Assistance
October Government 3, 2011
Designing welfare Policies
Care primarily about three elements
Provide adequate Income
Minimize Public Costs
Minimize Employment Disincentives
Neoclassical Model of Labor Supply
Indifference Curve
Preferences for income (Y) and leisure (L)
Slope:
utility increases with both Individual is indifferent between all points on the same indifference curve reflects a worker's willingness to give up income for additional leisure
Indifference curves
Income (Y) $160 $120 ... and $40 of income and 12 hours of leisure Y L Equally happy with $100 of income and 8 hours of leisure ...
$80 $40
U1
4 8 12 16 Leisure (L)
Indifference curve represents the combination of leisure (L) and income (Y) where the individual is equally as welloff
Indifference curves
Income (Y) $160 $120
B
$80 $40
A U1
4 8 12
U2
16
Leisure (L)
Moving to a higher indifference curve (farther up and right) means better off [Note that more of both goods means definitely better off]
Indifference curves
Income (Y) $160 $120
$80 $40
$62 $35 L 8
U1(Blue) U1(Red)
12 16 Leisure (L)
Which individual is more of a workaholic, Red or Blue? BLUE requires less money to compensate for lost leisure
4
Neoclassical Model of Labor Supply
Indifference Curve
Preferences for income (Y) and leisure (L), utility increases with both Slope:
reflects a worker's willingness to give up Y for additional L
Budget constraint
Time: T = L + H (H = hours of work)
Money: Y = wH + N, (w = wage, N = nonlabor income) Slope: Wage Rate
Assume T=16 (24 hr. day, 8 hrs. of sleep)
Budget Constraint : Basic
Income (Y) $160
$120 Slope is the wage rate ($7.50/hr in this example)
$80 $40
8 4 12 16 Simplest case is a budget constraint with no transfers or nonwage income ... Can have only leisure and no income, work 16 hour days and have $(16*w) income, or any point in between
Leisure (L)
Budget Constraint: Fixed Transfer
Income (Y) $160 Slope is still the wage rate ($7.50/hour)
$120
$80 $40 Transfer $40 Leisure (L)
4
8
12
16
Effect of offering everybody $40, no matter how much they work
Budget Constraint: phaseout transfer
Income (Y) $160 After making $80 of labor earnings, entire $40 transfer is phased out and effective wage returns to $7.50/hr Effective wage falls due to phaseout ... Now effectively make $3.75/hr ($7.50 $3.75 phaseout of transfer)
$120
$80 $40 Transfer $40 Leisure (L)
4
8
12
16
Effect of offering everybody $40, but phase it out at a rate of $1 for each $2 of wage income until completely phased out
Neoclassical Model of Labor Supply
Indifference Curve
Preferences for income (Y) and leisure (L), utility increases with both Slope:
Budget constraint
reflects a worker's willingness to give up Y for additional L
Time: T = L + H (H = hours of work) / Assume T=16 Money: Y = wH + N, (w = wage, N = nonlabor income) Slope: Wage Rate
Optimal choice
Point of tangency between budget constraint and highest indifference curve
Optimal Choice
Income (Y) $160 Unachievable given the budget constraint
$120 Optimal Choice Suboptimal... could do better at point A 4 8
$80 $40
A U0
12
U2 U1
16 Leisure (L)
Work # of hours where indifference curve tangent to budget constraint
Income and Substitution Effects
Income effect
Increase in income > buy more of all "normal" goods Leisure is a normal good
How do you buy more leisure?
Income effect example: $40 transfer to all people
Income (Y) $160
$120
$80 $40
B U2 A U1
4 8 12 16 Leisure (L)
Increase in income income effect says you will "buy" more leisure by working less
Income and Substitution Effects
Income effect
Increase in income > buy more of all "normal" goods Leisure is a normal good
How do you buy more leisure?
Substitution Effect
Change the relative price of goods, buy more of the good that is relatively cheaper Suppose wage goes up ...
Leisure is now relatively more expensive (give up more income for each hour you chose not work) to Substitution effect says you buy more leisure
Substitution effect example increase wage rate
Income (Y) $160
$120
$80 $40
B
Leisure (L)
4
8
12
A 16
Make leisure more expensive substitution effect says you will "buy" less leisure by working more (in this case, induce to start working)
Income and Substitution Effects
Income effect
Increase in income > buy more of all "normal" goods Leisure is a normal good
How do you buy more leisure?
Substitution Effect
Change the relative price of goods, buy more of the good that is relatively cheaper Suppose wage goes up ...
Combination of the two
Leisure is now relatively more expensive (give up more income for each hour you chose not to work) Substitution effect says you buy more leisure
Does a wage increase definitely mean work more?
Substitution effect vs. Income effect
Income (Y) $160
Point B: substitution effect dominates
(decrease leisure since more expensive)
Point C: income effect dominates
(increase leisure since more income)
$120
B
$80 $40
C U2 U1
4 8 12
A
U2
Leisure (L)
Note that increasing wage both increases the income and changes relative prices ... effect on labor depends on which effect dominates
16
Why this matters for government policy
Determines what labor response will be to the policy Also determines how many will people claim transfer Example: Consider a policy that guarantees everybody at least $40/day of income. If you start working, the transfer is reduced by $1 for every $1 of earned income How does this effect the budget constraint?
Optimal Choice Person #1
Income (Y) $160
$120
$80 $40
B A
8
U1
12 16
U2
Leisure (L)
4
Individual Decides to stop working as a result of the policy!
Optimal Choice Person #2
Income (Y) $160
$120
$80
U2 A U1
$40
Individual continues to work same # of hours with the new policy (can't reach a higher indifference curve)
4
8
12
16
Leisure (L)
Why this matters for government policy
Example: Consider a policy that guarantees everybody at least $40/day of income. If you start working, the transfer is reduced by $1 for every $1 of earned income How does this effect the budget constraint? How will it impact individual work decisions?
Some individuals won't change their work decisions Some will chose to stop working Nobody will chose to work more
"Iron Law" of Welfare Programs
Provide adequate Income
Minimize Public Costs
Minimize Employment Disincentives
These goals work against each other when designing transfer policies cannot achieve all three!
Income (Y)
Example 1: Offer $45/day ($11,700/yr) to lowincome individuals Phaseout $1 of transfer per $1 of wage income
$160
$120
$80 $40
B U2 A U1
Leisure (L)
8 4 12 16 Adequate income: Yes, none in poverty Cost: moderately expensive but well targeted to the poor Labor effect: VERY LARGE (many drop out of labor market from IE & SE)
Income (Y)
Example 2: Offer $45/day ($11,700/yr) to lowincome individuals Phaseout $1 of transfer per $2 of wage income
$160
$120
$80 $40
B U2 A U1
Leisure (L)
8 4 12 16 Adequate income: Yes, none in poverty Cost: much more expensive (less well targeted) many nonpoor receive $ Labor effect: Smaller (fewer individuals stop working, although IE & SE reduce hours)
Income (Y)
Example 3: Offer $20/day ($5,200/yr) to lowincome individuals Phaseout $1 of transfer per $2 of wage income
$160
$120
$80 $40
U2 A U1
Leisure (L)
8 4 12 16 Adequate income: No inadequate to get nonworkers out of poverty Cost: less expensive smaller transfers, and never goes to people out of poverty Labor effect: Small (fewer individuals reduce hours / stop working)
$45 transfer only to people who are unemployed
Phaseout completely once starting work
Other transfer policies to try drawing (for all assume $7.50/hr wage rate)
Introduce $1 of transfer for each $1 of wages up to $20 per day. Keep $20 transfer until making $40 of wages. Then phase out at $1 for each additional $2 of wages.