Question

Suppose that the government imposes a proportional income tax on the representative consumer’s wage income. That is, the consumer’s wage income is

w(1-t)(h-l)

where t is the tax rate. What effect does the income tax have on consumption and labour supply? Explain your results in terms of income and substitution effects.

Answer 1

Ans-According to question when the government imposes a proportional tax on wage income, the consumer’s budget
constraint is now given by:
C = w 1( − t)(h − l) + π −T ,

where t is the tax rate on wage income. i provide you a figure A.figure A the budget constraint for t = 0, is FGH.
When t > 0, the budget constraint is EGH. The slope of the original budget line is –w, while
the slope of the new budget line is –(1–t)w. Initially, the consumer picks the point A on the
original budget line. After the tax has been imposed, the consumer picks point B. The
substitution effect of the imposition of the tax is to move the consumer from point A to point
D on the original indifference curve. The point D is at the tangent point of indifference
curve, I1, with a line segment that is parallel to EG. The pure substitution effect induces the
consumer to reduce consumption and increase leisure (work less).
The tax also makes the consumer worse off, in that he or she can no longer be on indifference
curve, I1, but must move to the less preferred indifference curve, I2. This pure income effect
moves the consumer to point B, which has less consumption and less leisure than point D,
because both consumption and leisure are normal goods. The net effect of the tax is to
reduce consumption, but the direction of the net effect on leisure is ambiguous. Figure A.
shows the case in which the substitution effect on leisure dominates the income effect.