econs 305 - welfare...econs 305 - welfare eric dunaway washington state university...

EconS 305 - Welfare

Eric Dunaway

Washington State University

[email protected]

August 31, 2015

Eric Dunaway (WSU) EconS 305 - Lecture 4 August 31, 2015 1 / 51

Introduction

Today, we are going to discuss welfare, a method for measuring howwell o¤ society is.

When policy makers are trying to �nd the economic impact oflegislation, they almost always frame it in terms of a welfare analysis.


Economic Measurement

Before we get in to welfare, we need to talk about how well-being ismeasured in economics.

The most common way we measure well-being for an individual isthrough utility.

I am going to give a very brief overview on utility today, but we�ll betalking a lot more about it in a couple of weeks.

Utility is a measure of satisfaction that one obtains throughconsuming a good or a service.



A measure of satisfaction?

The problem with utility is that we don�t have a consistent scale formeasuring satisfaction.Formally, we measure the amount of utility a person obtains in "utils,"but still, the number itself is really meaningless.

How can you tell how many utils you get from eating a piece of pizza?Or how many utils the person next to you gets?

This is ok though in economics, because most of the time we reallydon�t care how much better one choice is than another; just that it�sbetter.



Utility is known as an ordinal measurement.

We are only concerned with the ranking of outcomes, not the actualvalues of those outcomes.

The opposite of an ordinal measurement is a cardinal measurement.

In these, the actual numbers, along with their distance to the nextalternative, matter.These are what we see more often in the real world.



Welfare (also knows as total surplus) is a cardinal measure ofwell-being.

We can actually �nd a dollar amount (in the case of the US) for howwell o¤ a consumer or �rm was made.We can take all the possible consumers and �rms, add up all of theirindividual surpluses, and have a value for the total welfare of society.

This is great for economists, because it gives us an easy way tocompare alternatives.

It�s also much easier for non economists (i.e., politicians) tounderstand.


Welfare

When we do economic modelling, we make several assumptions abouthow people behave based on unobservable factors, which may or maynot be correct.

Fortunately, we obtain welfare calculations from the Supply andDemand functions, which are generally observable.If we have data on a large population, we can �gure out how manypeople buy a good, given the price and their demographic data.


Welfare

How do we calculate welfare?

First, we need to �gure out how well o¤ each consumer and �rm areindividually, calculating their surplus.Then, we sum up all of the individual surpluses to get the total surplus,or welfare.

Let�s talk about consumer surplus �rst.


Consumer Surplus

Think of a bunch of people that all fall along the demand curve. Wewould sort them by their willingness to pay.

The person at the top of the demand curve would be willing to pay alot more for the good than the person in the middle or at the bottom.Everyone who buys, however, pays the same equilibrium price.

The di¤erence between a person�s willingness to pay and the actualprice they pay is their surplus.


Consumer Surplus

q

pD S

q*

p*


Consumer Surplus

q

pD S

q*

p*

Carl


Consumer Surplus

q

pD S

q*

p*

Carl

Surplus


Consumer Surplus

q

pD S

q*

p*

Lenny


Consumer Surplus

q

pD S

q*

p*

Lenny

Surplus


Consumer Surplus

q

pD S

q*

p*

Barney


Consumer Surplus

As we can see, both Carl and Lenny have a willingness to pay higherthan the equilibrium price. Thus, they purchase the good and thedi¤erence between their willingness to pay and the equilibrium price istheir individual surplus.

Barney, however, has a lower willingness to pay than the equilibriumprice. Thus, he does not purchase the good and recieves zero surplus.

To get the consumer surplus, we add up all of the individual surplusesof Carl, Lenny, and everyone else who falls on the demand curveabove the equilibrium price.

All of these lines added up should resemble a familiar shape.


Consumer Surplus

q

pD S

q*

p*


Consumer Surplus

q

pD S

q*

p*

ConsumerSurplus


Consumer Surplus

Fortunately, when demand curves are straight (which they will be forthis class) this is actually easy to calculate if we remember ourformula for the area of a triangle.

A =12base � height

In our scenario, the base would be our equilibrium quantity, and theheight would be the di¤erence between the vertical intercept of thedemand curve (pMAX ) and the equilibrium price.

CS =12q�(pMAX � p�)


Example

Consider the supply and demand functions

qS = p

qD = 10� p

Solving for the market equilibrium (practice this!), we would get

q� = 5

p� = 5


Example

To �gure out our verical intercept, we just need the inverse demandcurve, which we get by solving the demand curve for p

p = 10|{z}Vertical Intercept

�qD

Thus, we can calculate the consumer surplus as


CS =125(10� 5) = 12.5

and consumer surplus is 12.5 dollars.


Consumer Surplus

Note that the consumer surplus level will vary with the slope of thedemand curve.

The less steep the demand curve, the less consumer surplus.

With a �atter demand curve, consumers aren�t willing to pay muchmore above the market equilibrium price.

We are going to talk a lot about this later this week.


Consumer Surplus

q

pD S

q*

p*

ConsumerSurplus


Consumer Surplus

q

pD S

q*

p*Consumer

Surplus


Producer Surplus

Let�s look at the other side of welfare: producer surplus.Think of the supply curve having a whole spectrum of �rms, eachwith a di¤erent willingness to sell.

Some �rms are willing to sell at a very low price, which is representedat the bottom of the supply curve.Likewise, some insist on selling at a very high price, at the top of thesupply curve.

Since everyone sells for the same market price, the di¤erence betweenthe price received and the willingness to sell is the surplus for the �rm.


Producer Surplus

q

pD S

q*

p*


Producer Surplus

q

pD S

q*

p*

ProducerSurplus


Producer Surplus

We can also use the triangle formula to calculate the producer surplusfor straight supply curves.Like with consumer surplus, the base is equal to the equilibriumquantity, while the height is equal to the di¤erence between theequilibrium price and the vertical intercept of the supply curve(pMIN ). We can get pMIN by solving for the inverse supply curve

p = 0|{z}Vertical Intercept

+qS

which yields a producer surplus of

PS =12q�(p� � pMIN )

PS =12(5)(5� 0) = 12.5

and producer surplus is 12.5 dollarsNote: Consumer and producer surplus won�t always be the samenumber.


Welfare

All that is left is to put both consumer and producer surplus togetherto obtain the total level of welfare.

W = CS + PS = 12.5+ 12.5 = 25

and this market experiences a welfare level of 25 dollars.


Welfare

q

pD S

q*

p*

ConsumerSurplus

ProducerSurplus


Example

Let�s look at another example.

Consider the following supply and demand curves

qS = �6+ 2pqD = 12� p

Solving for the market equilibrium, we have

p� = 6 q� = 6


Example

D

S

q

p

6

6

12

3


Example

Looking at the �gure, we should expect that the consumer surplus ishigher than the producer surplus.

Let�s calculate it to �nd out.

Solving for our inverse demand curve,

p = 12� qD

Thus, our vertical intercept (pMAX ) is equal to 12 in this case.Applying the triangle formula,


=12(6)(12� 6) = 18


Example

For the producer surplus, we again solve for the inverse supply curve,

p = 3+12q

and our vertical intercept (pMIN ) is equal to 3. Again, applying thetriangle formula,

PS =12q�(p� � pMIN )

=12(6)(6� 3) = 9

Adding up the consumer and producer surpluses gives us our totalsurplus,

W = CS + PS = 18+ 9 = 27


Example

D

S

q

p

6

6

12

3

CS

PS


Dead Weight Loss

Great! Are we done?

Sure, if we just limit ourselves to single priced, perfectly competitivemarkets with no distortions.Those are pretty boring.

When markets become distorted, consumer and producer surplus areboth a¤ected. We also see the rise of a new factor in our welfarecalculations, dead weight loss.What if some external force pushed the equilibrium price up to p� = 7and kept it there without a change in supply or demand.

This can and will happen frequently later in the semester.


Dead Weight Loss

D

S

q

p

6

12

3

7

5


Dead Weight Loss

D

S

q

p

6

12

3

CS

PS

7

5


Dead Weight Loss

Let�s calculate the consumer and producer surpluses for this case.

The consumer surplus follows from the same as before. We just needto apply our triangle formula with our new equilibrium price andquantity.


=12(5)(12� 7) = 12.5

As we can see, the higher price has hurt the consumers. Not only arethey all paying a higher price, but some have left the marketcompletely.


Dead Weight Loss

The producer surplus, however, has changed in this case. It is nolonger a triangle, but a trapezoid. Recall that the formula for atrapezoid is

A =12(b1 + b2)h

where base 1 is the di¤erence between the price and the verticalintercept of the supply curve, and height is the quantity (same asbefore)

Base 2 is a bit harder to �nd.


Dead Weight Loss

D

S

q

p

6

12

3

CS

PS

7

5


Dead Weight Loss

To �nd base 2, we plug the market quantity into the supply anddemand curves and �gure out what the price would be.

5 = 12� pDpD = 7

5 = �6+ 2pSpS = 5.5

Then, we take the di¤erence between pD and pS .

b2 = pD � pS = 1.5

Intuitively, we just needed the length between the demand and thesupply curves at our market quantity.


Dead Weight Loss

D

S

q

p

6

12

3

CS

PS

7

5

pD

pS

b2


Dead Weight Loss

Thus, our producer surplus is

PS =12(

b1z }| {hp� � pMIN

i+

b2z }| {[pD � pS ])q�

PS =12(4+ 1.5)5 = 13.75

This producer surplus level is higher than what we calculated with nodistortions. Since we raised the price, each �rm is actually capturingmore of the surplus than before.

They are actually stealing surplus away from the consumers!Note also that some �rms dropped out of the market since there aren�tenough consumers buying anymore. It is possible that this loss couldoutweigh the gains made from the theft of consumer surplus, causingthe new producer surplus to be lower.


Dead Weight Loss

Adding up our new welfare level

W = CS + PS = 12.5+ 13.75 = 26.25

Notice that this welfare level is lower than what we calculated whenthere were no distortions, 27.

The distortion in the market has caused a loss of $0.75 of welfare.

The di¤erence between the undistorted welfare and the distortedwelfare is the dead weight loss.

DWL = WUND �WDIS = 27� 26.25 = 0.75


Dead Weight Loss

D

S

q

p

6

6

12

3

CS

PS

7

5

DWL


Dead Weight Loss

There is another way besides the di¤erence between the undistortedand distorted welfares to calculate the dead weight loss. We can use atriangle formula!

DWL =12(pD � pS )(q�UND � q�DIS )

where the two quantities are the undistorted and distorted equilibriumquantities. Plugging those numbers in,

DWL =12(7� 5.5)(6� 5) = 0.75

which is the same result that we got from before.


Dead Weight Loss

The only way for a market to be e¢ cient is if there is no dead weightloss.

Essentially, it has to be distortion free.

Unfortunately, almost every market in the world has some kind ofdistortion.

Thus, economists focus their policy recommendations on minimizingthe amount of dead weight loss that their policies cause.


Summary

Welfare allows us to calculate the total bene�t to society caused byequilibrium prices and quantities.

Distortions in the markets will lead to the creation of dead weight loss.

We like it when there is no dead weight loss, but it is oftenunavoidable in the real world.


Preview for Wednesday

We are going to talk about what happens when markets are regulated.

When is it in the government�s interest to cause distortions to themarket?


Assignment 4

1. Consider the following supply and demand functions

qS = �1+ pqD = 14� 2p

a. Find the equilibrium price and quantity.b. Calculate the Consumer Surplus, Producer Surplus, and total Welfare.c. Let p� = 6 (a market distortion). Calculate the Consumer Surplus,Producer Surplus, total Welfare, and Dead Weight Loss.


econs 305 - welfare...econs 305 - welfare eric dunaway washington state university...

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