suppose for example : U= a.ln(c)+(1-a).ln(s), where s=y-c;

As you can see, with such an assumption, U depends positively on s. If we considered the simplest static case (just to explain the problem), we would have an optimum defined by :

c=a.y

s=(1-a).y

where marginal utility of c is zero. Consuming more than "a.y" would cause a negative marginal utility of consumption. But this is technically ruled out by optimisation, because the first condition of the Max principle is to set Marginal utility of consumption equal to the shadow price of capital (lambda), and lambda must be greater than zero. In other words, all solutions over time (the consumption vector) will always lie on the portion (0,a.y).

Therefore, and very basically, it is just as if there was some lower bound level of savings "(1-a).y" due to social motives (or due to the 3 motives I gave previously), and an additional part of savings "s - (1-a).y" explained by interest opportunities and impatience as usual. Of course, the real separation is technically more complicated than that. What is important is that the the resolution leads to differences in terms of variable effects (both qualitatively and quantitatively). This makes the paper more important. If it had not been the case, omitting savings in Utility might have been not seriously mattering (if it was only a kind of scale effect on the saving rate for example..)

Implications on theoretical and empirical results coming from the standard version should be analyzed.

A simple detail about savings bequeathed: it means we assume a different generation each time t. This has already been done before me by Barro as I explain in the paper.

The point is of course that this utility function is badly conceived and operationalized: what is it? The very question you pose shows this: neoclassical economists have *no idea*  what to incorporate into this 'function'. One main item which is for instance lacking is 'government consumption', i.e. expenditure of the government on things like primary education, streetlights and the like. When I pay a teacher to teach my kids - it is supposed to increase utility in these models. When I pay taxes and the government pays the teacher the additional utility is, by assumption, literally zero. This is called market fundamentalism and is characteristic of many neoclassical models. Now, you can start a discussion if private education would be more efficient and effective than govenrment education (I doubt it) but assuming that it is not effective at all is bonkers. As such, the utility curve clearly is a pre-scientific concept, badly conetualized, defined, operationalized, let alone measured, Skip it from your article, it is not so much a waste of time but a phliston like concept which will lead you astray.