Most economists, who refer to utility as representing wellbeing, do so under the assumption that utility increases with consumption. In contrast, lately researchers have found evidence that individuals' wellbeing is by far a more complicated matter than to be represented solely by their consumption choices. Adopting a broader approach to human wellbeing, we have modified the traditional theory to include income aspirations. Following this new line of thinking, this paper assumes that individuals seek to minimize the gap between their consumption aspirations and their consumption desires, namely minimizing their frustration. We present an overlapping generation model and assume that desires increase with current and lag consumption. Our theoretical results show that in an economy with agents minimizing frustration, as greed increases, the steady state level of capital might be higher while people would certainly be more miserable.
Utility maximization is assumed to be the ultimate target of individuals. Almost all economic models that try to maximize the wellbeing of an individual or a group of individuals, assume that each one of them is trying to maximize utility from consumption. This school of thought is based on long living ideas starting with Hicks [
Surveying the literature regarding human happiness and the connection between wealth and happiness reveals that most economists who make pronouncements about economic matters do so under a set of assumptions about human happiness. Chief of these is the belief that by raising income or output an individual is better off.
Significant deviation from this paradigm has been shown by Pigou [
In the years after Pigou argued his revolutionary claim, economic theory has dealt with the issue of the relationship between income and happiness. Easterlin [
Recognizing that economic variables are not what interest the public, but rather the happiness derived from them, Oswald [
Further deviation from the traditional utility theory was made by Rabin [
Finally, significant strengthen regarding the importance of happiness rather than utility comes from Kahneman and Krueger [
As we can see, the main points raised in the literature review are that an increase in income does not necessarily increases individuals’ utility or happiness. Past consumption, future consumption and aspirations play a major role in determining individuals’ happiness. Although growing income and consumption raise utility, it may raise the desire for even more and therefore create a growing and painful gap, causing disutility.
Based on Pigou [
Consider a perfectly competitive world where economic activity is performed over infinite discrete time,
All individuals live during two periods of time. An individual works during the first period and retires at the beginning of the second. Each individual saves part of his first period income so that the savings, including the return, finance his second period consumption. During each period, both young and old people are alive. The rate of population growth equals zero.
In every period, t, a generation which consists of
During the first period, they work and earn a certain wage, and during the second period they are retired. Individuals, i, born at time t, are characterized by their intertemporal pleasure function
non-negative consumption during the first and second periods of their live, Where
Each individual has desires he tries to fulfill. Let us define
During the first period of their lifetime, individuals born at time t supply their unit endowment of labor in- elastically. The resulting wage income is allocated between first period consumption
Each individual tries to maximize his utility subject to his two period budget constraint:
t is the tax rate.
For simplicity’s sake, we can define
(2.1.1) Specific Utility
Let us assume that the pleasure function of each agent in the economy is:
While desire function is formulated according to the assumption that the level of desire increases with consumption, which relies on the thought that rising income changes an individual's tastes causing him to have ever-increasing aspirations (see Cantril [
According to this way of thinking, we assume that in each period desire increases with current and with lag consumption, and define it as:
where:
γ < 1 is the discount factor of utility in period 1.
λ < 1 is the discount factor of utility in the desire function-D at period 1.
η > 1 is a factor that increases desires in period 0 as consumption in period 0 is higher.
δ > 1 is a factor that increases desires in period 1 as consumption in period 1 is higher.
ψ > 1 is a factor that increases desires in period 1 as consumption in period 0 is higher.
Notice that discounted desire level in the second period increases with consumption in period 0 and 1 (according to term
The agent is trying to maximize the term:
subject to his budget constraints, as presented in Equation (1b).
where, t represents the tax rate.
We get:
St is the amount saved in period 0.
For simplicity’s sake, let us assume that there is one active firm in the market in period t.
The output produced by the firm at time t is:
(2.2.1) Income distribution
The product,
where
In each firm we get that:
The income of the firm owners is:
(2.2.2) Aggregate savings
Assuming that the number of workers is N and that there is 1 firm owner, the aggregate savings in the economy would be:
Since λ and γ, the discount factors of utility in period 1, are smaller than 1 while the factor that increase desires δ, η and ψ are much larger than 1 (we suppose that desires grow exponentially with current and past levels of consumption),
The amount of capital in the next generation would be
Substituting (4) in (5) we get:
Substituting the production function (2) into (6) we get:
Given that population size is fixed, we get that the capital stock of the next generation is determined by the current stock of capital.
Stationary equilibrium will exist for:
Substituting (7) into (6a) we get:
or
For Kt the stationary amount of capital.
Substituting (7b) into (2) we get the stationary amount of production is:
or
Substituting (7b) into (3) we get the stationary wage of each worker is:
Substituting (9) into Equations (1c) and (1d) we get the stationary level of consumption in period 0 and 1 are:
or
and
or
While substituting (8) into (4) we get the stationary level of total saving is:
or:
Minimum frustration in steady state (2.3.1)
Substituting (10a) and (11a) into (1a) we get that frustration level in steady state is:
We can present (13) as:
We concentrate at the effect of the greed parameters
Differentiating (7b) and (8a) with respect to η we get:
As we explained above, since
Differentiating (7b) and (8a) with respect to ψ we get:
As we can see, the same analysis regarding (14) and (15) applies here and the expressions in (16) and in (17) are smaller than zero.
Differentiating (7b) and (8a) with respect to
As we can see for
According to the comparative statics in (14), (16) and (18) as greed increases in the first period due to current consumption, and as greed increases in the second period due to consumption memory of the first period, capital and output levels in steady state would be lower. However, as greed increases in the second period due to the consumption level in the second period, capital stock in steady state will be higher.
In other words, economic growth is negatively affected by greed originated by rising consumption in the first period and is positively affected by greed originated by rising consumption in the second period.
Differentiating (13a) with respect to η we get:
(20)
See more details on differentiation in (20) in Appendix 1.
As we can see, all the terms in (20) are smaller than zero, except the term
Differentiating (13a) with respect to
As we can see, all the terms are smaller than zero, except the term
smaller than 0.333. The same analysis regarding (20) applies here and all the expressions in (21) are smaller than zero.
Differentiating (13a) with respect to
The analysis regarding (20) applies here as well and the expressions in (22) are smaller than zero.
As we can see, increased greed would make people less happy (
In this section, we compared steady state levels of capital in two models. The first is a standard overlapping generation model with individuals that maximize utility while the second is an overlapping generation model with individuals that minimize frustration.
Appendix 2 presents the results for the first model. We get that steady state levels of capital and production are:
Comparing steady state levels of capital and output in the first model (Equations (23) and (24)) to their steady state levels in the second model (Equations (7b) and (8a)), we can see that if:
then the steady state level of capital and production in the second model are higher.
After some manipulations, we get that Equation (25) is true if
ψ | η | δ | |
---|---|---|---|
↑ | ↑ | ↑ | K |
↑ | ↑ | ↑ | Y |
↓ | ↓ | ↓ | U − D |
We can present (25a) as:
Notice that γ and λ are discount factors of utility (smaller than 1).
We get that as ψ and η, the factors that increase desires in period 0 and period 1 according to consumption in period 0 are higher, an economy with agents that takes into consideration the effect of greed will converge to a lower steady state level of capital and production. However as
These results are in the same direction pointed by the comparative statics (In the comparative statics, we showed that
In order to interpret the results, let us assume the existence of one economy with agents that maximize utility and a second economy with agents that maximize the net utility (U-D). The second economy would reach higher steady state level of capital as agents become greedier due to higher consumption in the second period of their lives and as their greed increases in smaller magnitude due to their consumption in the first period of their lives.
In summary, in an economy with agents that take into consideration the frustration caused by unsatisfied desires, a higher steady state level of capital will be reached compared to a traditional economy with maximizing utility agents if the evolving greed is higher when people are old and lower when people are young.
Classic economic literature refers to a human agent as a homo-economicus who has one main aim, namely to maximize utility from consumption. According to this school of thought, all the economic decisions made by an agent are meant to reach the goal of maximizing utility. However, we find many researchers who find economic behaviors that do not meet this approach.
In this paper, we suggest a revised approach and assume that individuals are trying to maximize the net utility which we define as the difference between utility and desires (which is similar to an approach of trying to minimize misery). According to our model, the agents’ desires are strengthened by current and past levels of consumption. Although this way of thinking is not new (see for example Cantril [
We present an overlapping generation model with agents that have desires which increase with current and past consumption. We define misery (or frustration) as the difference between the level of utility and the level of desires. Each agent lives for two periods: working during the first and being retired during the second. The agent uses his first period income for consumption and for savings. During the second period, the agent consumes his savings plus interest earned. The aggregate amount saved in the first period finances investment which changes the amount of capital in the second period. As capital increases, production and income increase.
Steady state for the amount of capital, production and wage is calculated. Given steady state level of wage, the difference between utility and desire, which we defined as frustration is calculated in steady state.
The amounts of capital, production and frustration in steady state are defined as a function of the desire parameters. Using comparative statics, we find that as agents become greedier due to higher consumption in the second period of their lives and as their greed increases in smaller magnitude due to their consumption in the first period of their lives, steady state level of capital and production will be higher.
In order to examine the findings, we compared capital steady state level in our model to steady state of capital in a standard model with agents that maximized their utility, while using the same production function.
We find that an economy with agents minimizing frustration will reach higher steady state of level of capital compared to a traditional economy if the evolving greed due to consumption in the first period is smaller and the evolving greed due to consumption in the second period is higher.
According to our comparative statics, higher greed at any stage of life is accompanied by a reduction in agents’ wellbeing.
The results indicate that in cases where people become greedier in the second period of their life, the economy will grow in a larger magnitude while people will be more miserable.
Ben David Nissim,Tavor Tchai,Winer Zvi, (2016) Greed Supports Economic Growth But Might Make Us More Miserable. Theoretical Economics Letters,06,494-506. doi: 10.4236/tel.2016.63057
Comparative Statics
1. Detailed differentiation with respect to η:
2. Detailed differentiation with respect to ψ:
3. Detailed differentiation with respect to δ:
Let us assume that the utility function of each agent in the economy is
The agent is trying to maximize the utility:
We get
Production
The output produced by the firm at time t is:
Income distribution
The product,
where
In each firm we get that:
The income of the firm owners is:
Aggregate savings
Assuming that the number of workers is N and that there is 1 firm owner, the aggregate savings in the economy would be:
Equilibrium
The amount of capital in the next generation would be
Substituting (A.10) in (A.11) we get:
Substituting the production function (A.8) into (A.12) we get:
Given that population size is fixed, we get that the capital stock of the next generation is determined by the current stock of capital.
Stationary equilibrium will exist for
or
Substituting the in production function (A.8) we get:
or