Question

Consider the model of welfare discussed in class, where individuals are guaranteed at least a minimum income of y and there is an implicit tax, t, applied to earnings.

(a) Graph an individual's budget constraint under the welfare program, assuming the individual has no other non-labor income and could potentially earn a wage, w, if he/she chooses to work. Be sure to label all aspects of the graph, including the slopes of the budget line segments, the axes, and the values of income at the various `kink' points on the budget line.

(b) If the lump sum component of welfare is reduced (from y ! y0) and the implicit tax is also reduced (from t ! t0) such that the breakeven level of income remains unchanged, what is the e ect on the time allocation of an individual initially working only a few hours? Be sure to discuss the income and substitution e ects.

(c) If y = 100, t = 0:5, and y0 = 50, what must the new implicit tax rate, t0, be such that the breakeven level is unchanged?

Answer 1

Answer a :-

In the above diagram we see the minimum wage is $30 and the working hours is 12 hours .

Thus the above indifference curve shows various points at which the wages can be increased by reducing the leisure hours .However the budget line starts from point where leisure hours are 12 because (24-12 working hours )=12

The minimum wage at this point is $30(assumption)

Wages (Income)	Hours of leisure
30	12
40	11
50	10
60	9
70	8
80	7
90	6
100	5
110	4
120	3
130	2
140	1
150	0

At $150(highest wage ) , the leisure hours are 0 that means he is working for full 24 hours .

The labour will not work even for 1 hour if the wages are below $30.

Answer b :-

When the income reduces to Y0 it's leads to more work at a lower wage

1) Income effect - To show this effect a budget line is drawn parallel to the old line with same slope and the hours of leisure are reduced from P to Q . Thus wage and income decreases

2) Substitution effect - It indicates that what happens to the workers consumption bundle as the wages decreases holding the utility constant . Thus according to this effect in the above diagram leisure has become relatively inexpensive.

Answer c :-

At an initial wage of of 100 the hours worked were 19 hours .

Thus hourly wage above minimum wage were (19-12)/(100-30) =10 / hour

Average wage =100/19=5.26/hour

Now with the same amount of hours the new rates are :-

Hourly above minimum wage =(19-12)/(50-30)=2.86/hour

Average wage = 50/19=2.63/hour .

Thus with 50% tax rate the above changes occur

New tax rate should be :-

The amount at which the minimum wage / hour remains constant

Minimum wage / hour = 30/12=2.5

x/19=2.5

X =7.6

What tax rate should be charged to keep minimum wages 30 only

20=50*y/100

=40%