Question

QUESTION TWO:

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.

1. Beginning with no tax, draw a diagram to show the effect of the introduction of the proportional tax.                                                                                                     [6 Marks]

2. Given that leisure is a normal good, provide a theoretical prediction about the effect of the tax on hours worked.                                                                                              [4 Marks]

3. Decompose the overall effect of the tax into income and substitution effects.      [6 Marks]

                                                                                                          

4. What assumption is required for the tax to cause a decrease in hours worked?     [4 Marks]                                                                                                                                 

Answer 1

a) 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. Let this number of hours be "x" hours. Let the wage rate that the consumer earns per hour be denoted by w. Let the amount of consumption that this consumer can do be denoted by C. Also, let the hours of leisure be denoted by L.

Price of leisure can be measured by taking into consideration the opportunity cost of leisure. When the consumer indulges in 1 hour of leisure, he foregoes $w (which he would have earned by working the same hour). Hence, the opportunity cost of leisure = $w. So, price of leisure = opportuinty cost = $w

If the consumer sells entire x hours in the form of work, then they can earn $w * x = $wx. This is the maximum amount of consumption that this person can achieve.

Let the price of consumption be p2. If he spends x hours working, then he can get $wx/p2 units of consumption. Hence, y-intercept = $wx/p2.

The consumer's consumption budget constraint (for a single week)

price of consumption * units of consumption + price of leisure * units of leisure = income

p2C + w L = wx

Where p2 = price of consumption

C = consumption

w = price of leisure

L = units of leisure

Plot consumption on y-axis and hours of free time on x-axis. The consumer's budget constraint has been plotted in figure 1.

Let us say that the consumer's equilibrium is at point e1 where the consumer consumes C1 consumption and enjoys leisure for L1 hours while working for the remaining (x-L1 ) hours.

The consumer has their hourly wage cut due to imposition of a proportional tax (t). Consumer's new wage = $w- t% of $w = $w' (say)

While he works, consumer earns $w' per hour. consumer's maximum income = x*$w' = $w'x.

If he decides to enjoy the entire week, then he would get x hours of leisure and $0 consumption. Hence, the x-intercept is x hours. X-intercept remains the same because the number of hours in a week that he has have not changed.

Price of leisure can be measured by taking into consideration the opportunity cost of leisure. When consumer indulges in 1 hour of leisure, he foregoes $w' (which he would have earned by working the same hour). Hence, the opportunity cost of leisure = $w'. So, price of leisure = opportunity cost = $w'.

If he spends x hours working, then he can get $w'x/p2 units of consumption now. Hence, y-intercept = $w'x/p2.

Consumer's new consumption budget constraint (for a single week).

price of consumption * units of consumption + price of leisure * units of leisure = income

p2C + w' L = w'x

Where p2 = price of consumption

C = consumption

w' = new price of leisure

L = units of leisure

Plot consumption on y-axis and hours of free time on x-axis. Jordan's new budget constraint has been plotted in red color in figure 2.

Now the consumer's equilibrium is at point e2 where the consumer consumes C2 consumption and enjoys leisure for L2 hours while working for the remaining (x-L2 ) hours.

b) Given that leisure is a normal good, if the price of a normal good falls, then the quantity demanded of that good should rise. Going by the same argument, if the price of leisure falls, it means the consumer would indulge in more leisure and should work less. Wages have fallen after the proportional tax from w to w'.

Price of leisure can be measured by taking into consideration the opportunity cost of leisure. When consumer indulges in 1 hour of leisure, he foregoes $w' (which he would have earned by working the same hour). Hence, the opportunity cost of leisure = $w'. So, price of leisure = opportunity cost = $w'.

Since the price of leisure has fallen, the consumption of leisure should increase. So, proportional tax should make him work less.

c) The overall effect of the tax into income and substitution effects has been decomposed in figure 3

Figure 3

Wage is the opportunity cost of leisure. As wage rate falls, it means the Opportunity cost of leisure has decreased. In a sense it means that leisure has become cheaper now. So substitution effect says that consumer should increase the amount of leisure and he should decrease the amount of consumption.

On the other hand income effect induces consumer to work more at a lower wage rate and consume less. This is because at a lower wage, income of person reduces and with decrease in income, demand for all normal goods falls. Since leisure can be assumed to be a normal good, with the decrease in wage rates, leisure should fall and work should increase.

In order to find substitution effect, use Hicksian approach. Use figure 3 as a reference. Give consumer an amount of income such that he is able to just afford the level of utility (IC1) which he was getting at a when wage rate was high. Budget constraint is shown in light blue color in figure 3. Consumer now consumes at point e3 in the diagram where L3 is corresponding leisure hours. Since, the increase in leisure is just due to change in wage rate, shift from L1 to L3 is substitution effect.

Now, take the income back from him (so that budget constraint is now red line), he reaches L2. Since this change is entirely due to a change in income, we say that it is the income effect. Therefore, the shift from L3 to L2 is income effect.

The total effect is substitution effect plus income effect. Total effect is change from L1 to L2.

Substitution effect induces consumer to increase leisure and income effect compels him to reduce it. But the net effect is increase in leisure so it can be argued that substitution effect is powerful than income effect.

d) The assumption required for the tax to cause a decrease in hours worked is that the substitution effect is powerful than income effect. If the substitution effect is weaker than income effect, it would lead to an incrase in the hours worked.