Question

2.         The current wage rate is $10 per hour, and there is no non-labor income.

a)         Draw this budget constraint on a graph. How much income is earned if no leisure is taken?

            Show this on your graph.

            Consider the following plan for a progressive income tax. If income is below $50 per day, there is no income tax. For incomes between $50 and $100 per day, there is a 10%          tax. For incomes above $100 per day, there is a 20% tax.

b)         Draw this budget constraint on your graph. For what range of hours worked is the tax:

            i) 0

            ii) 10%

            iii)20%

            Show these on your graph.

c)         Consider a worker who is working 8 hours per day. What tax bracket are they in? What is their daily take home income? If they increase their hours to 12 hours per day, what tax bracket are they in? What is their daily take home income? Briefly describe why their income does not go down, even though they are now in a higher tax bracket.

d)         Briefly describe the work incentives/disincentives of this plan.

Answer 1

The constraint which the worker faces is the following

Y = w × (24 – N)

Y = Income, w = Wage Rate, and N = Leisure Time

Y = 24w – wN

Since, the wage rate is $10 per hour so

Y = 24 × 10 – 10N

Y = 240 – 10N

When no leisure is taken the income is

Y = $240

Now it is given that there is progressive tax. If income is below $50 per day, there is no income tax. For incomes between $50 and $100 per day, there is a 10% tax. For incomes above $100 per day, there is a 20% tax.

So, till income level of $50, the new budget line will coincide with the older budget line. For income higher than $50 per day the budget constraint is following.

Y = w(1 – 0.1)(24 – N)

Y = 10(1 – 0.1)(24 – N)

Y = (10 – 1)(24 – N)

Y = 9(24 – N)

Y = 216 – 9N

So, the new budget line will have a kink from point e. If there is only 10% tax for income above $50 then for 0 leisure time income would have been $216 per day. However, it is given that for income above $100 the tax is 20%. So, the new budget line will now have another kink at point f.

Y = w(1 – 0.2)(24 – N)

Y = 10(1 – 0.2)(24 – N)

Y = (10 – 2)(24 – N)

Y = 8(24 – N)

Y = 192 – 8N

If the worker is working for 8 hours per day, then his income would be $80 per day. This means that the worker will be paying 10% tax on the income. So, the worker’s take home income will be

Take home income = $80(1 – 0.1)

Take home income = $80 – $8

Take home income = $72

Now, if the worker increases the work hours to 12, then his income would be 12 × 10 = $120. This means that the worker will be paying 20% tax.

Take home income = $120(1 – 0.2)

Take home income = $120 – $24

Take home income = $96

The reason why the income of the worker does not go down despite being in higher tax bracket is that is the higher number of hours being worked by the worker. The scheme has created incentive for the workers to work more to compensate for the income loss due to the tax.