Individual Satisfaction and Economic Growth in an Agent-Based Economy

Abstract

We combine macro and microeconomic perspectives in an agent-based endogenous growth model that uses individual satisfaction as a driver of human capital accumulation. The micro perspective is based on individual satisfaction: an utility function computed from the income variation in space (relative to others) and time. The macro perspective emerges from micro decisions that, at an aggregate level, determine an important social decision about the share of the working population engaged in producing ideas (i.e. skilled workers). Underlying our analysis is the Easterlin hypothesis (Easterlin, in: David, Melvin (eds) Nations and households in economic growth: essays in Honor of Moses Abramowitz, Academic Press, New York, 1974, J Econ Behav Organ 27(1):35–47, 1995) which states that individuals care much more about their relative income than about increases in their own income, weakening the link between growth and income. Simulations show that growth and satisfaction levels are higher when relative and absolute incomes are equally weighted in satisfaction computation and are lower when satisfaction only depends on relative incomes.

Appendix: \(\beta (\rho )\)

At the beginning of period t, an agent has perfect knowledge of period $t-1$ wages, namely $w_{t-1}^{S}$ and $w_{t-1}^{U}$, the skilled and unskilled labour wage, respectively. Assume that agents take these values as the ones that will prevail in the future, and, for the sake of simplicity, denote them by $w^{S}$ and $w^{U}$. Suppose skilled agents spend nine more years at school than unskilled agents. For example, one can think they spend two more years at secondary school, four additional years to take a first degree, and finally three more years in some form of post-graduate studies. PVE, the present value of future wages for an agent that is starting his or her education to become skilled is then:

$$\begin{aligned} \textit{PVE}=w^{S}\left[ (1+\rho )^{-9}+(1+\rho )^{-10}+\cdots +(1+\rho )^{\tau }\right] \end{aligned}$$

(12)

where $\rho$ is a rate of time preference or discount rate, and $\tau$ is the number of years to the end of active life, likely to be comprised between 45 and 50.

At the same time a future skilled agent starts his or her education, unskilled agents start working. With the hypothesis above, this means they work nine more years when compared to skilled workers. Let PVU be the present value of all wages earned by unskilled workers:

$$\begin{aligned} \textit{PVU}=w^{U}\left[ 1+(1+\rho )^{-1}+(1+\rho )^{-10}+\cdots +(1+\rho )^{\tau }\right] \end{aligned}$$

(13)

Comparing Eqs. (12) and (13), it is apparent that ws must be greater than wu for there to be any chance of PVE being greater than PVU. In this case, and from a pure income perspective, i.e., taking aside any subjective preference for education, the agent would chose to proceed into further education and not to remain unskilled. Let $\beta$ be the ratio between $w^{S}$ and $w^{U}$ that makes the present value of skilled labour wages equal to the present value of unskilled labour wages:

$$\begin{aligned} \frac{w^{S}}{w^{U}}=\beta =PVE=PVU \end{aligned}$$

(14)

From Eqs. (12), (13) and (14), it gives:

$$\begin{aligned} \beta =\frac{1+(1+\rho )^{-1}+(1+\rho )^{-10}+\cdots +(1+\rho )^{\tau }}{(1+\rho )^{-9}+(1+\rho )^{-10}+\cdots +(1+\rho )^{\tau }}=\frac{A}{B} \end{aligned}$$

(15)

with $A=1+(1+\rho )^{-1}+(1+\rho )^{-10}+\cdots +(1+\rho )^{\tau }$ e $B=(1+\rho )^{-9}+(1+\rho )^{-10}+\cdots +(1+\rho )^{\tau }$. Is is easy to show that $A=\frac{1+\rho -(1+\rho )^{-\tau }}{\rho }$ and that $B=\frac{(1+\rho )^{9}-(1+\rho )^{8-\tau }}{1-(1+\rho )^{8-\tau }}$. Replacing A and B in expression (15) and simplifying, it gives:

$$\begin{aligned} \beta =\frac{(1+\rho )^{9}-(1+\rho )^{8-\tau }}{1-(1+\rho )^{8-\tau }} \end{aligned}$$

(16)

Note that$\beta$ approaches $(1+\rho )^{9})$ when $\tau$ tends to infinity, and that $\beta$ is an increasing function of $\rho$. When the discount rate is higher, the future is less valued, and therefore the skilled labour wage has to be higher for agents to become indifferent between acquiring skills through education and to remain unskilled. In our simulations, we set $\tau =48$.