503 Applied Macroeconomics Chapter 3. The Ideal Labor Market 2004 Kevin D. Hoover Applied Intermediate Macroeconomics Prof. M. El-Sakka Dept of Economics Kuwait University
Labor is the most important factor of production. Most of us derive our main source of income from labor. In this chapter, we investigate the labor markets when they are working well. Some of the questions considered are : How much labor do firms want to hire? How many people want to work? For how long? How do taxes, technological progress, and immigration affect real wages? Our analysis has three parts: (i) What factors govern the decisions of firms to hire labor? (ii) What factors govern the willingness of workers to supply it? And (iii) How do the decisions of firms and workers interact to determine the mount of labor used in production?
Labor Demand THE FIRM’S DEMAND FOR LABOR Deriving the Firm’s Labor-Demand Curve The labor-demand curve shows the amount of labor a firm would optimally choose to hire ceteris paribus at each real-wage rate. Recall the rule for profit maximization: a firm hires labor until the marginal product of labor is equal to the real wage (mpl = w/p). Because of diminishing returns, the relationship between real-wage rates and the marginal product of labor is inverse: a firm can profitably hire more labor only if real wage falls enough to match the fall in the marginal product. We apply the profit maximization rule to the production function to derive a labor-demand curve (see the following Figure).
Imagine that the firm faces a real wage of (w/p)1. The optimal point is found where the MP=(w/p)1. This point corresponds to a particular level of labor l1. The combination (l1, (w/p)1) forms point A’ which is one point on the labor-demand curve. If the firm paid its workers anything more than (w/p)1 to produce at A, it would reduce its profits. If the firm do if it faced a lower wage, say, (w/p)2?. the new optimal production point will be at B. At B the firm demands l2. The combination (l2, (w/p)2) shown as point B’ in the lower panel is another point on the firm’s labor-demand curve. The labor-demand curve connects A’, B’, and every other profit-maximizing point. It is downward sloping because of diminishing returns to labor.
Factors that Shift the Labor-demand curve The labor-demand curve is not independent of the production function. As a result, anything that shifts the production function will, in general, shift the labor-demand curve, and the labor-demand curve cannot shift unless the production function also shifts. Technological progress or an increase in the capital stock shifts the production function upward. Consider an increase in the capital stock, how does it shift the labor-demand curve? An increase in capital raises MPL at every level of labor demand, the higher MP means that the profit-maximizing firm can afford higher real wage at each level of labor. The labor-demand curve shifts vertically upward.
But why would the firm pay workers more for a particular level of labor when additional capital raises their marginal products? Why does the firm not just pocket the windfall? The answer: competition. When the marginal product rises, each firm tries to hire more workers. Since we have assumed that markets are all in equilibrium, all available workers are already employed, and it is only by paying higher wages that the firm can attract them.
THE AGGREGATE DEMAND FOR LABOR In macroeconomic analysis we are more concerned with the aggregate demand for labor. If all firms produced the same products and if all workers were alike, then aggregation from the firm to the economy as a whole would be easy (see the figure). Unfortunately, it is not that simple. The first problem is that all firms are not producing the same product. When different firms produce different goods, we must find a common unit of measurement. The second problem is that not all workers are alike. Different kinds of workers may face different wage rates and, therefore, have different marginal products at the optimum. For our purposes, the wage structure can be summarized in the average wage rate. Though It provides an imperfect index of the movements of the wage structure.
Labor Supply Two measures reflect two aspects of the worker’s labor supply decision: (i) participation – that is, whether to work or not work; and (ii) intensity – that is, how many hours to work. It is easier if we consider intensity first: conditional on having decided to work, what factors govern the worker’s choice of how many hours of work to supply? THE WORKER: CHOOSING HOURS OF WORK The Price of Leisure People work for a variety of reasons. The most obvious is to earn the income. Many people – though not all – find their work fulfilling and interesting. Still, even those people, will generally prefer another hour of leisure to another hour of work. It is, therefore, reasonable to assume that leisure is a good.
Goods generally have a price. Yet there is nomarket for leisure. Even though there is no explicit price, there is an implicit price or opportunity cost. The OPPORTUNITY COST of any choice is the value of the best alternative choice that it forecloses.The implicit price of leisure is its opportunity cost, which is measured by the real wage (w/p).
The Labor-Leisure Choice Once we see leisure as a good and the real-wage rate as its price, it is easier to understand the choices a worker faces. There are 168 hours in a week. If a worker chooses not to work at all, he enjoys 168 hours of leisure, but forgoes the income needed to buy any other goods. If the worker instead takes fewer hours of leisure, he supplies labor l = 168 – hours of leisure, and he gains the ability to purchase goods worth w/p × l. The problem for the worker is to choose the hours of labor (l ) that at the margin makes the psychic value of a small loss further loss of leisure time (i.e., a small increase in labor time) exactly equal to the psychic value of the small gain in consumption goods that would be purchased by that labor.
INCOME EFFECT. How would your supply of labor change if you could receive the income that results from the increased wage rate without facing a changed opportunity cost of leisure? As a general rule, an increase in income ceteris paribus increases the demandfor all goods. The extra $20 per week would permit you to buy more goods, including leisure without reducing your purchases of other goods. The reduction in the supply of labor as the result of an increase in income is called the income effect.
SUBSTITUTION EFFECT If the wage rate rose would people work more or less? As a general rule, whenever ceteris paribus the price of anything rises relative to alternatives, the demand for it decreases. Here the price of leisure (its opportunity cost) has risen relative to the price of other goods, the supply of labor would rise. The change in the wage rate encourages people to substitute the now cheaper goods (what you buy using your wage) for the now more expensive leisure. The increase in the supply of labor as the result of an increase in the price (or opportunity cost) of leisure is called the SUBSTITUTION EFFECT.
The Labor-supply Curve The following figure represents the worker’s labor-supply decision. Look first at panel (A). Suppose that at point A, where the real wage is (w/p)1, the worker decides that providing l hours of work balances the advantages of a little more consumption against a little more leisure at the margin. Now consider what happens when the real wage rises to (w/p)2. There is a substitution effect shown by the arrow pointing to the right, which encourages the worker to supply more labor. The size of the substitution effect is measured by the length of the arrow. There is also an income effect shown by the arrow pointing to the left, which encourages the worker to supply less labor.
The net effect is measured by the difference between the substitution and income effects shown at point B. so that an increase in the wage rate increases the worker’s supply of labor to l2 to the right of l1. If the substitution effect is always stronger, then the labor supply curve slopes upward. Substitution effects are not necessarily stronger than income effects. Panel (B) shows the construction of the labor-supply curve, starting from point C, when income effects are stronger than substitution effects. When the real-wage rate increases from (w/p)1 to (w/p)2, the dominant income effect overwhelms the substitution effect, and labor supply (point C) falls from l1 to l2. If income effects are stronger for all wage rates above (w/p)1, then the labor-supply curve will slope downward toward point C: higher real wage rates lower labor supply.
Although the labor-supply curve can slope downward towards a point like A, it is not reasonable to believe that it could slope downward for every possible wage rate. At very low wage rates it is more reasonable to suppose that, with very low incomes, the worker’s need for food, clothing, shelter, and other “essential” goods, the income effect is weak and the substitution effect is strong. We should, therefore, expect the labor-supply curve to be upward sloping when wage rates are low. Hence labor supply would be backward bending.
Adding Realism: Taxes How does the tax affect the income from a little more or a little less work? To answer this question we must know the marginal tax rate(the fraction of an additional dollar of income that is paid as taxes). To keep things simple, assume that all income is taxed at the same flat rate τ. In this case the marginal tax rate must also be τ, which takes a value between zero and one. If a worker earns w/p for an hour of work, the government takes τ(w/p) as taxes and leaves the worker (1–τ)(w/p) as the after-tax real wage. Since the worker actually receives the after-tax real wage, it is the true opportunity cost of leisure. Any increase in the marginal tax rate represents a decrease in the opportunity cost of leisure. If substitution effects are stronger than income effects, then any increase in marginal tax rates reduces the supply of labor as shown in the following figure.
The labor-supply curve with no taxes is shown on the right of the figure. At (w/p)1, the worker supplies labor l1. If a tax of τ1 is imposed, the after-tax real wage is (1–τ1)(w/p)1. The worker should react exactly as if he paid no taxes but suffered a cut in his wages. This is shown as a movement from point A to point B where labor supply has fallen to l2.But of course the wage rate did not really fall; the employer still pays (w/p)1. This means that (l2, (w/p)1) is the labor-supply (point C). Since this would apply for any real-wage rate, every point on the original curve shifts to the left. Because the tax rate is proportional, its absolute effect is greater, as is the shift in the labor-supply curve, at high wage rates, resulting in a steepening of the curve. Any further increase in the tax rate to, say, τ2, would shift the labor-supply curve further to the left.
The length of the line segment BC measures the TAX WEDGEbetween the real wage paid by employers and the after-tax real wage received by workers. The larger the tax wedge, the larger the leftward shift of the labor-supply curve and the greater the reduction in labor supplied at any real wage. The idea that tax increases lower labor supply, and conversely that tax cuts increase labor supply, was a major tenet of the so-called supply-side economics popular in the early 1980s. President Ronald Reagan and his advisors used it to argue that cuts in marginal tax rates would stimulate people to work harder and to earn larger incomes.
Adding Realism: A Standard Workweek Another way in which the simple analysis of labor supply is unrealistic is that many workers are not given an option about the number of hours they work. Although people work part-time and overtime, either may be voluntary or mandatory. Assuming that workers are not permitted to work more than 40 hours a week, the following figure includes a constraint of 40 hours. If the worker were permitted to choose freely, then the labor-supply curve would backward bending curve. The overall effect is to of the standard work week is to reshape the labor-supply curve as indicated by the heavy curve with the vertical segment that runs through points A, F, G, D, and E. Any worker on this vertical segment is constrained.
The Individual Labor-Supply Curve in Practice What does the individual labor-supply curve look like in reality? It is difficult to answer this question, because in reality we can observe only one point on the labor-supply curve for a single worker at a particular time. All the other points are conjectures about what the worker would supply if faced with different wage rates. If we imagine that on average workers are substantially similar, we might nonetheless get some idea of what the individual labor-supply curve might look like. The National Longitudinal Survey (Youth) has catalogued the work histories of a large sample of individuals starting at a young age. The following figure plots the real-wage rates and average weekly hours of labor for about 10,000 male workers from this survey for a single period with the best fitting flexible line through these points serves as our empirical estimate of the labor-supply curve for these workers.
The regression line traces out a shape very like the backward-bending labor-supply curve with a 40-hour constraint. What looks like a vertical line above 40 hours is not really a solid line at all but a reflection of the fact that about 7,500 of the 10,000 workers in the sample supply 40 hours per week at a variety of wage rates. The labor-supply curve traces out a segment above the 40-hour point that corresponds to the constraint. There are points to the right of 40 hours. This is reasonable since, in the real world, workers do work overtime – either because they are supervisors or professionals or because employers offer them the required time-and-half wage rate. The fit of the regression line is far from perfect; points lie on both sides of the line. We should interpret it as a snapshot of the behavior of the typical worker. But ofcourse, the typical worker is not any actual worker in particular.
THE WORKER: CHOOSING TO PARTICIPATE So far, we have examined only one aspect of the worker’s labor-supply decision: how many hours to work for given real wage. We now take up the second aspect: participation – that is, whether or not to work at all. A labor-supply curve that starts at the origin and slopes upwards for at least a portion of its length suggests that even if the wage were very low – say, 1¢ per hour – the worker would work a little bit. That is clearly unrealistic: no one would work at all for 1¢ per hour. What factors determine how high the wage must be to induce a person to participate in the labor market?
The labor force participation decision is a question of opportunity cost. Idleness has its charms. Before anyone enters the labor force, the wage rate must be high enough to overcome them. The opportunity cost of participating in the labor force is sum of the implicit value the worker places on complete idleness; the explicit costs of working compared to not working such as, clothing, transport, childcare); and the explicit losses from working (for instance, housework not done). The opportunity cost is partly psychological and partly material. If people were completely independent of each other, the worker might place a lower value on the opportunity cost of participation because then the choice might be literally between work and starvation.
But most people are not completely independent. Whether or not to participate in the labor force could be a genuine choice and would depend on the real wage. The RESERVATION WAGE is defined to be the opportunity cost of working compared to not working – that is, the real wage that is high enough to make it just worthwhile for a worker to participate in the labor force. Taking account of the opportunity costs of participation affects the shape of the labor-supply curve. As long as the real wage is below the reservation wage ((w/p)R), the worker supplies no labor at all. Above the reservation wage there is a normal labor-supply curve.
The following captures the two stages of the labor supply decision: First, at low wages, the worker will not supply any labor at all, and small increases in wages have no effect. But, second, as soon as the wage rises enough for the worker to bite the bullet and join the labor force, the minimum labor supplied will be well above zero, and the worker will decide how many hours to supply above this minimum through the usual process of balancing the opportunity cost of leisure against the desire for consumption goods.
AGGREGATE LABOR SUPPLY How can we move from the microeconomics of the labor supply back to an aggregate relationship usable in macroeconomic analysis? If workers were essentially alike, the problem would be easy. As we have seen labor supply has two dimensions – participation in the labor force and choice of hours of labor. Take the participation decision first. If all workers were alike except for differences in their reservation wage, then we could rank them from lowest to highest reservation wage. The aggregate labor-supply (participation) curve is strictly upwardsloping.
Of course this is too easy. Just as we observed in deriving the aggregate labor demand curve, workers are not all alike. Once again we must interpret the vertical axis as measuring the average real wage that, at best, provides a kind of index for the level of the wage structure. The problem remains the same when we turn to the choice of hours. Workers are all different and face a structure of wages. For each worker individually there is a jump from supplying zero to supplying some positive number of hours when his own wage rate surpasses their reservation wage. But in aggregate we are unlikely to see such a jump. Not only are there a variety of wages offered at any time but reservation wages differ.
A curve like the one in this figure can be used to display either the participation decision or the hours. The horizontal axis can either be used for workers or worker-hours as measures of the labor supply. The two meanings are not completely independent: by definition workers ≡ aggregate worker – hours/ average hours per worker .
The Participation Rate and Average Hours Let us look first at the aggregate participation decision. The aggregate number of workers who have decided to participate is known as the labor force; the civilian labor force over 16 years of age.This number excludes uniformed members of the armed services and the small number of workers under 16 years old. The labor force, of course, has grown right along with population. The participation rate (PR) measures the labor force as its ratio to the relevant population: participation rate = labor force/relevant population . “non-institutional” excludes people in prison or in homes for the aged).
The aggregate number of hours worked is not as easy as the participation rate to relate to the individual worker’s choices. If every worker had the same labor-supply curve, we would have to know the wage offered to each one in order to calculate the total number of labor hours supplied. In reality, workers are not all alike. Labor-supply curves may vary systematically according to the sex, age, ethnic group, education, experience, or other social or economic characteristics of the workers. And within any group, the labor-supply curves of individuals are likely to vary.
In principle, if we had a good statistical estimate of the typical distribution of the wages, we could make a reasonable calculation. But statisticians at the Bureau of Labor Statistics (BLS) do not try to calculate the labor supply in this way. Instead, they count the number of hours that workers actually work and the averagewages and salaries they are paid. In USA, the total hours of labor in 1998 was 236,882 million The average hours of work is 1721 hours per year = 34.4 hours per week (assuming a 50 week year). This number is 14 percent below the full time 40-hour week, which makes sense since it averages over full-time, part-time, and overtime workers.
Labor Market Equilibrium MARKET CLEARING When both demand and supply curves are plotted on the same diagram, the crossing point defines the equilibrium real-wage rate and the equilibrium level of labor employed. The real wage looks different from the point of view of the firm and the worker. For the firm, the relevant real wage is the product-real wage defined as the number of units of the good the firm produces that the wage will purchase (price of product= w). For the worker, the relevant real wage is the consumption-real wage defined as the number of typical consumption baskets that the wage will purchase (price of consumption basket = w).
For aggregate analysis, we might use the Producer Price Index or the GDP deflator to approximate the product price and the CPI to approximate the consumption price. Suppose that the product-real wage and the consumption-real wage in the following figure start out with the identical value (w/p)* at the market-clearing point A. Now suppose that imported Japanese cars are a large portion of the typical worker’s consumption basket and that ceteris paribus the price of Japanese cars rises sharply. This means that the real wage from the point of view of the consumer falls to (w/pCPI )1at point B on the labor-supply curve (LS), so that the worker would want to supply less labor (L1).
The rise in the price of Japanese cars has no effect on the price of their products. Nevertheless, they see a reduction of labor supply at the original market clearing wage. It is as if the labor-supply curve has shifted to the left to LS’, which passes through ((w/p)*, L1) at point C. At the original wage rate, labor demand exceeds labor supply, so firms raise wages in an effort to attract workers until they reach the new market-clearing wage at point D where they pay (w/pPPI )** for labor of L**. The rise in the price of Japanese cars has the effect of raising the wages that firms must pay and reducing labor employed. Higher wages partly compensate workers for the higher costs of consumption, but firms can afford to pay those higher wages only if marginal products rise as a result of their using less labor.
The rise in wage rates is not enough to compensate workers fully, so the consumption-real wage in equilibrium is (w/pCPI) ** atpoint E. We can think of import prices as a tax levied on consumers and of an increase in import prices as widening the tax wedge. Unless the issue that we want to analyze depends on the difference between product- and consumption-real wages we will treat the real wage as the same for both labor supply and labor demand.
An Increase in the Price of Consumption GoodsRelative to the Price of Output
ANALYZING IDEAL LABOR MARKETS The aggregate labor-supply/labor-demand diagram provides us with a powerful tool. We now analyze three important macroeconomic issues: (1) the effect of tax cuts on employment; (2) the effect of technological progress on the well-being of workers; and (3) the effect of immigration on existing workers. Issue 1. Tax Cuts: What are the effects of a cut in marginal income-tax rates on employment and the level of GDP in the economy?Recall from section that a lower marginal income-tax rate increases labor supply at each real wage (a rightward shift of the labor-supply).
Labor-market equilibrium moves from point A to point B in the lower panel of the following. Notice that the amount of labor available to firms increases, so that firms move production from A’ to B’ on the labor production function in the upper panel. Also notice that the real wage falls from (w/p)1 to (w/p)2. Since the cut in taxes increases the number of workers willing to work at each wage. Workers care about their take-home pay – that is, about their after-tax real wage. This is perfectly consistent: the new after-tax real wage, (1–τ2)(w/p)2, can be greater than the old after-tax real wage, (1–τ1)(w/p)1, so long as the rise in the take-home share (1 – τ) is proportionately greater than the fall in the before-tax real wage (w/p).
The analysis depends on substitution effects dominating income effects, which they probably do in aggregate, if not for every worker. So the supply-siders of the Reagan years are correct in principle. How much output will increase depends on how large the substitution effect is. If most people work a standard 40-hour week, the effect could be quite small, and the increase in output might also be very small in practice.