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, Beginning with no tax, draw a diagram to show the effect of the introduction of the proportional tax. Given that leisure is a normal good, provide a theoretical prediction about the effect of the tax on hours worked. Decompose the overall effect of the tax into income and substitution effects. What assumption is required for the tax to cause a decrease in hours worked? ( this is a 30 mark question so could you please elaborate more on it for me

Answer 1

When proportional tax is imposed on the wages , the disposable income of the labour decreases.

Since leisure is a normal good , decrease in income decreases the demand for leisure.

But we also know that for an hour of leisure, the labour looses an hour of wage , which means wage is the opportunity cost of leisure or wage is price of leisure .By imposing tax wages left at the hand of labour decreases, hence the price of leisure falls. As the price of a commodity falls , its demand increases due to substitution effect.

Hence we see substitution and income effect acts in opposite directions.

In the figure , vertical axis represents income after tax payment and horizontal axis represents hours spent on leisure.

Without any taxes maximum possible income that could be earned (i.e., when zero units of leisure is consumed)is OM and on tax imposition it decreases to OM'.

LM is the budget line before imposition of tax, which rotates inward after tax imposition to LM' . Slope of the budget curve represents the hourly wages remaning after paying tax.

Leisure hours = OL - working hours

Where OL is the endowment of leisure value which is assumed to be constant.

If OL' is the leisure consumed then L'L is the hours spent working.

In the figure we can observe that after the tax is imposed the hours of leisure consumed changes from OL' to OL". This is both , due to income effect and substitution effect .

As discussed earlier , substitution effect and income effect acts in opposite directions.

To show the decomposition of the total effects into the above 2 effect we first draw a line TT parallel to LM curve and tangent to the after tax indifference curve U'U' . The point P so obtained would have been the Optimal choice of labour had the tax affected only the income of the labour and not the opportunity cost or the price of leisure. Leisure at P is L"' . The change in leisure due to change in its price is shown by L'L"' i.e., L'L"' is the income effect of tax imposition.

Now since we have already identified the effect of income , the remaing change in leisure L"'L' is due to change in price of leisure, we can easily decompose total effect L'L" .

Total effect = Income effect + substitution effect

L'L". =. L'L"' + L"'L"

We can observe in the given figure.

As we can see the imposition of tax decreases the income earned which causes decreases in the leisure consumption whereas it decreases the opportunity cost of leisure which causes increase in leisure consumption.

Total effect depends on both of the opposing effects.

If income effect of tax imposition< substitution effect of tax implication, leisure hours consumed increases overall .

If both the effects are equal, there isn't any overall change in leisure consumption.

If income effect of tax imposition>substitution effect of tax imposition, leisure hours consumed decreases overall as shown in the figure.