Notes 4: Labor Markets and Unemployment

Notes 4: Labor Markets and Unemployment

I.  The Labor Markets - some analysis

Last week in class, we went over in gory detail the difference between income and substitution effects. The income effect says that as people become richer, they want to work less. The substitution effect says that as the price of a good goes up today (i.e., leisure), then you want less of that good and more of other goods (in this case, less leisure and more consumption - how do you get more consumption - work more to earn more).

In micro, you probably learned models with two goods. I am going to go through a quick example of two goods and then we will take it to the macro level. Suppose you only want to consume apples and bananas. Suppose further that you like consuming these goods. Think about your own consumption decision. If the price of apples increases - you are going to switch towards bananas. Remember from micro, we are going to consume until the marginal utility of (apples)/ price of (apples) = marginal utility of (bananas)/ price of (bananas). Or,

MU(apples)/P(apples) = MU(bananas)/P(bananas)

If the price of apples increases, you need the marginal utility of apples to increase in order to make this equality hold. How do you get the marginal utility of apples to increase? You consume LESS apples (this is the law of diminishing marginal utility - the more you consume of a good, the LESS extra utility you get - think about it, the 10th hamburger is not as satisfying as the 1st.). This is the substitution effect. As the price of apples increase, you are going to substitute away from apples towards bananas.

But, as the price of apples increase, you spend more for the apples you do buy. That means, in some sense - you are relatively poorer. You could not have bought the same bundle of apples and bananas as you did before the price changed at the same cost after the price change. Given that you are poorer (due to the price change), you will buy less of everything you like (apples and bananas). This is the income effect. As the price of apples increase, you will decrease your consumption of BOTH apples and bananas.

Notice, as the price of apples increase, you will definitely decrease your consumption of apples (income and substitution effect both say that you will consume less apples). However, your change in your consumption in bananas in response to an increase in the price of apples is ambiguous.

This is exactly the same type of analysis we will do in our class. In macro, we assume households only care about 2 aggregate goods: consumption and leisure. If the price of leisure increases, households will switch away from leisure and work more (substitution effect). The price of leisure is foregone wages. As wages increase, it is more expensive to take a day off. That means as wages increase, the price of leisure will increase. This will lead to a substitution effect between consumption and leisure. The substitution effect says that as wages increase households will substitute away from leisure (which is expensive) towards consumption. As a result, if leisure falls, households will be working more. So, the substitution effect of a real wage increases says households will work more (take less leisure).

But, if wages increase, we will be richer for every hour we worked. This will lead to an income effect. This means we consume more of all the goods that make us happy: in our macro world, leisure and consumption. As a result, the income effect says that we will take more leisure and (as a result) work less (by definition, more leisure means less work - if we are not working, we are taking leisure).

If real wages permanently change, both effects will happen simultaneously! <As we discussed in class, if wages only change temporarily, then there will be little effect on lifetime income - i.e., little (no) income effect.>

Summary: Substitution effect of labor supply says that as wages increase, you will work more (leisure is more expensive so you will substitute away from leisure). Income effect says that as wages increase, you will work less (we are richer so we want to consume more of the goods we like - one of those goods is leisure). Both effects happen simultaneously. So what happens to the total quantity of labor supply when wages increase? Depends on which effect is stronger - theory does not give us any guidance as to which effect is bigger.

i) Representing Labor Demand

The labor demand curve tells us how much labor firms want to hire at given wages (see lecture notes). The labor demand curve comes straight from the MPN. It tells how profit maximizing firms want to hire additional workers. They will hire an additional worker up until the cost of that worker equals the benefit from that worker. What is the cost to the firm of an additional worker? - the nominal wage that the firm pays (w). What is the benefit to the firm of an additional worker? - that worker makes some output and the firm sells that output. How much output does the worker make? - that is simply the marginal product of labor (MPN). The value of that output is the additional output times the price of that output. Let’s call the price of output (p). The profit maximizing condition for hiring another worker will be:

w = p*MPN or w/p = MPN.

w/p = the real wage (the nominal wage (w) deflated by the price level (p) - given there is only one good in our aggregate economy - the price of the good is the price of the output).

The MPN is a function of N, K and A (see Notes 2).

So, we can draw the labor demand curve as:

w/p = ND = MPN = MPN(N,K,A)

where ND is labor demand curve and MPN(.) is the mathematical representation of the marginal product of labor.

The Labor Demand Curve can be drawn as:

w/p

ND(N,K,A)

N

Anything that increases the MPN increases labor demand. An increase in N will not increase MPN, but causes a downward movement along the labor demand curve (labor demand curve is drawn in {N, w/p} space (i.e., x,y space, where x = N and y = w/p). An increase in K or A will cause the labor demand curve to shift to the right.

ii)  Representing Labor Supply

The labor supply curve is exactly what we were talking about earlier - how consumer’s desire to work responds to changes in wages (to be specific, before tax wages). As we discussed, this response depends on the strength of the income and substitution effects. In graphing the labor supply curve, we are going to separate out the income and substitution effects. This is the most important concept of this lecture (or, at least, the part that students seem to get stuck on the most). We are going to represent a function for the labor supply curve as:

NS = Ns (w/p, PVLR, population, Value of Leisure, taxes)

Notice - we separated out the current real wage (w/p) and the present value of life time income (PVLR). The present value of life time income is basically all the resources that you will earn over your lifetime (in present value terms). In other words, PVLR represents the income effect. If your lifetime resources do not increase, then you are not richer - so, there is no income effect. We are going to start by analyzing the change in real wages (w/p) holding PVLR constant. This assumption shuts off the income effect - we are going to separately analyze the income effect and the substitution effect. How do we get wages changes with little or no income effect? Basically, the wage change that occurs today must be temporary. If that is the case, lifetime income will move but only by a small amount. As a short hand, we essentially equal little income effect with no income effect.

Let’s draw the labor supply curve:

Ns(PVLR, population, Value of Leisure, Taxes)

w/p

N

The labor supply curve shows the representation between real wages and hours worked holding PVLR, population, the value of leisure and taxes constant. Why does the labor supply curve slope up? This is easy (although, most students get it wrong when I ask it on the test - make sure you know the intuition, I will test it!). As we saw above, when real wages go up, leisure becomes more expensive, so we consume less leisure (work more). The labor supply curve slopes up because of the substitution effect. What about the income effect? We shut the income effect off because we are holding income (life time income - PVLR) fixed. Now, I know what are you are thinking - how can wages increase and not affect income. The answer is - usually wages will affect income! But, we are going to represent this effect as a SHIFT in the labor supply curve - not a movement along the labor supply curve. Think of an example where you boss tells you that the firms profits will be high this year, but will be low next year. He tells you that your wage is going to rise this year, but next year your wage will fall. In total your expected lifetime income has not changed (but the timing has changed – you are a little richer than expected now and will be a little poorer than expected next year).

To make our analysis easier - we are going to represent the substitution effect- with changes in the real, before tax wage, as a MOVEMENT along the labor supply curve. We are going to represent the income effect that results from a change in the before tax wage as a shift in the labor supply curve.

Three other things effect the labor supply curve:

1.  Population - the more people working , the greater the labor supply - labor supply shifts right.

2.  Value of Leisure - as welfare programs become more lucrative or as our preferences for working decrease for some other reason besides before tax wages, we will work less - labor supply shifts left.

3.  Taxes - we draw the labor supply curve as a function of before tax wages. If taxes are important, after tax wages will change - we make our labor supply decisions on after tax wages - see the examples below!

Below, I go through some examples of how changes in the economic environment affect the labor market.

A. Consumption taxes

We went through the example of permanent changes in technology in class. I will come back to this later. I want to start with an analysis of changes in tax policy. There are two taxes we will focus on: labor tax (i.e., income tax) and a consumption tax (i.e., sales tax). Let's start with the consumption tax first (I care more about the labor tax - we will do that in great detail next).

When the tax on consumption increases - the price of consumption increases. As a result, households will want to switch toward leisure. Remember the example with apples and bananas above. When the price of apples increases (consumption), you will switch towards consuming more bananas (leisure). As a result, they will choose to work less (leisure is relatively less expensive compared with consumption). This is the substitution effect. Let's illustrate this below:

Illustration of Substitution Effect of Increasing Consumption Tax

Ns1 Ns

N

This graph only illustrates the substitution effect resulting from the change in consumption taxes (The substitution effect of changing taxes causes the labor supply curve to shift – the substitution effect of changing before tax wages causes a movement along the labor supply curve – that is why I am making a big deal out of distinguishing between before tax and after tax wages – changing before tax wages causes us to move along the labor supply. Changing taxes causes the labor supply curve to shift. BOTH ARE SUBSTITUTION EFFECTS!!!). If the tax change was temporary, this would be the end of the story. Temporary consumption tax changes will increase real before tax wages today. But, tomorrow, before tax real wages will return to their original level. Given that the real wage increase was only temporary, the income effect will be small. As defined in class, we will assume that ANY temporary change has no effect on the present value of lifetime resources. So, with a temporary consumption tax change, households should respond by working less today - leisure is relatively more enjoyable. I have to work more to get the same amount of consumption as before. Why should I spend all that effort? I will just substitute towards leisure. Again - think of the apple and banana story. If we like both apples and bananas and the relative price of apples increase, we will switch towards bananas. In this case, the substitution effect says we will consume less apples and more bananas. This substitution effect in our macro labor market with consumption taxes changing says the same thing. We care about consumption of goods and leisure. If consumption becomes more expensive, we will switch towards leisure. Some of you will say - 'Erik, wont we have to work more now to get the same level of consumption?'. This would be SOOO wrong!!!! Consumption is not the only thing that makes us happy. Leisure also makes us happy. We will take less consumption - but the benefit is more leisure (which makes us happy). This is exactly analogous to the fact that we will be consuming less apples when the price of apples increase.

Notice, there are two substitution effects shown in the above figure. The movement from point (1) to point (z) is the substitution effect that results from the price of consumption increasing (because of the consumption tax). As the price of consumption increases, we will take more leisure and work less (this is a shift in of the labor supply curve). However, as labor supply falls, before tax wages will rise. A rise in before tax real wages makes taking leisure more expensive. As a result, we take less leisure and work more. This is represented as a movement along the NEW labor supply curve from point (z) to point (2). The net effect is we will work less (the substitution effect from the tax change will dominate the substitution effect from the wage change). However, for completeness, you should realize that there are two separate substitution effects occurring!