Why parents and teachers may prefer punishment to encouragement for child education?

I. introduction

Although educators and psychologists persistently advocate encouragement rather than punishment for children's education, many teachers and parents often argue that punishment is more effective than encouragement to make a child study diligently. This issue is of importance in the field of educational psychology, and some studies have tried to explain the phenomenon from alternative points of view. This note is a new attempt to furnish a preliminary solution for this observed phenomenon from the economic perspective.(1)

The remainder of the paper proceeds as follows. The theoretical framework is developed in section II. Section III investigates the impact of punishment and encouragement on diligence. Some concluding remarks are offered in section IV.

II. The Theoretical Framework

The optimization problem for a representative child is given by:

[Mathematical Expression Omitted],

s.t. S = [Alpha] + [Beta][F(T - l) - [Gamma]]; F[prime] [greater than] 0, F[double prime] [less than] 0.(2)

Equation (1) states that the representative child seeks to maximize his utility U, which depends positively on leisure I and encouragement S. The encouragement may be something tangible (money) or intangible (praise).(2) Leisure is specified as an element in the utility function of a child to reflect the fact that students dislike studying at school and doing homework,(3) just as leisure is an element in the utility function of a worker which expresses his dislike for working.(4) Equation (2) specifies how encouragement for studying is created. Define T as the total time endowment, the production function for performance in studying F then can be specified as an increasing function of studying hours T - l. If his performance in studying F(T - l) exceeds the given threshold level [Gamma], the child will enjoy encouragement from parents and teachers. However, if his performance in studying F(T - l) falls short of the given threshold level [Gamma], the child will suffer punishment from parents and teachers. To generalize the analysis, we specify that encouragement is composed of a component which is independent of studying [Alpha] and a component which is related to the performance of studying [Beta][F(T - l) - [Gamma]]. (5,6)

The constrained maximization problem reported in equations (1) and (2) can be solved by setting up the Lagrange function L:

L = U(l, S) + [Lambda]{[Alpha] + [Beta][F(T - l) - [Gamma]] - S}, (3)

where [Lambda] is the Lagrange multiplier. The first-order conditions for a maximum at optimal values [l.sup.*], [S.sup.*] and [[Lambda].sup.*] are:

[L.sub.l] = [U.sub.l]([l.sup.*], [S.sup.*]) - [[Lambda].sup.*] [Beta]F[prime] (T - [l.sup.*]) = 0, (4)

[L.sub.S] = [U.sub.S]([l.sup.*], [S.sup.*]) - [[Lambda].sup.*] = 0, (5)

[L.sub.[Lambda]] = [Alpha] + [Beta][F(T - [l.sup.*]) - [Gamma]] - [S.sup.*] = 0. (6)

The second-order condition requires that the following condition be met:

D = 2[Beta]F[prime] [U.sub.Sl] - [([Beta]F[prime]).sup.2] [U.sub.SS] - [U.sub.ll] - [Lambda][Beta]F[double prime] [greater than] 0. (7)

III. The Effects of Encouragement and Punishment

Now we are in a position to examine how the choice between leisure and studying will respond to changes in encouragement-punishment parameters [Alpha], [Beta], and [Gamma]. From equations (4)-(6), we have the following comparative static results:

[Delta][l.sup.*]/[Delta][Alpha] = ([U.sub.lS] - [Beta]F[prime] [U.sub.SS])/D [greater than] 0, (8)

[Delta][l.sup.*]/[Delta][Beta] = -([[Lambda].sup.*] F[prime]/D) + [F(T - [l.sup.*]) - [Gamma]]([Delta][l.sup.*]/[Delta][Alpha]) [greater than or equal to] [less than or equal to] 0, (9)

[Delta][l.sup.*]/[Delta][Gamma] = -[Beta]([Delta][l.sup.*]/[Delta][Alpha]) [less than] 0. (10)

The results reported in equations (8)-(10) reveal some interesting implications. In what follows we will discuss them respectively.

First, equation (8) indicates that, when leisure is a normal good, an increase in the constant reward [Alpha] will induce more leisure and less studying hours. As might be expected, a richer family will give their children more monetary rewards which are independent of studying effort. Teachers thus often find that students from richer families display less diligence.(7)

Second, equation (9) states that the total effect of a rise in [Beta] on leisure can be divided into the substitution effect and the income effect.(8) The substitution effect -[[Lambda].sup.*] F[prime]/D is negative. The income effect [F(T - [l.sup.*]) - [Gamma]] ([Delta][l.sup.*]/[Delta][Alpha]) is negative when the child is punished F (T - [l.sup.*]) - [Gamma] [less than] 0, and positive when the child is encouraged F(T - [l.sup.*]) - [Gamma] [greater than] 0. As a consequence, the total effect of a rise in [Beta] on leisure is definitely negative under the punishment situation while the total effect is ambiguous under the encouragement situation. This result may explain the fact that some teachers and parents prefer punishment to encouragement.

Finally, equation (10) indicates that students will allocate more time to studying following an increase of the threshold level. This conclusion can explain the phenomenon that students will display better performance in studying if teachers demand a higher standard.

IV. Concluding Remarks

A main concern of modern parents and teachers is to discover what educational method can improve their children's scholastic performance. This topic is of importance in the field of educational psychology, and some studies try to explain how punishment, on the one hand, or encouragement, on the other hand, affect study habits. This paper develops a simple economic model to interpret why punishment is more effective than encouragement in increasing children's diligence in studying. Based on the framework, three main conclusions are drawn:

(i) If the children are given more monetary rewards which have nothing to do with their scholastic performance, they will show less diligence.

(ii) A rise in the proportional rate of monetary rewards will definitely have a negative effect on leisure if the children are under the punishment situation, while an ambiguous effect is revealed under the encouragement situation.

(iii) The children will allocate more time to studying if parents and teachers raise their threshold level of studying performance necessary to avoid punishment.

Chung-cheng Lin Institute of Economics, Academia Sinica Taiwan, Republic of China

Ching-chong Lai Sun Yat-Sen Institute for Social Sciences and Philosophy, Academia Sinica Taiwan, Republic of China

1. The field of the economics of education mainly concerns the issues of human capital theory, the calculation of rates of return to education, the cost structures of education, finance for education, and education and economic growth [1; 3; 6]. However, a burgeoning literature suggests that labor supply theory will be useful to understand the study effort of children. Owen [7] offers a comprehensive survey.

2. This paper assumes that money and praise are equivalent forms of encouragement, so that there is no difference in the child's behavior depending on the form of encouragement.

3. In recent years psychologists and sociologists have undertaken systematic studies concerning student attitudes towards study. The studies find that students dislike studying. To take some examples, Csikszentmihalyi and Larson [5, 39] examine middle-class students in a "very good high school" with excellent teachers. They find that the teenagers feel best when they are with their friends; in school they are bored; at home they tune out. Covington [4] argues that students dislike studying because tests, grades, and teacher comments are all structured to provide estimates of the child's ability, and for many students the result is that learning diminishes their self-esteem. Furthermore, Owen [7] indicates that there are many other activities that compete with study time. Students find that studying interferes with other activities that they prefer, such as eating, sports, hobbies, listening to music, taking naps, watching television, and spending time with friends.

4. In Becker's [2] terminology, the proper elements in the utility function are "commodities," which are produced by combining leisure time with other inputs.

5. This paper does not consider parents' possible strategy "do well and you can spell less time on homework."

6. It seems reasonable to assume that students intend to please not only their parents (or teachers) but also their peers. Under such a situation, it is plausible that it takes time for the students to please their peers. This means that there is one more activity which competes with study time and leisure. Such consideration will complicate the model, but will not alter the basic outcomes.

7. The model ignores that the richer family may provide a better learning environment for their children. To incorporate this idea, the production function for studying should be modified as:

F(T - l, W); [Delta]F/[Delta](T - l) [greater than] 0, [Delta]F/[Delta]W [greater than] 0, [[Delta].sup.2]F/[[Delta]W[Delta](T -/)] [greater than] 0,

where W is the wealth of the family.

8. in equation (9), the first term on the right hand side is the substitution effect, and the second term is the income effect.

References

1. Atkinson, G. B. J. The Economics of Education. London: Hodder and Stoughton, 1983.

2. Becker, Gary S., "A Theory of the Allocation of Time." Economic Journal, September 1965, 493-517.

3. Blaug, Mark. The Economic Value of Education: Studies in the Economics of Education. Aldershot, U.K.: Edward Elgar, 1992.

4. Covington, Martin V. "The Motive for Self-Worth," in Research on Motivation in Education: Student Motivation, edited by Russell E. Ames and Carole Ames. Orlando: Academic Press, 1965.

5. Csikszentmihalyi, Mihaly and Reed Larson. Being Adolescent: Conflict and Growth in the Teenage Years. New York: Basic Books, 1984.

6. Johnes, Geraint. The Economics of Education. New York: St. Martin's Press, 1993.

7. Owen, John D. Why Our Kids Don't Study: An Economist's Perspective. Baltimore: Johns Hopkins University Press, 1995.