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Government in Microeconomics

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Public Choice Theory

You and I know the government provides some of the goods and services we consume (highways, air traffic control, etc…).

We have a democratic process and we often use a majority voting rule. This means which ever plan or candidate that gets the most votes wins.

Another place where some of this material is useful is when you are on a committee at work or in a civic group.

Remember that actions folks take have costs and benefits. It is generally conceded in economics that if a total benefits are at least as great as total costs then the actions enhance the well-being of society – what we call efficient.

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Majority voting problem IHere we consider some problems of majority voting. We use as examples situations with 3 voters. These relatively simple examples are designed to give you hints about more general problems. Another point is we will use $ amounts as a reflection of how much folks benefit from something.

Say government has a program with total cost of $900. 3 people value the good in total at $1150, where person A values at $750, person B at $250 and person C at $200. The program is efficient. But, if put to a vote where each person will have to pay $300 to cover the cost (they will be taxed), B and C will not vote for it._____So, majority voting sometimes leads to efficient goods not being provided. This would mean too little of the good is produced. (Can we make each person pay how much they value the good?)

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Majority voting problem II

Say government has a program with total cost of $900. 3 people value the good in total at $800, where person A values at $100, person B at $350 and person C at $350. The program is inefficient. But, if put to a vote where each person will have to pay $300 to cover the cost (they will be taxed), B and C will vote for it._____So, majority voting sometimes leads to inefficient goods being provided. This would mean too much of the good is produced.

Note: If too much (little) of a good is produced then too many (few) resources are allocated to that good.

In these two example the intensity of the consumer preference for the good is not totally seen. Each person has just 1 vote.

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Problems I and II again

In problem I person A likes the good so much they might be willing to pay some of B and C’s taxes to get them to vote for the plan. Can you bribe people to vote a certain way?

In problem II person A dislikes the good a lot, but will get stuck with it. Ultimately person A will have to pay $300 in taxes. I am not sure person A can pay off the others in this case not to vote for the good.

What we see here is that 1 person 1 vote sometimes is not in line with how much a person may like or dislike a good – what we call the strength of their preference.

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Attempts to overcome problems

Problems 1 and 2 above may be overcome in the following ways.

1) Interest group formation: folks with strong preferences may get together and organize a campaign of some sort to convince others of the merits of some good. The end result would be that others may increase their estimation of the good and in turn change their vote from a no vote to a yes vote.

2) Logrolling – this is a situation where if you vote for my cause I will vote for yours, or what is called the old quid pro quo. This method could lead to efficiency, but not always. You could have two proposals that are bad in general, but my vote for yours and yours for mine puts both over the top.

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Paradox of Voting

This is a situation were when we have 3 (or more) proposals for action we may not be able to rank the preferences consistently through paired-choice majority voting. This means we set up voting like a sports tournament where you have a vote of 2 proposals at a time.

This reminds me of a joke: A guy goes to a doctor and says doc it hurts when I go like this. The guy is wiggling his arm as he says it. The doctor says well, don’t go like that!

The point is don’t set up voting two choices at a time! Well some folks still want to do it that way. They may be ignorant of the paradox, or they may be trying to get what they want. Let’s see why it might be a problem.

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Paradox of voting

Proposal Mr. A.’s ranking Aunt B’s Ms. C’s

X 1 3 2

Y 2 1 3

Z 3 2 1

Election Winner

X vs Y X wins (A and C rank X over Y)

Y vs Z Y wins (A and B rank Y over Z)

X vs Z Z wins (B and C rank Z over X)

What is going on here? I have no idear! Really, let’s see on the next slide.

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Paradox of VotingOn the previous screen we have three proposals, X, Y, and Z. Plus, we have three people, Mr. A, Aunt B and Missy (get it?). Mr. A ranks the proposals as X being his highest rank or most preferred. This means he will always vote for it over Y or Z. Then he has Y his second rank, meaning he will always vote for it over Z. We have a similar story for the other two people.

Now, in an election of X vs Y X wins because A and C rank X over Y.

In an election of Y vs Z Y wins because A and B rank Y over Z.

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Paradox of Voting

Now since X is voted over Y and Y is voted over Z, then you would expect X to be voted over Z. This is a transitive property that holds in math, but maybe not here. But, Z will win a vote over X. This is a problem with the voting system.

To me the real problem is if in a system like this if they only vote on X vs Y and Y vs Z and then conclude the transitive property holds so X would win over Z and then go with X.

Another way to handle this might be to think about a sports analogy again. This time if a voter ranks a plan 1 give it 20 points, rank 2 give 15 points and so on. Then make the top choice the one with the highest points (We could still have a tie here).

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Tax on a market

Sometime the government, in an attempt to raise revenue will impose a tax on a market. Sometimes the tax is put on the consumer (like cars in Nebraska) or sometimes on producers (like on cigarettes in Nebraska).

Sometimes the tax is a lump sum per unit purchased (like 5 cents per gallon of gas) or sometimes the tax is a percentage of the dollar value of the product (like 7% of the purchase value of a house).

Here we will deal with a lump sum tax.

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A sales tax on consumers

P

Q

D1

P1

Q1

Say that at a certain time there is no sales tax on an item. Then if the price is P1, Q1 is the quantity demanded. We will consider a sales tax one where the consumer pays a tax directly to the government.

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A sales tax on consumers

With a sales tax not only does the consumer have to pay the merchant, but money must be sent to the government as well. The amount paid to the merchant is called the price of the product. The amount the customer ultimately takes out of their pocket for the product is the price plus the tax.Your first inclination, when I say the product now has a lump sum tax of 10 cents per unit on it, would be to say the demand curve should shift up by 10 cents - P is paid to the merchant and the tax is added on and paid to the government. Let’s look at how we really want to handle this situation.

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A sales tax on consumers

Without a sales tax the amount the consumer pays the merchant and the amount taken out of pocket are the same. What really matters to the consumer is how much is taken out of the pocket.Say P1=50 cents and Q1=2 cups of coffee per day. Then before a tax the consumer is willing to pay $1 per day for coffee.Now say a tax of 10 cents per cup is imposed on the consumer. But the consumer wants 2 cups of coffee when $1 comes out of the pocket. With this tax the only way this is going to happen is if the price per cup is now 40 cents.

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A sales tax on consumers

This doesn’t mean the seller will lower the price to 40 cents!!! It just means the consumer will not demand 2 cups unless the price is 40 cents per cup.Thus the demand curve shifts DOWN by the amount of the tax. In our analysis we like to draw the demand curve both before and after the tax.

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effect of sales tax on the demand curve

P

Q

D1D2

D1 = demand curve before taxD2 = demand curve after tax

Note1) If Pbt is the price before the tax the quantity demanded would be Q1.2) With the tax Q1 will only still be demanded if the price is Pat. Then the

Q1

Pbt = Pat +tax

Pat

consumer will still only have to take out of their pocket Pbt for Q1.

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excise tax

An excise tax is a tax on the seller of a product. We treat the tax as a cost of doing business. If there is no tax the seller will offer Q1 for sale when the price is P1. In other words the seller is indicating they need P1 to supply Q1.

Q

S1

P

P1

Q1

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excise taxIf a lump sum excise tax is imposed then the seller still needs to get P1 for their own efforts in order to supply Q1. This means the price in the market will have to be P1 plus the tax to supply Q1. Thus the supply curve shifts up by the amount of the tax.

Q

S1

P

P1

Q1

P2 = P1 + tax

S2

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Something seems weird about the sales tax and the excise tax when I compare the two.

The sales tax is paid by the consumer. So prices on the demand curve WILL NOT include the sales tax because consumers know after they take the item they will also have to pay the tax to the government. But, consumers only want to pay a certain amount for a good or service, regardless of taxes or not.

The excise tax is paid by the producer. So prices on the supply curve WILL include the excise tax because after the government gets the tax the suppliers still need to get the amount they want for the item sold.

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effect of sales tax on the market

P

Q

P2 + taxP1

P2

S1

D1D2

S1 = supply curveD1 = demand curve before taxD2 = demand curve after taxP1, Q1 = initial equil.P2, Q2 = new equil.

Note1) Q2 < Q1 - lower output2) P2 < P1 - lower market price3) Consumer pays P2 to the seller and pays a tax on each unit purchased to the government,the total paid per unit is P2 + tax.

Q2 Q1

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effect of sales tax on the market

4) Tax = P2 + tax - P1 + P1 - P2

Amount of increase in per unitpay out made by the consumer.

Amount of decrease in the per unit amountseller receives.

For tax incidence purposes we say both the consumer and the producer pay the tax!

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effect of excise tax on the market

P

Q

P3P1

P3 - tax

S1

D1

S1 = supply curve before taxD1 = demand curve S2 = supply curve after taxP1, Q1 = initial equil.P3, Q2 = new equil.

Note1) Q2 < Q1 - lower output2) P3 > P1 - higher market price3) tax = P3 - P1 + P1 - P3 + tax = P3 – P1 + P1 – (P3 – tax)

Q2 Q1

S2

increase in amount paidby consumer on per unit basis

decrease in amount seller keeps after the tax, per unit

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Comparing excise and sales tax

P

Q

S1

D1

Q2 Q1

S2

D2

If the excise tax and the salestax are of the same amount,but only one is imposed,we would end up at Q2.

Pd is what consumers takeout of pocket, Ps is what sellers keep and Pd - Ps is the tax(all on a per unit basis).

Pd

Ps

The economic incidence of a marketplace tax is independent of its legal incidence. In other words, sales or excise taxes have the same real impact on the market.

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Hey you ever heard of a wedgie, or what is sometimes called a herman? Well, I am not going to talk about that now. I wanted to talk about a wedge. In our supply and demand graph we have seen that when a per unit tax is imposed on the buyer the demand shifts down by the amount of the tax and when a tax is imposed on the seller the supply shifts up by the amount of the tax.

This vertical line here is the amount of the tax. I have shown my right hand as well because I am going to push the line with my hand into a supply and demand graph on the next few slides and WEDGE the tax into the S & D curves. Here goes.

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Q

P

S

D

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Q

P

S

D

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Q

P

S

D

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Q

P

S

D

So, you can see by the graph, when we wedge the tax into the graph we can see either the demand shifts down by this amount or the supply shifts up by this amount. We end up at the same market quantity and our story is the same as before.

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Deadweight loss of taxP

Q

P3P1

P3 - tax

S1

D1

Q2 Q1

S2

a b cd e f

Again, when an excise tax is imposed on a market the output falls from Q1 to Q2. This bums some people out.

The tax revenue in the market is made up of the areas a, b, d and e because you take the units sold, Q2, times the unit tax, which is the height difference between the two supply curves.

Consumers lose surplus a, b, and c and producers lose surplus d, e, and f.

The tax revenue gain can be thought of as offsetting part of the loss in surplus value. But c and f is still lost. Notice this area is above the reduction in output. It is called the deadweight lose of the tax and measures the amount folks are bummed out by the tax. This is similar to the deadweight loss of monopoly.