Problem Set 3a

Thursday, 10/11/01

Starting Friday 10/12/01, problems 2 and 3 will be due in discussion. Problem 1 is not due because Dr. Schwab decided to skip the material in chapter 12.

Problem 2 - Do Problem 6 on page 176 in Mankiw. After economics class one day, your friend suggests that taxing food would be a good way to raise revenue because the demand for food is quite inelastic. In what sense is taxing food a "good" way to raise revenue? In what sense is it not a "good" way to raise revenue?

We know that if there are no taxes, no restrictions, no transportation costs, no transaction costs, and we let people do what they want to do, then we get to equilibrium. In this case, there is zero deadweight loss and we have maximum total surplus (total surplus = consumer surplus + producer surplus).

What causes deadweight loss? Anytime we somehow restrict the behavior of economic agents (whether they be producers or consumers) and prevent them from doing what they want, we cause deadweight loss. This is true regardless of who you are restricting and how much you have restricted them - there will be some deadweight loss for sure.

Now the thing to think about in the first part of this problem (Is it a "good" way to raise revenue?) is what determines the size of the deadweight loss. There are three things to consider here:

How far does the restriction push the agent from his equilibrium choice? - The equilibrium quantity is what the agent would like to do. A binding (this is important! It MUST bind to have any effect!) restriction will prevent the agent from doing this. The bigger the gap between what quantity the agent would like to pick and the quantity he actually ends up picking, the bigger the deadweight loss. To convince yourself of this, look at figure 8-6 in Mankiw on page 171. Note that the further the tax pushes actual quantity traded away from equilibrium quantity, the bigger that deadweight triangle gets.
How elastic is the demand curve? - Take a look at figure 8-5 in Mankiw on page 167. Why is this important? Because when a restriction is slapped on someone (doesn't matter who - remember economic incidence does not care about statutory incidence!), economic agents will try and dodge the tax by changing the amount they buy or sell. Remember: The bigger the gap between what quantity the agent would like to pick and the quantity he actually ends up picking, the bigger the deadweight loss. What determines how much someone changes their quanitity pick when they try to dodge the tax? You got it: elasticity of their curve.
How elastic is the supply curve? - Likewise, we have the exact same logic for suppliers. Suppliers will also try to dodge the tax by changing their behavior; changing the quantity they pick. Remember: The bigger the gap between what quantity the agent would like to pick and the quantity he actually ends up picking, the bigger the deadweight loss.

The bottom line is that something causes deadweight loss if and only if it makes people change what quantity they pick. This is what Dr. Schwab means when he talks about distortion - agents have control over what quantity they pick. If they don't pick the equilibrium quantity, then something is wrong and we don't get maximum total surplus.

The problem tells us that food demand is relatively inelastic. What will happen when a tax on food goes into effect? Does this cause a lot of change in what quantity of food will be traded? Why or why not? What does this tell you about how much deadweight loss this tax will cause?

The second part of the problem (Why might it not be a "good" idea?) has to do with the material Dr. Schwab skipped in chapter 12. This part wants you to think about issues of fairness.

How much food does a poor person need to eat? How much food does a rich person need to eat? Yes, I know it is possible to buy cheap food (oatmeal, frozen vegetables, etc) or expensive food (steak, lobster, etc), but in the end there is only so much money you can spend on food. The issue at hand is whether this tax is regressive or progressive. Let's go to the stuff in chapter 12 that got skipped:

Read the paragraph titled Vertical Equity on page 256.
Suppose everyone spends about the same amount of money on food each month - say $200. Ignore the fact that cheap and expensive food types exist for now.
What percentage of the rich (monthly income $20,000) person's income is being spent on food? One percent. What percentage of the poor (monthly income $2,000) person's income is being spent on food? Ten percent.
What percentage of the rich person's income is subject to the food tax? One percent. What percentage of the poor person's income is subject to the food tax? Ten percent.
Is this tax proportional, regressive, or progressive?

Problem 3 - Do problem 12 on page 12 on page 177 in Mankiw. This chapter analyzed the welfare effects of a tax on a good. Consider now the opposite policy. Suppose that the government subsidizes a good: for each unit of the good sold, the government pays $2 to the buyer. How does the subsidy affect consumer surplus, producer surplus, tax revenue, and total surplus? Does a subsidy lead to a deadweight loss? Explain.

Dr. Schwab said to be very methodical when attacking problems such as this. First, what you want to do is draw a diagram of this market and figure out what all the surpluses look like before the subsidy goes into effect.

Then the subsidy goes into effect. Make a second copy of your "Before Subsidy" diagram and then add the effect of the subsidy to create an "After Subsidy" diagram. Now figure out what all the surpluses and the tax revenue looks like.

Generally, this is what you want to do. Make a snapshot of the world before the policy, make a snapshot of the world after the policy and compare the two. This is exactly what Dr. Schwab did in class when he gave the example of the tax and its effect in the chapter 7 lectures.