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

• Author: Lin, Chung-cheng

1. 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.

2. 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...