Labor Supply
Neoclassical LS model specifies 3 things
1) Individual preferences (Marginal rate of substitution between market goods and leisure) 2) Budget Constraint = the "Opportunity set" 3) Demand for leisure: determines the work decision.
What are the institutional details of government programs such as AFDC, TANF and the EITC?
AFDC - is welfare - 100% tax - huge income and substation effects because wages are so much lower, net wage is 0 so they will not work TANF - Reduces invectives to work but provides social insurance EITC - tax credits - tries to create incentives Neoclassical theory predicts that the effect of EITC on LS can be small. Fewer "distortions" to the B.C. 2) LS should increase in lowest income groups. Substitution effect dominates at low hours of work and income. 3) In equilibrium, however, wages paid by employers may decrease. Will discuss later when we cover labor market equilibrium. 4) Some argue that EITC is more effective subsidy program for the working poor than the min wage - will not reduce employment 5) (Was) politically popular on both sides of the aisle as neoclassical theory predicts improved incentives to work. E.g., no "welfare trap".
Why would an individual's labor supply curve bend backwards?
An individual's labor supply curve bends backwards due to the two effects. Initially, as wage increases, the sub effect dominates and one will work for longer hours, eventually, the income effect will dominate so an increase in w will cause the person to work less hours
Optimal Benefit level (This is different for different preferences)
Benefit level such that the utility is the same after injury as before the injury - no loss in utility. Benefit level such that the wage one had, w, becomes the reservation wage after the injury/layoff. Attempts to preserve the work benefits. For steep IC, there is low optimal benefit For Flat IC there is high optimal benefit
Corner Solutions
Choice depends entirely on tastes - person loves money (loves work) Persons loves leisure (hates work) So with same exact BC, there are large differences in ICs.
Demand for leisure
Demand for l determined by tastes and opportunities (BC) for individuals i. w = price of leisure ii. y = wealth (purchasing power Individuals preferences = f(w,y) = l*
Neoclassical model of time allocation between labor and leisure
Demand for leisure determines the number of hours worked, with the price of leisure equal to the offered wage rate These are affected by work incentives in changes of wages, wealth, taxes, and govt. social insurance programs
How do the magnitudes of these effects depend on individual tastes (e.g., the shape of an individual's indifference curves)?
IF the substitution is lager the number of hours worked will increase with an increase in the wages. IF the income effect is larger, the amount of hours worked will decrease with an increase in wages. This depends on the IC of the individuals - the flatter the IC the larger the substation effect plays a role, while the steeper the IC curve (higher MU(l)) the larger the income effect is.
What is the effect that dominates if the person is on the backward bending segment of the labor supply curve with an increase in the wages
If the person is on the backward bending portion of the labor supply curve, an increase in the wage rate would result in a drop in labor supply and that person would want to consume more leisure.
When will the substitution effect dominate and when will the income effect dominate?
In the figure above, hours worked increases when moving from w1-w3. This implies that the sub effect dominates the income effect. this is the section where it is forward bending. Then, from w4-w5 hours worked decreased as w increases, implying the income effect dominated.
What is the labor/leisure choice for an individual in the neoclassical model? What is the constrained optimization problem that the individual solves? How does the wage rate and nonlabor income function in this choice?
In the neoclassical model, there are 16 hours available to work in one day. The individual must chose how to allocate their time during these 16 hours between labor and leisure. The labor/leisure they chose is based on their utility indifference curve and their marginal utility for an extra hour of labor/consumption or an extra hour of leisure. Price of leisure, wealth and indium tastes. The constrained optimization problem the individual faces is maziming their utility with respect to consumption (w(16-l)
Define the income effect
Income Effect: when wealth increases, consumers want to consume more leisure and more market goods. The increase in desire for leisure consumption is a forces towards decreases in labor supply Change in l due to change in y IF leisure is a normal good, more y --> buy more l , which decreases h
If you have STEEP IC, aka higher MRS then which effect dominates?
Income effect wins, work less
Budget Constraint with ) -net wage (100% tax rate)
Income maintenance (welfare ) programs: AFDC; TANF, SNAP Eligibility criteria = income needs (guaranteed income level form govt) - safety net for those at or near the poverty level Gov benefit = income needs - actual earnings For every dollar earned below the income needs threshold, the govt benefit falls by a dollar Receive no benefits if one's earnings are above the needs threshold Identical to a 100% tax rate on every dollar earned below the needs threshold. Implies net w = 0 for earnings below the threshold. Yet again, individual preferences matter: • If flat I.C. (Oprah), person who might otherwise be eligible for AFDC will work and earn above the income needs threshold • If I.C. steep (Paris), person will take-up welfare
What is the marginal rate of substitution of leisure for consumption (MRS)? How does the MRS depend on the shape of one's indifference curves? How is it related to the marginal utilities of consumption and leisure? What condition holds at one's optimal choice of leisure (hours worked)?
MRS = MU(L)/MU(C) - this depends on one's indifferent curves because it is the slope of the indifferent curves. If the IC curse is very steep, the person gets a larger marginal utility from leisure. At one's optimal choice of leisure MU(l)/MU(c) = w c*=w(16-l*)
Mathematical representation of optical point of Leisure and consumption
MRS = |Slope of the IC| = MU(L)/MU(C)=|slope of the BC| - w
Empirical evidence on the elasticity of labor supply:
Male LS: o Income effect dominates. Tax rate decrease will reduce hours worked (slightly) → decline in tax revenue if tax rate falls. o Neoclassical theory suggests that this will be more so as wealth increases
How do you find the reservation wage of someone using corner solutions?
Need to find the wage that creates a tangency between the budget constraint along with the corner solution.
Budget Constraint with a Spike
One only qualifies for income benefits if not working -->receive no benefits if one works even on hour(minute0 Leads to a spike in the BC at 0 hours; unearned income = benefits, implies a negative wage rate for the 1st hour worked - lost income if one works even one hour - negative wage rate - large substation effect against working
How do the magnitudes of these effects depend on an individual's initial hours of work before a wage change? Which effects operate in the labor force participation decision (extensive margin) and in the hours of work decision (extensive margin).
People with higher hours worked have a larger income effect when then wage changes. People with no hours worked have small income affected relative to sub effect. Sub effect tends to dominate in the LF participation decision - larger elastic of participation margin then hrs margin.
LS elasticity
Percent change in h in response to percent change in w if it is greater than 0, the sub effect dominates the income effect
What is the reservation wage? How does it depend on individual preferences and opportunities - e.g., the fixed costs of working?
Reservation wage is the lowest wage at which a person is willing to work. If w<Wr the individual will not work. It depends on their utility curve and non labor income Steeper IC curves, higher reservation wage This depends on the size of fixed costs, jobs are far way , high travel costs, higher res wage- reduces the LFPR compared to others with identical tastes.
If you have FLAT IC, aka lower MRS then which effect dominates?
Sub effect wins, work more
What are the substitution and income effects of a wage change on labor supply? In what directions do these effects operate? How do you derive this graphically?
Substitution Effect = the individual will chose to work more if wages are increased. Will substitute leisure with working more (change in slope of BC) Income Effect = Individual will choose to work less if wages are increased because their income is higher. They will consume m ore leisure (barrel shift in BC)
Time constraint in a given day
T = Sleep + leisure + work 24 = 8 + l + h if Demand for leisure Increases then hours of LS decrease (one for one) Use demand theory to solve for l* which gives us h*
The offer curve
The Laffer Curve suggests that, as taxes increase from low levels, tax revenue collected by the government also increases. It also shows that tax rates increasing after a certain point (T* on the diagram below) would cause people not to work as hard or not at all, thereby reducing tax revenue. Eventually, if tax rates reached 100 percent, shown as the far right on his curve, all people would choose not to work because everything they earned would go to the government. Governments would like to be at point T* because it is the point at which the government collects maximum amount of tax revenue while people continue to work hard There are some fundamental problems with the Laffer Curve — notably that it is far too simplistic in its assumptions. While the curve assumes that societies function on a single tax rate and a single supply of labor, that can't be further from the truth. In reality, public finance structures are much more complex. The curve does not take into account how revenue is affected by multivalued tax rates. Simply, the fact that any increase in the tax rate to a certain percentage may not necessarily equate to the same revenue as a decrease in the tax rate. The curve also does not take into account any avoidance of taxes at any level.
Show graphically how to construct an individual labor supply curve as a function of wages. That is, given a set of indifferent curves, how does an individual's optimal choice of work hours vary with changes in the w rate?
The effect of a change in wages on total hours worked depends on the relative size of the income and substitution effects.
What is the reservation wage?
The reservation wage is the minimum wage at which a person works at all. This is given as w0 from the y axis in the figure below
Given an hourly wage rate, w, show graphically and explain an individual's optimal choice of leisure and hours of work.
To determine the optimal choices made by consumers, we need a graphical representation that shows the highest possible utility while making choices that are within the budget set. A simple graph has leisure on the x axis and total income on the y-axis. Because consumers want to use all of their income, total income will also be total spending on marketing goods. To represent utility, we make use of IC which give combinations of income and leisure that provide the consumer with equal utility. The graph below shows the budget constraint and IC in the same space. This graph has no-non labor income. To maximize well being, the consumer wants the IC to just touch the BC, which implies the two are tangent (i.e. have the same slope. So the optimal point is given as A. y = w∙h + y0, y0 = non-labor income (assume y0 = 0 for now) h = 16 - l → y = 16∙w - w∙l → B.C. slope = dy/dl = −w
How do you graphically show a change in the budget constraint when either the wage rate or the level of unearned income change. How about when an individual is eligible for social insurance?
When the wage increases, the slope of the budget constraint is changed. When the amount of unearned income changes, the slope remains the same but the BC is shifted to the right or left. When someone is eligible for social insurance the budget constraint is pushed up.
Define the substitution effect
When wage rate increases, the reward to working increases relative to the reward for leisure. This is a force that increases the labor supply Chang in l due to change in w Increase w = increase in p1 _> reduce L* (Increase h*)
How do these two effects in a change in the wage rate on hours worked
When wages go up, the price of leisure goes up, leisure gets down, work goes up at a constant y (wealth) When wages go up, y goes up, leisure goes up, hours worked goes down, at a constant wage Net effect, ambiguous, depends on which affect is stronger, which in turn, depend son the slope of the indifference curves and budget constraints.
How do social insurance programs like worker's compensation, unemployment insurance, and welfare affect an individual's budget constraint? How about the Earned Income Tax Credit (EITC)? According to neoclassical labor supply theory, how does each program affect work incentives? How does an individual's labor supply response to social insurance depend on his preferences?
Worker's compensation: replaces lost earning when worker is injured on the job. Disability insurance: insurance for health issues that limit work ability (spike at 0). Unemployment insurance: income paid for job less people - spike at 0 need to be above the reservation wage. Unemployment insurance (UI) provides time-limited income for job loss (see BvO, Ch 11 for more on UI) EITC: Tax credits, earnings subsidy - income maintenance preserves work incentives.
How do you construct an individual's opportunity set (budget constraint) given the wage rate and her amount of unearned income?
y=w*h+y0
