Question

.Curious George must decide how much to work. He has 60 hours per week available that he can spend either working or engaging in leisure (which for him is creating various kinds of mischief). He can work at a wage rate of $5 per hour. The Man with the Yellow Hat (who looks after George) also gives him an allowance of $100 per week, no matter how much George works. George's only source of income that he can use for consumption (mostly bananas) is this allowance plus his wage earnings. A. In a carefully labelled diagram, draw George's consumption-leisure budget constraint. Show an equilibrium where George chooses to work 40 hours per week. b) In an effort to have George pay for other household expenses, The Man in the Yellow Hat decides to tax George 50 percent of his wage income. Using the same diagram you drew in part (a) (where George worked 40 hours), show what happens to his labour supply. To do this, show one possible outcome, and break it down into income and substitution effects. Explain the diagram below

Answer 1

solution:

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

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.