BUEC 280 ECTURE 6 Individual abour Supply Continued
ast day Defined budget constraint Defined optimal allocation of leisure and consumption Changes in non-labour income generate a pure income effect Change in wage rate generates both income and substitution effects Don t know which dominates Today Isolating income and substitution effects Tracing out the individual labour supply curve Reservation wages
Isolating Income and Substitution Effects Wage changes generate both income and substitution effects Income effect: Δ in hours worked due to Δ in income, holding wages (price of leisure) and preferences constant W income consume more leisure because it s a normal good Substitution effect: Δ in hours worked due to change in W (price of leisure), holding income and preferences constant W price of leisure consume less leisure Theory doesn t tell us which one dominates When W, H (and =T-H) can rise or fall Can we isolate these effects graphically?
A wage increase where the substitution effect dominates The observed change (total effect of wage change from W 1 to W 2 ) W 2 T 2 W 1 T 1 U 2 2 1 T U 1 The income effect (response to change in income, holding W and preferences constant) 1 3 The substitution effect (response to change in price of leisure, holding income and preferences constant) 2 3
Isolating income and substitution effects: when the substitution effect dominates Substitution effect U 2 Income effect U 1 Total effect
A wage increase where the income effect dominates The observed change (total effect) W 2 T 2 W 1 T 1 U 2 1 2 T U 1 The income effect (response to change in income, holding W and preferences constant) 3 The substitution effect (response to change in price of leisure, holding income and preferences constant) 2 3
Isolating income and substitution effects: when the income effect dominates Substitution effect Income effect U 1 U 2 Total effect
Which effect is stronger? Size of the income effect is proportional to hours worked For a person initially at A (working a lot) the upward movement of the budget constraint is much greater than for a person initially at B. Extreme: consider person at C (not working) W increased command over resources But only if you work! Bigger increase the more you work Extreme: at C, increase in wage can only have one of two effects (can t reduce H): 1. no change in labour supply (zero income effect) 2. decide to participate (dominant sub effect) Decision to participate always represents a dominant substitution effect A B C
Empirical Evidence Researchers attempt to identify and measure income and substitution effects by looking at labour supply responses to wage changes in survey data Most studies focus on men. Why? Cross-sectional studies ook at lots of people at a point in time, try to identify hypothetical wage changes (two people with same characteristics & similar jobs earning different wages), and look for differences in hours worked and/or participation Men: both effects about zero (why?) Married women: big substitution effects (why?), mostly at participation margin Time-series studies ook at changes in wages and labour supply over time Hard: too many other things that affect labour supply also change (value of pensions, dishwashers, etc.)
Tracing out the individual labour supply curve Goal: identify the relationship between an individual s desired hours of work and the wage Use our theory of leisure-consumption choice ook at hours chosen at different wage rates & connect the dots
Deriving individual labour supply W 5 T W 4 T W 3 T Trace out desired labour/leisure at each wage rate. In this case, the income effect dominates for a wage change from W 4 to W 5. W 2 T W 1 T W W 5 W 4 W 3 W 2 W 1 4 = T-H 4 1 = T-H 1 T Map those choices into the space of wages and hours and connect the dots to get the individual labour supply curve. Here it s backward bending between W 4 and W 5. H 1 H 2 H 5 H 3 H 4 H
Reservation wages Remember that the decision to work zero hours (i.e., not participate) is what we call a corner solution These people choose not to work at the offered wage W because the MU from one more hour of leisure exceeds the MU of W dollars of consumption If a person who is not working puts a value of $X on an extra hour of leisure, they will only work if W>X. We say that $X is this person s reservation wage: the lowest wage at which they are willing to work, denoted W R
Reservation wages and fixed time costs of work Suppose Chetan is not working. He lives in the suburbs, and all the jobs are downtown. It takes him 1 hour to commute to downtown and 1 hour to return at the end of the day. What does his reservation wage look like? U R Chetan gets utility U R from working zero hours. Slope = - W 1 Slope = - W R At wage WR he is indifferent between working (T-R hours) and not working. If he cannot work exactly T-R hours, he prefers not to work. At any lower wage (e.g., W0), he prefers not to work. At any higher wage (e.g., W1) he prefers to work. Slope = - W 0 U 1 WR is his reservation wage. R T-2 T
Policy Applications Many government programs (taxes, transfers, etc.) affect the labour supply of individuals E.g., income taxes, payroll taxes, EI, worker s compensation, etc. We can analyze the labour supply response to such policies using the leisureconsumption choice model In general, policies affects the worker s budget constraint, not preferences
Budget constraints with spikes Some policies compensate individuals who are unable to work EI: replace (some) lost earnings due to layoff Worker s compensation: replace (some) lost earnings due to injury/disability We call these income replacement programs They only pay benefits to those who are not working Creates a spike in the budget constraint Example: consider a workers compensation program that pays injured workers 100% of their pre-injury earnings if they are unable to work (work zero hours), but pays them $0 is they work even 1 hour. How does this affect the incentive to return to work? Can we change the program to improve incentives?
A very generous worker s compensation program Before injury, the worker s wage was W 1, the optimal allocation was ( 1, 1 ), the worker earned 1 =W 1 (T- 1 ) dollars, and utility was U 1. After injury, the worker receives income replacement of 1 dollars, works zero hours, and has utility U 2 >U 1. What s the new reservation wage? W 1 T Budget constraint of injured worker 1 U 2 U 1 1 T
Programs with a zero effective wage Some government programs (e.g., welfare or income assistance) are designed to guarantee a minimum level of income Minimum is based on assessed need (depends on if you re married/not, have kids, how many, etc.) If you are eligible, welfare pays: benefit = need earnings If you earn less than your assessed need, your effective wage rate is zero If earn $1 from working, you receive $1 less in welfare benefits Makes price of leisure zero We call the dollar-for-dollar reduction in welfare benefits when you work a 100% clawback
A basic welfare system min is the minimum income defined by the welfare program (the assessed need). At wage W 1 our worker must work (T- min )=( min /W 1 ) hours to earn this much. In the absence of welfare, the optimal allocation is ( 1, 1 ) which gives utility level U 1. With this welfare program, the optimal allocation is ( min,t), which gives utility level U 2. When working less than T- min hours, the effective wage (the price of leisure) is zero. We see this from the slope of the budget constraint. What is the new reservation wage? W 1 T Slope = - W 1 1 Slope = 0 min 1 min T U 1 U 2 Budget constraint under basic welfare system
But some people work, right? W 2 T The decision to work, under AN set of policies that affects labour supply, depends on: 1. The parameters of the policy (i.e., shape of the budget constraint) 2. Preferences (shape of indifference curve) 3. The wage rate you can earn (W 1 vs. W 2 ) W 1 T U 1 min min T
An aside: convex budget constraints make for multiple optima W 2 T When a policy makes the budget constraint convex, then multiple tangencies are possible. What is the optimal allocation? W 1 T min U 1 min T
Income and substitution effects from a welfare program We can analyze the labour supply effects of a policy like this in terms of income and substitution effects. Shifting out the southeast corner of the budget constraint creates an income effect (discourages work). W 1 T But the clawback reduces the effective wage rate to zero. This creates a huge substitution effect this time in the same direction as the income effect. 1 min U 1 U 2 1 min T
Welfare Reform Basic welfare programs create big disincentives to work This has prompted governments to explore welfare reform: changes that reduce the disincentives to work Self-Sufficiency Project A social experiment started in 1992 ower clawback rate Time limits on welfare receipt Have to work full time to qualify Workfare (Ontario Works) Some earnings exempted from clawback, others at lower rate Access to education, training, job search assistance Have to work
Example: welfare reform Here, the assessed need is min. To qualify for assistance, you have to work at least T- min hours. The clawback rate is 70% (you get to keep 30% of your hourly earnings for hours beyond T- min ) How many hours do you expect people to work? WT min W(T- min ) D C B A Region A: you don t work enough hours to qualify for assistance. Slope = -W. Point B: you work exactly T min hours, receive W(T- min ) dollars from work, and min -W(T- min ) dollars in assistance. Region C: you work more than T- min hours, receive assistance, and get to keep 30 cents of each dollar you earn on hours in beyond T- min. Slope = - (0.3)W Region D: you opt out of the program. Slope = - W. min T