Labor Supply

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On the fist Friday of every month, the Bureau of Labor Statistics(BLS) releases its estimate of unemployment rate for the previous month. The Current Population Survey (CSP) survey nearly 50,000 households about their work activities during a particular week of the month. The CPS classifies all persons age 16 or older into one of three categories: the employed, the unemployed, and out of labor force. To be employed, a worker must have been at a job with pay for at least 1 hour or worked at least 15 hours on nonpaid job. To be unemployed, a worker must either be on a temporary layoff from a job or have no job but be actively looking for work in the four-week period prior to the reference week.

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To be considered unemployed, a person must either be on temporary layoff or claim that he or she has “actively looked for work” in the past four weeks. persons who have given up and stopped looking for work are not counted as unemployed, but are considered to be “out of the labor force.” At the same time, some persons who have little intention of working at the present time may claim to be “actively looking” for a job in order to qualify for unemployment benefits.

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Hidden unemployed or discourage workers dropped out of the labor market. The employment rate may provide more objective measure of aggregate economics activity. The employment rate simply indicates the fraction of the population at a job.  A decrease in the employment rate could be attributed to either increase in unemployment or unrelated increases in fertility or school enrollment rates.  The employment rate provides a better measure of fluctuations in economic activity than the unemployment rate.

 

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The decline in average weekly hours of work shown below Figure was accompanied by a substantial increase in the number of hours that both men and women devote to leisure activities.  the number of weekly leisure increased by 6.2 hours for men and 4.9 hours for women between 1965 and 2003.

 

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Economists typically use the neoclassical model of labor-leisure choice to analyze labor supply behavior. The economic trade-off is clear: If we do not work, we can consume a lot of leisure, we have to do without the goods and services that make life more enjoyable.  The model of labor-leisure choice isolates the person’s wage rate and income as key economic variables that guide the allocation of time between the labor market and leisure activities.  The representative person in our model receives satisfaction both from the consumption goods (C) and from the consumption of leisure(L). The utility function (U) summarizes the consumption goods and leisure. Utility function measures the individual’s level of satisfaction or happiness from the person’s consumption of goods and leisure.Slide9

 

Indifference curve yields same utility level.

 

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The following chart shows that Ux = Uy but Uz > Ux=Uy. The marginal utility of leisure is defined as the change in utility resulting from an additional hour devoted to leisure activities, holding constant the amount of goods consumed. MU(L) = Marginal utility of leisure.

 

 

 

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Cindy’s indifference curves are relatively steep, indicating that she requires a substantial bribe to give up an additional hour of leisure. Mindy’s indifference curves are relativey flat, indicating that she attaches a much lower value to her leisure time.

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The person’s consumption of goods and leisure is constrainded by her time and by income.   The person’s budget constraint can be written as C=wh (Earning Income) +V (Nonlabor Income). T hours per week, so that T=h+L

C=(wT+V)-wL

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Point E is the endowment point, telling the person how much she can consume if she does not enter the labor market. The worker moves up the budget line as she trades off an hour of leisure for additional consumption. The absolute value of the slope of the budget line is the wage rate. The consumption and leisure bundles that lie below the budget line are avaiable to the worker; the bundles that lie above the budget line are not. The budget line, therefore, delinates the frontier of the worker’s opportunity set – the set of all the consumption baskets that a particular worker can afford to buy.

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The optimal consumption of goods and leisure for the worker, therefore, is given by the point where the budget line is tangent to the indifference curve. The type of solution is called an interior solution because the worker is not at either corner of opportunity set.

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MU(L) / MU(C) = w  or MU(L)/ w = MU(C)

The quantity MU(L) gives the additional utility received from consuming an extra of leisure The extra hour costs w dallars.

 

 

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Before the nonlabor income increases, the worker maximizes utility by choosing the bundle at P0. At this point, the worker consumes 70 hours of leisure and works 40 hours. The increase in nonlabor income to $200 weekly shifts the endowment point to E1, so that the new budget line is given by F1E1. – Income effect

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A commodity is a normal good when increase in income, holding the prices of all goods constant, increase its consumption. A commodity is an inferior good when increase in income, holding prices constant, decrease its consumption.

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What happens to Hours of Work When the Wage Changes? If a wage increase from $10 to $20 an hour, holding nonlabor income V constant The wage increase rotates the budget line shift the opportunity set.  Income effect moves the consumption point from P to Q and the substitution effect moves the consumption point from Q to U

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An  increase in the wage rate increases hours of work if the substitution effect dominating the income effect.

An increase in the wage rate decreases hours of work if the income effect dominates the substitution effect.

 

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If the person chooses not to work, she can remain at the endowment point E and get U0 units of utility. At low wage (Wlow), the person is better off not working. At a high wage(Whigh), She is better off working. The reservation wage is given by the slope of the indifference curve at the endowment point.

The reservation wage gives the minimum increase in income that would make a person indifference between remaining at the endowment point E and working that first hour.

A rise in the wage rate, therefore, increases the labor force participation rate of a group of workers. As we shall see, this positive correlation between wage rates and labor participation rates helps explain the rapid increase in the labor force participation rate of womaen observed in the United States and many other countries in the past century.

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The labor supply curve predicts the relationship between hours of work and wage rate.

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The figure implies that substitution effects dominate at lower wages and that income effects dominate at higher wages.  The labor supply curve traces out the relationship between the wage and hour of work. At wages below the reservation wage($10), the person does not work. At wages higher than $10, the person enters the labor market. The upward-sloping segment of the labor supply curve implies that substantial effects are stronger initially; the backward-bending segment implies that income effect may dominate eventually.

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To measure the responsiveness of hours of work to changes in the wage rate, we define the labor supply elasticity which is positive when substitution effects dominate and negative when income effect dominates.  For example, the worker’s wage is initially $10 per hour and that she works 1,900 hours per year. The worker gets a raise to $20 per hour, and she decides to work 2,090 hours per year. This worker’s labor supply elasticity is 0.1. When the labor supply elasticity is less than one in absolute value, the labor supply curve is said to be inelastic.  In other words, there is relatively little change in hours of work for given change in the wage rate. If the labor supply elasticity is greater than one in the wage –  the labor supply curve is said to be elastic.

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The market labor supply curve “adds up” the supply curves of individual workers. When the wage is below no one works. As the wage rises, Alice enters the labor market.  If the wage rises above Wb Brenda enters the market.

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As the wage increases, nonworking women have an incentive to reduce the time they allocate to the household sector and are more likely to enter the labor market.  In fact, the real wage of women increased substantially in most countries. The accoss-country relationship between the increase in labor force participation rates and the increase in the real wage is illustrated in the following figure.  the labor force participation rates grew fastest in those developed countries that experienced the highest increase in the real wage. The labor force participation decision is based on a comparison of the market wage with the reserve wage.  Hence, the increase in the labor force participation rates of women could be due not only to a rise in the market wage but also to a decline in women’s reservation wages. Between 1950 and 2000, the total lifetime fertility of average adult woman declined from 3.3 to 2.1 children, so the reduction in fertility probability contributed to the increase in female labor force participation.

Female labor force participation rates also are influenced  by technological changes in the process of household production. There have been remarkable time-saving technological advances in household production.  The economic model should not be interpreted as saving that only wage rates, reductions in fertility, and technological advances in household production are responsible for the huge increase in laobr force participation of married women in this cenury.  Changes in culture and legal attitudes forward working women, as well as the social and economic disruption brought by two world wars and Great Depression, also played a role.

It has been estimated that about 60 percent of the total growth in the female labor between 1890 and 1980 can be attributed to the rising real wage of women. The labor force participation rates and hours of work of married women respond to changes in the husband’s wage.

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A take-it-or-leave-it cash grant of $500 per month moves the worker from point P to point G, and encourages the worker to leave the labor force. An improvement in the endowment point (from E to point G) increases the worker’s reservation wage, reducing the likehood that a low-wage person will enter the labor market.

 

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A welfare program that gives the worker a cash grant of $500 and imposes a 50 percent tax on labor earnings reduces work incentives. In the absence of welfare, the worker is at point.  The income efffect resulting from the program moves the worker to point Q; the substitution effect moves the the worker to point R. Both income and substitution effects reduce hours of work.

 

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An alternative approach to improving the economic status of low-income persons is given by the Earned Income Tax Credit (EITC). This program began in 1975 and has been expanded substantially since. For the 2014 tax year,  27.5 million received about $66.7 billion in EITC during 2015.

https://www.eitc.irs.gov/EITC-Central/main

In 2005, for example, this woman could claim a tax credit of up to 40% percent of her earnings as long as she earned less than $11,000 per tax year, resulting in a maximum credit of $4,400. This maximum credit would be available as long as she earned between $11,000 and $14,370. After reaching the $14,370 threshold, the credit would begin to be phased out.  As long as the worker earns less than $11,000 per year, the worker can claim a tax credit of up to 40 percent of earnings. Suppose, for instance, that the wage rate is $10 an hour and that the worker decides work only one hour during the entire year. She can then file a tax return that would grant her a $4 tax credit. Therefore, the EITC implies that worker’s net wage is $14, a 40 percent raise.

 

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  1. EITC draws worker into Labor market 2. EITC reduces Hours of work

 

The labor participation rate of the eligible women increased from 72.9% to 75.3% before and after the 1986 tax reform went into effect, an increase of 2.5% points.

 

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(a) The age-earnings profile of a typical worker rises rapidly when the worker is young, reaches a peak at round age 50, and then wages either stop growing or decline slightly. (b) The changing price of leisure over the life cycle implies that the worker will devote relatively more hours to the labor market when wage is high and fewer hours when the wage is low.

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The model then suggests that the profile of hours of work over the life cycle will have exactly the same shape as the age earning profile: hours of work increase as the wage rises and decline as the wage falls. The theorical prediction that people allocate their time over the life cycle so as to take advantage of changes in the price of leisure is called the Intertemporal Substitution Hypothesis. It implies that the correlation between changes in hours of work and changes in the wage should be positive. As a worker ages, an increase in the wage rate should increase hours of work.

 

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The added worker effect thus implies that the labor force participation rate of secondary workers has a countercyclical trend (that is, it moves in a directiion opposite to the business cyele); it rises during recessions and falls during expansion.

 

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The relationship between the business cycle and the labor force participation rate als can arise because of the discourage worker effect.  The discourage workers are unemployed workers who can’t find jobs during a recession and simply give up. As a result of the discourage worker effect, the labor force participation rate has procyclical trend; it falls during recession and increasees during expansions.

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Discourage worker effect > Added worker effect during the recession. The official unemployment rate reported by the Bureau of Labor Statistics (BLS) might be too low. If an unemployed person becomes discouraged and leaves the labor force, he or she is no longer activiely looking for work and, hence, will no longer be counted among the unemployed.  As a result, the official unemployment rate may greatly understate the unemployment problem in the aggregate economy during severe recession.

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Part of  the declining labor force participation of older workers may be attibuteable to an increase in the pension benefits. Some studies argues that an important part of the decline in the labor market attachment of older workers in the United States can be attributed to the work disincentives created by the Social Security Disability Program.

 

 

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Overall, the theory suggests that the elimination of the Social Security earnings test is unlikely to substantially increse labor supply among retirees.

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There is a positive correlation between income and fertility.  An increase in income leads to more fertility; a decrease in income reduce fertility.  Malthusian model of fertility failed to predict what actually happened to fertility behavior in modern economies. As per-capital incomes roses, fertility rate did not rise. Instead, they declined! In other words, instead of families getting larger as countries got richer, families actually got smaller.

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N-Number of Childeren X-the quantitiy of goods

The household’s consumption activities, however, are constrained by its income (I).

P(N) – price of having an additional child and P(X) – price of other goods

Children are an extremely expensive and time-intensive commodity.

 

 

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a) An increase in income moves the household from point P to point R and encourages the household to have more children. b) An increase in the price of children rotates the budget line inwards Initially, the household wants three children (point P); the price increases reduces its demand to one child (point R). The shift from P to R can be decomposed into an income effect (P to Q) and substitution effect (Q to R).  The price of children for rural families is probably lower than for urban families. After all, children raised on the “family farm” are a source of cheap labor that can conduct a variety of chores around the farm, whereas children in urban households typically do not contribute to family income.

 

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