Question

Incorporate household production in the income- leisure model we derived in the class and derive the slopes of the budget constraint and indifference curve. Show the condition at which utility maximization will occur for this model.

Answer 1

Indifference curve analysis can be used to explain an individual’s choice between income and leisure and to show why higher overtime wage rate must be paid if more hours of work is to be obtained from the workers. It is important to note that income is earned by devoting some of the leisure time to do some work. That is income is earned by sacrificing some leisure. The greater the amount of this sacrifice of leisure, that is, the greater the amount of work done, the greater income an individual earns.

Further, income is used to purchase goods, other than leisure for consumption. Leisure time can be used for resting, sleeping, playing, listening to music on radios and television etc. all of which provide satisfaction to the individual. Therefore, in economics leisure is regarded as a normal commodity the enjoyment of which yields satisfaction to the individual. While leisure yields satisfaction to the individual directly, income represents general purchasing power capable of being used to buy goods and services for satisfaction of various wants. Thus income provides satisfaction indirectly. Therefore, we can draw indifference curves between income and leisure, both of which give satisfaction to the individual.

However, the actual choice of income and leisure by an individual would also depend upon what is the market rate of exchange between the two, that is, the wage rate per hour of work. It is worth noting that wage rate is the opportunity cost of leisure. In other words, to increase leisure by one hour, an individual has to forego the opportunity of earning income (equal to wage per hour) which he can earn by doing work for an hour. This leads us to income-leisure constraint which together with the indifference map between income and leisure would determine the actual choice by the individual.

The maximum amount of time available per day for the individual is 24 hours. Thus, the maximum amount of leisure time that an individual can enjoy per day equals 24 hours. In order to earn income for satisfying his wants for goods and services, he will devote some of his time to do work.

Now, we can bring together the indifference map showing ranking of preferences of the individual between income and leisure and the income-leisure line to show the actual choice of leisure and income by the individual in his equilibrium position. We will further show how much work effort (i.e. supply of labour in terms of hours worked) he would put in this optimal situation. Our analysis is based on two assumptions. First, he is free to work as many hours per day as he likes. Second, wage rate is the same irrespective of the number of hours he chooses to work.

Figure displays income-leisure equilibrium of the individual. With the given wage rate, the individual will choose a combination of income and leisure lying on the income-leisure line MT that maximises his satisfaction. It will be seen from Figure that the given income- leisure line MT is tangent to the indifference curve IC₂ at point E showing choice of OL₁ of leisure and OM₁ of income.

In this optimal condition, income- leisure trade off (i.e. MRS between income and leisure) equals the wage rate (i.e., that is, the market exchange rate between the two. In this equilibrium position the individual works for TL₁ hours per day (TL₁ = OT- OL₁). Thus, he has worked for TL₁, hours to earn OM₁ amount of income.