Effects of Income Tax on Work Effort | Labour Supply | Microeconomics

Any tax involves distortions. But a flat (lump-sum) tax is less distorting than any other tax (such as ad valorem tax or percentage tax). The comprehensive income tax is likely to distort the choices that are made concerning the allocation of time between work and leisure.

Income and Substitution Effects:

Since income tax generates both income effect (IE) and substitution effect (SE) which go in opposite directions, the impact of such a tax on the choice to work cannot be predicted unequivocally. The equilibrium allocation of time between work and leisure depends on an individual’s preference between work and income on the one hand and the market wage rate on the other, if we as­sume that he (she) seeks to maximise utility.

Fig. 12.6 shows a typical worker’s indifference curves for money income from work and leisure. Here we assume that leisure is a normal good for our rep­resentative worker. The indifference curves show diminishing marginal rates of substitution of leisure for income.

The line IJ shows the opportunities for the individual to trade leisure for money income through the sale of labour services to an employer (assuming that non-labour income is zero). At point I the individual enjoys 24 hours of leisure and thus earns no income.

For any other point along IJ, the individual’s income can be expressed as:

Y = w(24 – N) … … (1)

Or, dY/dN = -w

where N is the number of hours of leisure per day and w is the wage per hour. The maximum income the individual can earn here is Rs. 0J per day (when N = 0). It we assume diminishing MRS of leisure for income, an individual worker is likely to choose an optimum combination of income and leisure and maximise his utility at some intermediate point on the line IJ rather than choose any of the two extremes (viz., point J showing no leisure, or point I indicating no work).

In Fig. 12.6 the individual’s optimal choice occurs at point E, where the indifference curve IC₂ is tangent to the wage line HJ. At this point the slope of the indifference curve, i.e., MRS_NY is equal to the slope of the line HJ. From equation (1) the slope of the line IJ is simply dY/dN = -w, the return from work effort.

Since both slopes are negative, the equilibrium condition for the utility-maximising allocation of time between work and leisure is:

w = MRS_NY …….. (2)

The rate at which an individual is willing to substitute N for Y is the rate at which he is able to do so, i.e., the market wage rate (w).

The imposition of a flat-rate (proportional) tax on labour income of t% reduces the return to work effort at all levels of work.

In this case the net wage after the tax is gross wage less lax:

w_N = w_G(1 – t) …. (3)

The tax rotates the line IJ (which shows the possibilities for transforming leisure into income through work effort in the labour market) down to IJ’.

The equation for this line now is:

Y = w_G(1 – t) (24 – N) …….. (4)

The new equilibrium for the worker now occurs at point F.

The new equilibrium condition is:

w_N = w_G(1 – t) = MRS_NY

For our representative worker, the proportional income tax has the following three effects:

1. A reduction in utility or welfare from U₂ on IC₂ to U₁ on IC₁.

2. An increase in leisure hours per day from N₁ to N₂. This worker, therefore, chooses to work fewer hours per day as a result of the tax on labour earnings.

3. A consequent reduction in actual labour earnings per day from Y₁ to Y_G due to reduction in hours worked. Since taxes are levied on Y_G, net income available to spend falls to Y_N.

The government collects FB = T rupees per day of this individual’s income in taxes which is the difference between gross daily wages paid by employers, Y_G and the net wage received by the worker, Y_N after paying taxes. Net income after tax is Y_N = Y_G – T. In this case, the tax has been detrimental to work effort. The individual reduces the number of hours worked per day by N₁N₂ because of income tax.

Income and Substitution Effects of an Income Tax:

The impact of the tax on work effort of any rational worker depends on the income and substitution effects of the tax-induced reduction in wages received by him. The tax lowers the opportunity cost of an hour of leisure by reducing the wage that a worker receives, from w_G to w_N = w_G(1 – t). In effect, the tax lowers the implicit price of leisure by reducing the return from his labour.

Substitution Effect:

By reducing the return from work and making work less rewarding the substitution effect of the income tax is to reduce work effort. In other words, the tax increases the worker’s leisure preference. The worker is now induced to substitute leisure for labour because the hourly opportunity cost of leisure (the net hourly return from work) has fallen due to the imposition of the tax.

Thus due to substitution effect of income tax his consumption of leisure increases.

Income Effect:

The income effect of a tax-induced decrease in net wage is to increase work effort, i.e., the number of the hours worked provided leisure is a normal good. The reduction in income of the worker due to the tax, whether he works less or more per day, leads to a fail in consumption of all normal goods, including leisure.

This means that the number of hours worked per day must increase so that the worker can maintain the same level of income by working harder, i.e., for longer hours.

The Net Result:

The net effect on individual work effort depends on the relative magnitudes of the two effects: income effect (IE) and substitution effect (SE). If the SE is stronger than the IE individual will enjoy more leisure and consequently will work less as a result of the tax. This is indeed the case of an individual whose indifference curves have been depicted in Fig. 12.6.

If, however, the individual’s preferences are such that the IE outweighs the SE, the result of the tax-induced wage reduction is a fall in the daily consumption of leisure (a normal good) and a consequent increase in the number of hours worked per day.

Graphical Analysis:

Fig. 12.7 shows that after the imposition of the tax, the wage rate declines. As a result the budget line rotates from IJ to IJ’. The worker’s equilibrium point shifts from point E to F.

The SE is separated from the IE by giving the worker Hicks-type of compensating variation in income (a lump-sum daily pay­ment) equal to the average of Rs. BH per day. The substitution effect is the change in the daily number of hours of leisure due only to the decrease in the net wage caused by the tax.

The worker would be in equilibrium at point E’ if the income effect is removed in this way (i.e., through such a compensating increase in income). Here we see that the IE is opposite in direction to the SE if leisure is a normal good.

If daily income falls because of tax, leisure falls and work effort increases. In this case the income tax results in an increase in work effort because the income effect, ∆N_I, outweighs the substitution effect, ∆N_s. In other words, the worker chooses to work more hours per day. However, in Fig. 12.6 the opposite thing happens.

The SE of the tax- induced wage decrease outweighs the IE for that worker because he chooses to work fewer hours per day after the tax. We can also think of a situation in which the income and substitution effects are equal in magnitude and thus cancel each other out. In such a situation, the supply of labour would be perfectly inelastic so that income tax will have no excess (additional) burden.