Question

Consider the effect of a proportional tax on hours worked using diagrams to illustrate your answers. Assume consumers are endowed with a certain number of hours of leisure time each week that they can sell to the market in the form of work, decompose the overall effect of the tax into income and substitution effects.

Answer 1

Increase in tax on hours of income decreases the income one actually gets for consumption ie. disposable income decreases . Similarly a fall in tax on income increases the disposable income.

Following diagram (figure 1) shows change in budget constraint due to change in tax. LM is the initial budget constraint when tax is t and when tax decreases LM rotates outward to LM' .

Fig 1

Leisure is a normal good i.e., one would consume more leisure if income increases i.e., income effect on leisure would be positive.

But proportional tax also decreases the wage labour receives , and wage is the opportunity cost of enjoying leisure and so can be considered as price of leisure. As price decreases one would increase the units of leisure by substituting leisure for other goods

Substitution effect is negative

We see that substitution and income effects on leisure works in opposite direction.

In the following figure ( fig 2) , when the proportional tax rate falls , the budget constraint rotates outward from LM to LM' , income and substitution effect comes into play. Vertical axis represents income left after tax payment and horizontal axis represents leisure . Leisure = Total hours available in a week - working hours

fig 2

Leisure = K - working hours , where K is a constant externally determined.

In the initial situation, OL_{​​​​​o}​ hours of leisure is consumed as tax falls , budget constraint rotates outward, OL' amount of leisure is consumed.

Total change in leisure hour is L_o​​​​​L'

To study the income effect , we draw a tangent to the IC curve U'U' which is parallel to the LM curve, and note the leisure consumed at that point which is OL''. The tangent we are referring to is line is L''M'' in fig 2 .

Had the wage rate remained the same and the consumer been given enough income to reach utility U'U' , he would have increased the leisure by L_oL''

But since the decrease in tax rate increases the price of leisure , the consumption of leisure decreases due to negative substitution effect. That is why leisure consumption decreses from OL" to OL' . (-)L'L" is substitution effect in the figure.