Download Notes 4: Labor Markets and Unemployment

Notes 4: Labor Markets and Unemployment
I.
Labor Supply and Labor Demand
A)
Labor Supply Background
Recall from Topic 2, we discussed the difference between the income and substitution
effect. 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 for 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 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.
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B)
Formalizing Labor Supply
In macro, we assume households only care about 2 aggregate goods: consumption and
leisure. Consumption is everything we buy (apples, bananas, golf lessons, cars, etc.).
Leisure is how much we value not working. All else equal, people prefer to receive
money without allocating time to work. As discussed in class, which of the following
jobs would you prefer?
Job 1: Earn $250,000/ year and be expected to work 60 hours/week.
Job 2: Earn $250,000/ year and be expected to work 30 hours/week.
In both cases, the amount of consumption that could be purchased is the same (C =
$250,000 (in a static model with no saving)). But, most people would prefer job 2 to job
1. The reason is that people receive negative utility from the act of working itself. Or,
the way we write it, people get positive utility from leisure time (i.e., the time they do not
allocate to work). In other words, people will prefer hanging out with friends, sleeping,
doing nothing, watching TV, etc. compared to going to work. Not all people are like this.
Some people like working more than playing tennis or hanging out with friends. On
average, however, most people strictly prefer job 2 (above) to job 1 (above). To
represent this in our models, we assume that people get direct utility from “leisure”.
Some Assumptions:
Individuals in the economy maximize the following utility function (over consumption
and leisure):
U (C, L)
The only assumption on the model that we will make is that marginal utility is
diminishing in consumption (individually) and leisure (individually). This implies that
the marginal utility of consumption (leisure) decreases as consumption (leisure)
increases.
For simplicity throughout the remaining analysis, we will make three additional
assumptions:
1. We will only consider a static model. This means that households only have a
one-period planning horizon. In the next class (on consumption), we will relax
this assumption. For our labor supply discussion, it adds little.
2. Consumption and Leisure are independent of each other such that the marginal
utility of consumption (leisure) only depends on consumption (leisure).
3. There are only two things you can do with your time: either work (where N is the time
spent working) or take leisure (where L is the time spent in leisure). I normalize the time
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endowment to 1 such that N = 1 – L (by definition)). However, the normalization of the
time endowment does not matter. You could make that 24 (as in hours per day) or in 168
(as in hours per week). The key assumption is that N and L are negatively related with a
coefficient of 1 (a one hour increase in N implies – by definition – a one hour decline in
L).
Given this, we can express the optimization according to the following rules. To simplify
our analysis later on, I am going to directly embed consumption taxes (tc) and labor
income taxes (tn) into our analysis at this stage.
Equation 1: Substitution Effect
MU C
MU L

P(1  tc ) W (1  tn )
Where MUC is the marginal utility of consumption, MUL is the marginal utility of leisure,
P is the price of consumer goods in the economy (i.e., the CPI), W is the nominal wage, tc
is the marginal tax rate on consumption (i.e., sales tax), and tn is the marginal tax rate on
labor income (i.e., the income tax). The price of consumption is the cost of consumption
(P) plus any taxes someone pays on that consumption. The price of leisure is the wage
someone earns from working less any taxes they pay on that labor income.
The one interesting component of the above discussion is that the after tax wage is the
price of leisure. Why is that the case? In order for me to take one more hour of leisure, I
have to give up an hour of work. The cost of giving up an hour of work is the foregone
after tax wage that I would earn if I worked another hour. In other words, the price of
leisure is the wage I would have earned less any taxes I would have paid to the
government. As my wages go up, it is more expensive for me to take leisure.
For consistency, we will measure all prices in real terms. Given this, I can take the
above marginal utility equation and express it as the following:
MU c 
MU L
 W   (1  tn ) 

 
 P   (1  tc ) 
(1)
To get this, I divide both sides by P(1+tc). Under this expression, the price of leisure has
two components (we normalized the price of consumption to 1). The price of leisure is a
function of the real wage (W/P) and a tax component. If the price of leisure increases for
any reason, households will switch away from leisure and work more. We refer to this
as a substitution effect. Notice, just like our example with apples and bananas above, an
increase in the denominator of the right hand side of equation (1) means that either the
numerator of the right hand side increases or the left hand side falls. How does the
marginal utility of leisure increase and the marginal utility of consumption fall? The
answer is by decreasing leisure and increasing consumption (due to diminishing marginal
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utility). So, as the price of leisure increases, households will switch away from leisure
towards consumption in making them happy.
Remember, there are two things that drive the substitution effect: a change in real
wages or a change in the tax component (either tn or tc). An increase in real wages, a
decrease in labor income taxes or a decrease in consumption taxes will all increase in the
price of leisure and cause households to work more (take less leisure) resulting from a
substitution effect. We still have to consider the income effect.
Equation 2: Income Effect (driven by the budget constraint)
The households (static) budget constraint can be expressed as:
P(1  tc )C  W (1  tn ) N + X
We assumed a static model (people work and consume today with no regard to the
future). Again, we will relax this assumption next week in our consumption lecture. But,
in a static model, people will consume all their income within a period (there is no need
to save when you only care about today). We assume households have two types of
income – their labor earnings which equal the after tax wage times the amount they work
(N) and all other income (which could be asset income, transfers not linked to labor
supply, etc.). In this equation, all other (non labor) income is subsumed in X. Again, the
static budget constraint says that households will consume everything they earn.
For consistency, let’s set express the budget constraint in real terms such that:
 X 
 W   1  tn 
C   
N 

 P   1  tc 
 P(1  tc ) 
(2)
The income effect will come from changes in the real wage, changes in the tax
component, or changes in the real value of non-labor income (like stock market run ups –
we will discuss this example below). The income effect says that if real wages increase,
we will be richer for every hour we worked. This means we “consume” more of all the
goods that make us happy: in our macro world, those goods are leisure and consumption.
As a result, the income effect says that we will take more leisure (and by definition work
less) if real wages increase. A similar income effect would be generated if labor income
taxes fall, consumption taxes fall or non-wage income (X) increases.
Accounting for both effects
If real wages permanently change, both the substitution effect and the income effect
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.>>
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What happens to hours worked when real wages increase (holding taxes and X constant)?
Substitution effect on labor supply says that as real wages increase, you will work more
(leisure is more expensive so you will substitute away from leisure).
Income effect on labor supply says that as real 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? It depends on which effect is stronger - theory does not
give us any guidance as to which effect is bigger.
Representing the Labor Supply Curve
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, how it responds to changes
in the before tax real wage (W/P)). As we discussed above (and in class), 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 will represent the slope of the labor supply curve as being due to the substitution
effect. The substitution effect from changing tc or tn (which are embedded in equation (1)
above) will be SHIFTERS of the labor supply curve. Additionally the income effect
from changing after tax wages will also be SHIFTERS of the labor supply curve.
Let me pause for a second and draw your attention back to equation (1). There are two
separate components of the price of leisure that results in substitution effects. First, there
is the before tax real wage (W/P). Second, there is the tax component. In our class, the
first substitution effect (the change in W/P) will be the SLOPE of the labor supply curve.
The second substitution effect (changing the tax component) will be a SHIFTER of the
labor supply curve. Sometimes a substitution effect will move you along the labor
supply curve (when W/P changes). Sometimes a substitution effect will shift the labor
supply curve (when either tn or tc) change.
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Let’s graphically illustrate the labor supply curve:
Ns(PVLR, tn, tc, population, Value of
Leisure,)
W/P
N
Notice - we separated out the current real wage (W/P) and the present value of life time
resources (PVLR). PVLR is basically all the resources that you will earn over your
lifetime in present value terms. This includes the current real wage and all future real
wages that you earn plus any non wage income that you earn. In other words, PVLR
represents the income effect. If your life-time resources do not increase, 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. So, for the
rest of the class, we are going to assume that temporary changes in wages have no
income effect (by definition). We discussed this concept in much greater depth in class.
Two other things shift the labor supply curve:
1. Population – As more people are working, the labor supply expands. Thus,
the labor supply curve shifts right. The reason that the labor supply curve
shifts right is that there are more people working. This is not an income effect
nor is it a substitution effect. The initial shift is simply due to the fact that
more people are working. Now – as we saw in class, this initial shift in class
will result in both substitution effects (movement along curves are real wages
change) and income effects (additional shifts in the labor supply curve as
PVLR changes).
2. Value of Leisure - As welfare programs become more lucrative or as our
preferences for working decrease (for some other reason besides changes in
taxes or real wages), we will work less. This is represented as shift in the
labor supply curve.
It is interesting to think about how changes by
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Congress to the unemployment insurance program during this recession may
have affected the labor supply curve.
To recap: The labor supply curve shows the representation between real wages and
hours worked holding PVLR, population, the value of leisure, consumption taxes (tc)
and labor income taxes (tn) constant. A change in any one of those variables will shift
the labor supply curve.
For example, an increase in labor income taxes will shift the labor supply curve left.
This initial shift is due to a substitution effect. As labor income taxes go up, the price
of leisure falls (because the government takes more of our wages). Holding before tax
wages constant, we will have lower after tax wages. As we take more leisure, we will
work less. Below, I graphically illustrate that example:
NS(PVLR0, tn1)
Ns(PVLR0, tn0)
(W/P)0
N1
N0
N
As labor income taxes increase, the labor supply curve will shift in (because of a
substitution effect). Holding before tax real wages constant, after tax wages will fall and
we will work less (from N0 to N1) in this example. As we will see below, this can also
lead to a change in before tax real wages (once we add in a labor demand curve). This
will result in another substitution effect which would be represented as a movement
along the new labor supply curve (as W/P changes).
Also, this could lead to a
permanent change in PVLR which would result in another shift of the labor supply curve
(due to an income effect).
Finally, you should be able to answer this question: 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 take less leisure (work more). The labor
supply curve slopes up because of the substitution effect on labor supply resulting from
the changing price of leisure (due only to the changes in W/P).
C)
Formalizing Labor Demand
The labor demand curve tells us how much labor firms want to hire at given wages (see
Topic 2 slides). The labor demand curve comes straight from the MPN. It tells how
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profit maximizing firms want to hire additional workers. Recall from your micro class:
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? The 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(A,K)
N
Anything that increases the MPN increases labor demand. An increase in N will not shift
the labor demand curve, but instead will cause 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.
Labor Market Examples
Below, I go through some examples of how changes in the economic environment affect
the labor market.
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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 - tn) and a consumption tax (i.e., sales
tax - tc). 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 (see equation (2) above). 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
Ns(PVLR0,tc1)
Ns(PVLR0, tc0)
W/P
(W/P)1
(W/P)0
1
z
0
Nd
Nz
N1
N0
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! The movement from N0 to Nz is the substitution effect resulting
from changing the taxes. The movement from Nz to N1 is the substitution effect
resulting from the change in W/P (which is a movement along the new labor supply
curve).
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 (after tax wages will
fall!). 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 (as after tax wages fall) - leisure is relatively more
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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 fewer 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, won’t 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 fewer apples when the price of apples
increases.
In summary, with a temporary increase in consumption taxes, real wages will increase
today and total labor (N) will fall today. With a temporary change, both real wages and
labor (N) will return to their original levels tomorrow.
What if it is a permanent change in consumption taxes? In that case, there will be an
additional income effect (PVLR will fall). We are permanently made poorer by the
increase in taxes. The income in this example is more complex - taxes increase and
wages increase. We care about “after tax income”. We went over this in class. Even
though before tax wages went up, after tax wages fell (we are paying more taxes for
consumption out of every dollar we earned). Given our after tax income has fallen, we
are poorer. This will cause the labor supply curve to shift right (we cannot afford to take
as much leisure so we must work more). This example is analogous to the income effect
associated with income taxes. As a result, I will defer the results of a permanent increase
in consumption taxes until after we have done a permanent increase in income taxes (the
implications will be exactly the same!).
B)
Income Taxes
Changes in labor income taxes are nearly the same as changes in consumption taxes.
Before we begin, we should pay attention to some fundamentals. The after tax wage =
(1- tn) * W/P.
On our vertical axis of the labor market is always the before income-tax real wage. To
see what happens to after tax real wages, we need to see what happens to the before real
tax wage and the tax rate when the income tax rate changes. Income effects are
determined by after tax real wages.
Like above, changes in income taxes have both an income effect and a substitution effect.
I am going to start by only focusing on the substitution effect (we will do the income
effect soon). Remember what you learned above - the substitution effect with changing
before tax wages causes us to move along a given labor supply curve (i.e., causes no shift
in the labor supply curve). With a substitution effect due to an income tax change, the
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labor supply curve will ACTUALLY shift. This is not inconsistent with what we learned
above. The substitution effect with changes in before tax wages are movements along a
labor supply curve - this is by definition - this is how we draw the labor supply curve.
The substitution effect with changes in after tax wages will cause a shift in the labor
supply curve (holding the before tax wage constant). This is a subtle difference. Try
hard to understand it. The reason is that the substitution effect in equation (1) is due to
the change in the tax component. So, even if before tax real wages are held constant,
after tax real wages will change because taxes change.
Let's start our example with a situation where there is no labor tax at all on the market
(initial situation is labor tax = 0). Putting a tax on labor will increase the relative price of
working - causing households to switch towards leisure (after tax wages fall, all else
equal, so people work less). As a result, the labor supply curve will shift in the left.
Let’s graphically illustrate this below. Suppose the original equilibrium was at point (0)
in the economy.
Illustration of Substitution Effect of Labor Tax
Ns(PVLR0,tn1)
new W/P
(before tax)
initial W/P
(before tax)
Ns (PVLR0, tn0)
1
z
0
new W/P
(after tax)
Nd
Nz
N1
N0
How far will the labor supply shift in? The labor supply curve will shift in by the amount
of the income tax change (this is a result from micro - if you do not know this, you should
review your micro notes). In other words, if there were no change in before tax real
wage, households would choose to work Nz. All of this movement would be due to a
substitution effect resulting from our desire to switch away from working as income taxes
rise (i.e., it is cheaper to take more leisure so we work less).
Who bears the burden of this tax? Even though workers are responsible for paying the
tax, it does not mean they will bear the full burden of the tax. This is another concept
from micro. Workers and firms will usually share the burden of the tax (workers will get
a lower after tax wage, firms will pay a higher before tax wage - both are made worse
off). In other words, the before tax wage paid by firms and the after tax wage received by
workers will BOTH change. The share borne by workers and firms depends on the
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elasticity of labor demand. The more elastic (flat) the labor demand curve, the more that
workers will bear the burden (ie, firms will only pay a slightly higher before tax wage
and workers will receive a much decreased after tax wage).
Back to our example above: The labor income tax will shift in the labor supply curve
(substitution effect). <<remember, we are only focusing on the substitution effect right
now, we will add the income effect analysis in shortly>>. As people choose to work less,
before tax wages paid by firms will actually increase (firms are going to have to pay
higher wages in order to get people to work). This is analogous to when the supply of
apples falls, the price of apples will increase. The key concept in the labor market is as
workers work less, workers become more valuable to the firm (diminishing marginal
product of labor). As a result, firms will be willing to pay higher wages to workers. This
will induce us to work a little more (a substitution effect resulting from the increase in
W/P – in this example, this is represented as the movement up the new labor supply curve
from z to 1).
The new equilibrium before-tax wage is where the demand curve intersects the NEW
labor supply curve. However, even though before tax wages increase, after tax wages
received by households actually fall. (The new equilibrium after tax wages is W/P(1-tn)).
It will be the difference between the before-tax wage and the amount of taxes paid. What
are the taxes paid? The difference between the new and the old labor supply curve.
After-tax wages actually fall from their initial level (point 0). Like a tax in micro - the
burden is split between workers and firms (based on the elasticities). The steeper the
labor demand curve - the greater the burden borne by the firms (prove this to yourself).
The burden borne by the firms is the difference between the new before tax wage and the
initial wage. The burden borne by the worker is the difference between the initial wage
and the new after tax wage.
<<Technical Note - for those econ geeks, the labor supply curve probably will not shift
left in a parallel fashion - it will both shift and pivot. I am assuming the labor tax rate
changes - This pivot caused by changing the rate just complicates the analysis - without
adding much - that is why I ignore the change in slope.>>
According to the substitution effect, putting a tax on labor (increasing labor tax rate) will
increase before tax wages - but will decrease after tax wages. If this is a temporary labor
tax, this would be the end of the story. After-tax wages will fall today, N will fall today,
Y will fall today (as N falls), before-tax wages will increase today - i.e., firms pay a
higher wage than they would otherwise (note: the difference between the before tax and
the after-tax wage is the taxes paid). Given that the tax is temporary, tomorrow, things
will return to the initial positions. Additionally, the temporary decrease in after tax
wages would have little effect on the present value of lifetime earnings so there wouldn't
be an income effect.
A look at the income effect with an income tax change
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Let's take things further. Suppose the labor tax increase is permanent. In this case, aftertax wages are permanently decreased (from the permanent substitution effect - this is
what we just went over in the above paragraphs). As a result, workers are permanently
poorer (again, before tax wages will rise and after tax wages will fall). The income effect
says that we will work more as a result of having less life time income (we can no longer
afford the things we like - one of the things we like is leisure).
In this case, the labor supply curve will shift to the right. How far? Depends! It depends
on whether the income effect is big or small. I will assume that the income effect is big
(although, it need not be). When the income effect is big, relative to the substitution
effect, we call this ‘income effect dominating’.
Illustration of Both Income and Substitution Effects of Labor Tax
Ns1
Ns
W/P
Ns2
1
0
new equilibrium
W/P (before
tax)
2
Nd
N
REMEMBER - both the income and substitution effects take place simultaneously
(As an exercise, you should be able to illustrate a permanent change in income taxes
where the income effect is small, i.e., the substitution effect dominates).
In this case, I made the income effect really big (the income effect is bigger than the
substitution effect; i.e. .. the income effect dominates). What do I mean by that? The
substitution effect says we will work less. The income effect says that we will work
more. When you add them together, total work increases (N increases between points 0
and 2). This means the income effect must be stronger. If this is the case, before tax
wage will fall. Given that the income tax increased, we know that the after tax wage
must have fallen as well (see above formula). NOTE: I do not illustrate the after tax
wage on this graph - it is very complicated once you add the two effects - but,
mathematically, we know the after tax wage had to fall given that before tax real wages
fell AND the income tax rate increased. The before income tax wage is always the
intersection of the labor supply curve and the labor demand curve.
A permanent increase in income taxes could increase output if households feel the need
to work more because the increase in taxes makes them poorer. The exact opposite
would occur if the substitution effect dominated - a tax increase could reduce total output.
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This is very interesting - (these are long term effects). We will talk about short-term
effects later in the class. But, we can start to analyze how a large tax cut could affect the
economy (good test question)!!!!
An Erik Extra: The Laffer Curve
The Laffer curve represents the relationship between tax rates and tax revenues (and, as I
will show you, economic growth).
T
(tax
Revenue)
0
1
tax rate (tn)
The tax rate in the economy can go from 0 (0%) to 1 (100%). Tax revenue (T) is the tax
rate (tn) times income (Y). From the supply side, we know that Y is a function of N (we
learned this in class). 1) If there is a 0 tax rate, the government will not receive any tax
revenues from the income tax. 2) If there is a 100% tax rate, the government will also not
receive any tax revenues from the income tax. This one is obvious once we think of our
labor supply model. People work in order to fund consumption. If the tax rate is 100%,
there is no benefit to working and the cost of leisure is free. Households will only
consume leisure in this case. If no one worked, N would be zero and Y would be zero.
If Y is zero, tax revenues would be zero (100% of zero is still zero). So, the Laffer curve
anchors tax revenues equal to zero at a tax rate of 0 and 100%. 3) As you increase the
tax rate up from zero (like a 1% tax rate), people will still be working (think of our model
above). So, you will get positive tax revenue. Increasing the tax rate up slightly from
zero will give us increasing tax revenue. 4) On the other side, if the tax rate was really
close to one (like 99%), some people would still choose to work (maybe not many, but
some may choose to). As a result, as you get closer to 1, the tax revenues collected gets
close to zero, but is still positive. Taking these four facts together, you get a curve that
looks like what I have drawn above. We call this the Laffer Curve. We will talk more
about this in the government lecture (I will give us some history on it). The curve has to
increase to the right starting from a zero tax rate and it eventually has to decline as you
get close a 100% tax rate. At some point on the curve, there must be a maximum (where
the tax rate-tax revenue relation stops being positive and starts being negative). One thing
that labor market analysis does not tell us is where the hump is in the above curve.
People try to estimate it (as an aside, nothing in theory says that the curve need by
globally concave – we just know the derivative going away from zero is positive and the
derivative going towards 1 is negative).
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Basically, the question is at what rate will decreasing the tax rate actually INCREASE
output (OR at what tax rate does the income effect stop dominating?). Kennedy cut tax
rates in the 60s and output increased. Reagan did in the 80s and tax revenues fell. Each
of these had other factors - we will talk about this in class in week 5. However, it is
theoretically possible to cut the tax rate and increase tax revenues.
C)
Growth in the Labor Force
This is a fun one from a policy perspective given the retiring of the baby boom
population. If the baby boom population starts to retire - the labor supply curve will shift
in, raising real wages (the work force will get smaller and the labor supply will shrink).
If this effect is temporary, then that is the end of the story. But, if it is a permanent effect,
the present value of lifetime resources will increase and the income effect will cause the
labor supply curve to further shift in. Both effects will cause real wages to increase.
From class, we saw that W/P = .7(Y/N). So, the retiring of the baby boom population
could actually drive up output per worker (interesting) - but, this likely would not explain
the rising output per person (the baby boomers are just retiring - not dying). There is a
difference between output per worker and output per person. Think to yourself what
happens to income when the baby boomers retire?
D)
Stock Market Run Up
Increases in wealth affect PVLR (you should think about this as an increase in X in
equation (2) above). There would be a large income effect that would shift the curve to
the left (the only substitution effect would be the movement along the new labor supply
curve) - the rest is obvious (if it is not obvious now - you should DEFINITELY re-read
these notes again.)
E.
More on Technology
We went over this in class extensively. Increasing TFP will shift labor demand. If the
effects are permanent, it will cause shifts in labor supply. Go back to the slides from
Topic 2. If the income effect dominates - N actually falls when A increases!
Does this imply that increasing TFP actually destroys jobs? No, No, No. The MPN
actually increases. When firms experience an increase in TFP, they want to hire more
workers (they want to create jobs). But, the increase in TFP makes wages go up and
people feel richer - so people choose to work less. Jobs are out there. Firms would like
to hire people at prevailing wages – pre-existing wage. If there was no income effect, N
would increase when TFP increases. It is the income effect that causes N to fall when
TFP increases (note that N need not fall if the income effect is small). People choose to
work less - jobs have not been destroyed. This is due to the complementarity between
TFP and N (see last week's notes on the MPN).
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One last thing: Suppose that when TFP increases, N actually falls (income effect
dominates). We know that W/P increases. So – given the Cobb Douglass production
function - we know that Y/N increases. But, do we know what happens to Y?
A increases. N falls. So, you think the effect on Y is ambiguous. This is not the case.
Intuitively, the only reason that N falls is because of a strong income effect. The only
way to have a strong aggregate income effect is if Y increases (i.e., aggregate income
increases).
Additionally, empirically, we know that A is procyclical (we defined
procyclical in class). When A increases, Y increases (or when Y increases, A increases it is hard to disentangle which way the causation is going -think about the capital
utilization rate).
III.
Unemployment in Europe vs. U.S./Japan
Before I begin, I want to define for some (and redefine for others) some unemployment
concepts.
There are 3 types of unemployment: frictional, structural, and cyclical
Frictional unemployment is the unemployment that occurs from optimizing behavior of
workers and firms. If you quit your job because you do not like it and switch to another
job, you are frictionally unemployed. Or, if your firm fires you because you do not have
the skills to work at the job, you will be frictionally unemployed. Frictional
unemployment basically results from bad matches in the workforce. We believe
frictional unemployment is good and essential to the economy. The better the match
between the worker and job, the more efficient the productive process.
Structural Unemployment is the unemployment that occurs when jobs exist in the
economy but people do not have the skills to fill them. In other words, the unemployed
have skills that are no longer necessary to the economy. Steel workers who were
unemployed in the 1970s were structurally unemployed. There were jobs in other
industries, but these steel workers did not have the skills to fill those jobs. We may think
that structural unemployment is sad, but as economists we realize that is necessary. The
economy evolves over time due to shifting comparative advantages. As a result, different
skill sets will be needed at different times. It will take some time for skills to catch up
with the available jobs. Structural unemployment is necessary to help allocate skills to
match the available jobs.
We think frictional and structural unemployment are efficient types of employment. We
call the sum of frictional and structural unemployment, the 'natural rate of
unemployment'. In other words, we always believe that some unemployment is optimal
(zero unemployment should not be a policy goal).
The third type of unemployment is Cyclical unemployment. This is when there are
people who have the desire and the skills to work at prevailing wages but there are no
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jobs available. Firms have a desire to produce, but there is not enough demand to support
the production. This is the type of unemployment that we are concerned with as
economists.
As we discussed in class, the unemployment rate is highly correlated with output. That is
because the cyclical component is highly correlated with output. When Y is low, demand
is low, and firms have to fire workers (or hire fewer workers). That means the
unemployment rate goes up when Y is low. From the production side of the class -this
makes sense. When N is low, Y will be low!!!
Unemployment and our labor markets:
It should be noted that there is no unemployment in the labor market model we
analyzed above. At all times, the demand for jobs = the supply of jobs. This is subtle.
Cyclical unemployment says that there are people who want to work at a given wage (if
they didn't they would be out of the labor force). If unemployment exists, there is no
labor demand for those workers who want to work. However, in our labor model,
supply always = demand. There is always some wage that clears the market.
We can see that some friction is necessary to cause unemployment in the real world
(otherwise, labor markets would always adjust and the demand for workers would exactly
equal the supply - every one who wants a job would get a job at the going real wage).
The friction that I like to believe exists is that firms do not like to cut nominal wages.
Suppose for now that p (the price level) is always fixed. In that case, if firms are afraid to
cut nominal wages (or real wages given that p is fixed), then we can get unemployment.
Firms feel that cutting wages will affect morale and that a decrease in morale will
actually prove too costly in terms of long term production. As a result, they do not allow
wages to fall. Consequently, firms do efficiently hire the correct amount of labor. Wages
will not adjust to clear the market. Let us illustrate:
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Illustration of Unemployment with a Friction in Labor Market
W/P
Ns
W/P (0)
0
1
Unemp
Nd(1)
Nd1
Ns(1)
Nd
N
Suppose that labor demand falls (TFP falls). We originally started at position 0 (with
equilibrium wage W/P(0)). The new equilibrium is at point 1. However, suppose firms
will not cut wages to get to the new equilibrium. In this case, wages will stay fixed at
W/P(0) even though the new equilibrium wage is lower. As a result, there will be
cyclical unemployment. Households who want to work at that wage (Ns(1)) are greater
than the amount firms that want to hire at W/P(0). There will be an excess supply of
workers.
In order to get unemployment in our labor market analysis, we need a friction.
Otherwise, the labor market clears. A model without frictions says that anyone who
wants to work can work at the prevailing wage. The lack of desire to cut nominal wages
is only one reason (As we will see later in the course, this is why some inflation is good p will increase and W/P will fall even though w stayed fixed helping to restore
equilibrium in the labor market).
Other wage frictions include minimum wage laws (wages cannot fall by some level).
Other frictions do not prevent W/P from adjusting but prevent N from adjusting. This is
most prevalent with unions. If unions restrict hiring, then unemployment can occur
(think about this, this could be a good test question!!!).
Unemployment and Europe
There are two parts to this - differences in equilibrium employment levels (N) and
differences in unemployment rates. There are large differences in average and natural
rates of unemployment between Europe and U.S/Japan. I used to show data on this in
class. I cut it out as other things (the 2008 financial crises) became more a salient part of
the class. But, you could still look up the facts – the non-recessionary unemployment
rates in the U.S. and Japan are much lower than most other European countries.
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There are definite differences in social programs (value of leisure) between U.S. and
Europe. More lucrative welfare payments will increase the value of leisure and cause the
labor supply curve to shift in. As a result, equilibrium N, and hence Y, should be lower
in Europe. It is. But, this does not explain the unemployment rates (well, it partially
does) because, if equilibrium is allowed to occur, everyone who wants a job will get one
at some wage.
There are two main reasons why, on average, unemployment is higher in Europe: the
existence of unions and the duration of welfare benefits. The first is a friction (see
above). Unions sometimes prevent wages from falling and restrict hiring - both of which
prevent equilibrium from occurring. Unions exist in the U.S, but they exist much more
on a larger scale in Europe. Many countries have centralized wage contracts. This will
add additional frictions driving up the cyclical unemployment - especially when the
economy is hit with a labor market shock. The second is a measurement issue. In the
U.S., unemployment insurance only lasts 1/2 year. In Europe, it is much longer. As a
result, more people spend time on unemployment driving up the number of unemployed
for any given shock.
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