Question

You have 60 hours a week available to spend either working or leisure. You can work at a wage of $5 per hour. Your parents also provide you an allowance of $100 per week, no matter how much you work. Your only source of income is the allowance plus your wage earnings.

a) in a carefully labelled diagram, draw your consumption-leisure budget constraint. show an equilibrium where you choose to work 40 hours per week

b) in an effort to have you pay for other household expenses, your parents decide to tax you 50% of your wage income. Use the same diagram in (a) where you work 40 hours, and show what happens to your labour supply. To do this, show one possible outcome, and break the change down into income and substitution effect

Answer 1

a)

On the horizontal axis, we have the leisure and the vertical axis we have the consumption.

Maximum leisure that can be enjoyed is 60 hours and hence it is the horizontal intercept.

Maximum income is the maximum wage income plus the allowance.

Maximum wage income = 5*60 = $300. Hence maximum income(consumption) = $300+$100 = $400

Since the individual gets $100 when working for 0 hours The budget line is given by ABC. And then any wage income gets added to his total income.

At equilibrium, the individual enjoys 20 hours of leisure and hence works for 40 hours per week.

b)

When wage income is taxed at 50%, the budget line rotates inward to DBC. The maximum net wage income now becomes 50% of 5*60 = $150. Hence total income = $250

Since of the slope of the budget line is the after-tax wage rate, the budget line is now flattering and hence have a smaller slope.

Now in response to the tax, the individual may:

1. Increase work hours in order to achieve certain income
2. Reduce work hours due to lower wage and thus substituting leisure for labor.

Let's take the second case. With the tax, the leisure is increased to 25 hours and thus labor is reduced to 35hours. Thus the individual moves from point e to g.

The change can be broken into income effect (from e to f) and substitution effect (f to g)

Income effect:

We draw an imaginary line PQ that is parallel to the old budget line and tangent to old IC at f. The point f represents a combination of L and C that would have given the same utility with the same relative price of consumption and leisure if income had been reduced by a fixed amount. Thus income effect causes leisure to fall and labor to rise.

Substitution effect

The point f to g represents substitution effect with the effect of the change in the relative price of leisure and consumption holding utility constant. The substitution effect, on the other hand, reduced labor and increases leisure

In this case, Substitution effect (f to g) is greater than income effect(e to f), thus labor supply falls with tax.

Please give a thumbs up if you found the answer helpful.