Example: Suppose worker utility is given by The more C and L the happier is the worker Worker Utility C ($) L (hours) U (utils)

Example: Suppose worker utility is given by Holding C constant, the more L goes up the happier the worker is C ($) L (hours) U (utils) Worker Utility

Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal C ($) L (hours) U (utils) Diminishing Marginal Utility

Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal C ($) L (hours) U (utils) Diminishing Marginal Utility

Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal C ($) L (hours) U (utils) Diminishing Marginal Utility

Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal C ($) L (hours) U (utils) Diminishing Marginal Utility

Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal C ($) L (hours) U (utils) Diminishing Marginal Utility

Example: Suppose worker utility is given by If the worker is indifferent between all market baskets located on an indifference curve, then U is being held constant along it while L and C change Indifference Curves

Example: Indifference curve with U 0 = 10 LC U 0 = 10 Indifference Curves

Example: Indifference curve with U 1 = 20 LC U 0 = 10 U 1 = 20 Indifference Curves

Budget line C = (w)(H) + A T = L + H T – L = H C = (w)(T – L) + A C = (wT + A) – w L Constraints set boundaries on the worker’s opportunity set of all the consumption baskets the worker can afford

Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour) LC leisure Budget line

Example: What happens if A increases to 200 ($ per week) LC leisure Budget line

Example: What happens if w increases to 12 ($ per hour) LC leisure Budget line

The Hours of Work Decision Individual will choose consumption and leisure to maximize utility Optimal consumption is given by the point where the budget line is tangent to the indifference curve At this point the Marginal Rate of Substitution between consumption and leisure (slope of the indifference curve) equals the wage rate (slope of the budget constraint) Any other bundle of consumption and leisure given the budget constraint would mean the individual has less utility

Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour) leisure U2U2 U1U1 U0U0 L * = 41 H * = 80 – 41 = 39 C * = 900 – 10(41) = 490 The Hours of Work Decision

Change in non-earned income Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour) leisure U1U1 L * = 41 H * = 39 C * = 490 What happens if A increases to 200 ($ per week)? L * = 38 H * = 42 C * = 1000 – 10(38) = 620 Leisure is an inferior good since hours of leisure falls

Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour) leisure U1U1 L * = 41 H * = 39 C * = 490 What happens if A increases to 200 ($ per week)? L * = 50 H * = 30 C * = 1000 – 10(50) = 500 Leisure is a normal good since hours of leisure increases Change in non-earned income

Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour) leisure L * = 41 H * = 39 C * = 490 Since w is the price of Leisure, the law of demand holds L * = 40 H * = 40 C * = 1060 – 12(40) = 580 What happens if w increases to 12 ($ per hour) An increase in w increases H because SE > IE Change in the wage rate

Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour) leisure L * = 41 H * = 39 C * = 490 L * = 46 H * = 34 C * = 1060 – 12(46) = 508 What happens if w increases to 12 ($ per hour) An increase in w decreases H because IE > SE Change in the wage rate

When the Income Effect dominates: U1U1 U0U0 A TE Consumption ($) SE IE Leisure An increase in w decreases H because IE > SE Change in the wage rate

When the Substitution Effect dominates: U1U1 U0U0 A TE Consumption ($) An increase in w increases H because SE > IE SE IE Leisure Change in the wage rate

The reservation wage Are the “terms of trade” sufficiently attractive to bribe a worker to enter the labor market? Reservation wage: the minimum increase in income that would make the person indifferent between working and not working –Rule 1: if the market wage is less than the reservation wage, then the person will not work –Rule 2: the reservation wage increases as nonlabor income increases

Initially the individual does not work because w is too low U2U2 U0U0 A Consumption ($) Leisure U1U1 L * = 80 H * = 0 If w increases a little, H * = 0 If w increases a lot, L * = 70 H* = 10 The reservation wage

Labor Supply Relationship between hours worked and the wage rate –At wages slightly above the reservation wage, the labor supply curve is positively sloped (the substitution effect dominates) –If the income effect begins to dominate, hours of work decline as wage rates increase (a negatively sloped labor supply curve) –Labor supply elasticity (% change in hours worked) / (% change in wage rate) Labor supply elasticity less than 1 means “inelastic” (insensitive) Labor supply elasticity greater than 1 means “elastic”

Example of backward bending labor supply: Hours of Work 0 Wage Rate ($) SE > IE IE > SE Labor Supply

Female Labor Supply ( ) Source: Jacob Mincer, “Intercountry Comparisons of Labor Force Trends and of Related Developments: An Overview,” Journal of Labor Economics 3 (January 1985, Part 2): S2, S6.

Let A = $500 per month, w = $5 per hour, and BRR = –0.5 Welfare Programs and Work Incentives HwHA Benefit Reduction Actual Transfer Total Income

In some states the cash grant is reduced at the “benefit reduction rate”. The BRR acts as a tax on earnings. Consumption ($) 500 Hours of Leisure U1U1 L * = 40 H * = 40 L * = 55 H * = BRR = tax = 50% U0U0 Welfare Programs and Work Incentives

If states choose a BRR equal to 100%, workers will not work because earnings are taxed at a rate of 100%. Consumption ($) Hours of Leisure U0U0 L * = 40 H * = 40 BRR = tax = 100% U1U1 500 L * = 80 H * = 0 Welfare Programs and Work Incentives

Choosing a BRR equal to 0%, means the worker will work more than she did when the BRR was equal to 50%. Consumption ($) 500 Hours of Leisure L * = 40 H * = 40 L * = 55 H * = BRR = tax = 0% U1U1 U0U0 Welfare Programs and Work Incentives

The EITC phase in a cash grant at 40% for low-income workers is a wage subsidy (negative tax) of 40%. Consumption ($) 500 Hours of Leisure L * = 40 H * = 40 L * = 35 H * = EITC = -tax = -40% U1U1 U0U0 Welfare Programs and Work Incentives

Leisure Consumption ($) ,350 13,520 14,490 17,660 33,178 Net wage is 40% above the actual wage Net wage equals the actual wage Net wage is 21.06% below the actual wage 0 Welfare Programs and Work Incentives