course 2 - may 2000 #3 simple question

[palatka]

this question is pretty straightforward, but it seems like the answer given is wrong.....

3. the demand for books purchased from Internet booksellers is perfectly elastic. The Federal government institutes a sales tax on books purchased in this manner.

Which of the following will result?

a) the equilibrium quantity and equilibrium price will both decline. The sellers and the buyers will each pay a portion of the tax.

b) the equilibrium quantity will decline, while the equilibrium price will rise. The sellers pay the tax.

c) the equilibrium quantity will decline, while the equilibrium price will not be affected. the sellers pay the tax.

d) the equilibrium quantity will not be affected, while the equilibrium price will rise. the buyers pay the tax.

e) the equilibrium quantity will decline, while the equilibrium price will rise. the buyers pay the tax.

the answer states c is correct because the supply curve will be shifted upward. i never heard of the supply curve shifting up for a sales tax (it shifts for an excise tax, i know), i thought the demand curve always shifts down for a sales tax. shouldnt the answer be that the equilibrium price goes down and quantity decreases, and sellers pay all the tax (therefore its not one of the choices)......hopefully im not making a dumb mistake and missing something obvious....

[Dr T Non-Fan]

Look up the phrase "perfectly elastic." I don't recall what it means, but I'll fake it.
Working backward from the answer, I think it means a flat demand curve. I.e., Price is constant.

With a tax, the all-knowing suppliers realize that increasing the price is futile for this perfectly elastic good, so the supply curve shifts upward (which is also leftward) to convey an increase in the cost (not the price) of the good. Result is that sellers decrease quantity and in effect pay for the tax.

[ASA_Woman]

yes, perfectly elastic demand means a flat demand curve

[bg23516]

I've answered this question more times than I care to remember. Here's a chunk of a letter I wrote to Peter Murdza from CSM. As for your comment, remember, a sales tax is equivalent to an excise tax.

Enjoy:
The way I see it, C is really the only answer that seems to make sense. Drawing the graphs isn't necessarily going to be accurate, since depending on whether you impose the tax as excise or sales, you get different results. I just used the definitions and got the SOA answer.

Perfectly elastic means that ANY change in price will result in an infinite change in quantity demanded. If price increases even by a penny, Qd drops to zero. Similarly, if P decreases by a penny, Qd becomes infinite.

We draw this as a horizontal demand curve. Assuming an upward sloping supply curve, we have to look at it this way:
If a sales tax is imposed, the producer will have to take the entire burden of the tax, otherwise, it will sell ZERO units, because if it passes even the smallest percent of the burden on to the consumer, the consumer demands zero units. So the seller faces the entire burden of the tax. Because of this demanders will pay the same price as before. However, knowing that the producer will have to pay the entire tax, we know that it's profit maximizing output will decrease to account for the tax. So you obtain the answer C.

Note that this is also the answer that you get if you draw this as an excise tax, which we know has the same economic incidence as a sales tax. I'm not sure why drawing this as a sales tax doesn't produce the answer that matches the theory. My only guess is that when you draw it as a sales tax, the new lower price is the price to sellers. It can't be the price to demanders, because by definition, any price increase to demanders will mean that zero quantity will be demanded.

Also, this occurs if you analyze the general case of linear demand and supply. Given the following eqns:
Demand: P = a - bQ
Supply: P = c + dQ

General solutions for equilibrium P & Q are:
Q* = (a - c) / (b + d)
P* = (ad - bc) / (b + d)

In this case, we have b=0, as P=a is our flat demand curve.
So P*=a and Q*=(a-c)/d

The imposition of a tax affects the value of c, making it c + t. However, we can see that after tax,
P*=a and Q* = (a-c-t)/d

So, after tax we have a decrease in Q* and price unchanged.

That's my take on the subject. It's supported by theory and by the mathematics. For reference, the general derivation cited above is from Mathematical Economics, by Baldani, Bradfield, and Turner.

[palatka]

i didn't have a problem with the perfectly elastic demand curve part, but i think they meant to put excise tax instead of sales tax. you are correct when you say the economic incidence is the same for an excise tax and sales tax. but in both cases the equilibrum prices are not the same. if the demand shifts downward for a sales tax, the new equilibrium price is the price to suppliers, while for an excise tax the supply curve shifts up and the new equilibrium is the price that demanders pay (see exhibit 1-10 in landsburg) a sales tax should never cause a supply curve shift....in this question, the flat demand curve should shift downwards (a perfectly elastic demand curve does not mean that it can't shift) in the amount equal to the tax, which leads to a lower price that suppliers get (equilibrium price) and a lower quantity produced. consumers still pay the same price as before the tax (new equilibrium price + sales tax). therefore i believe that the answer isnt listed in the choices....

[bg23516]

I'm not sure what the problem is. The question asks for the effect on price and quantity. Well, the price is unchanged. Just because it says sales tax, that doesn't automatically imply that the demander pays it. In most cases, the tax burden is shared. So it's merely a technicality. The importance is the economic impact.

[palatka]

http://members.aol.com/act4ary/micro.jpg
i've done so many of these types of problems in my econ classes before, you have to be able to show what happens with a drawing. i dont know how other schools econ classes are. but we do a lot of theory at our school, and i've never had an econ classes where we didn't use diagrams.... sorry for my poor drawings. i just did it quickly in photoshop using my mouse.

anyways the first graph is what the original supply and demand curves look like. after the tax is set, the demand curve shifts downward by the amount of the tax. before the tax, equilibrium price was P1 and quantity was Q1. after the shift, the NEW equilibrium price is Pe, and quantity is Qe. Pe is the price that suppliers recieve. consumers, actually end up paying Pe plus the tax which ends up to be P1. PRICE THAT CONSUMERS PAY IS UNCHANGED but that is not EQUILIBRIUM price (i'm pretty sure i think). the supplier takes all the burden of the sales tax (see landsburg chapter 1 and effects of taxes part) the only time suppliers and demanders share the burden of the tax is when supply and demand curves are NOT perfectly inelastic or elastic....so, as you can see equilibrium price and quantity both drop in this case.

the way i think the SOA did it was in the picture below which shows the excise tax. supply curve shifts up by amount of excise tax and the effect is that equilibrium price stays same but equilibrium quantity decreases.....i didn't label this too much but you get the point.....
http://members.aol.com/act4ary/micro2.jpg
i hope someone who knows micro well can tell me if i'm right or not...its such a simple problem that i dont see how they could have messed it up. if they specified price that demanders (or consumers) pay instead of equilibrium price in the question, then i would agree with their answer.

[bg23516]

I understand what you are saying. But using a drawing is far from dealing with the theory behind the problem. You understand the theory; that's obvious. Everything else is completely irrelevant.

You've shown that the drawing is not going to give the proper answer. By drawing it as a sales tax, we find that equilibrium price and quantity deline. But that CONTRADICTS theory. We know what will happen. So we IGNORE the diagrams, and go with what we know. We know that economic incidence will be the same as an excise tax. So try drawing it as an excise tax. You did. You got the right answer. You don't need to draw anything.

The question is far from flawed. It asks what happens when the sales tax is levied. If you understand the theory, which you do, you realize what happens.

You've asked for someone who knows micro well to explain this. You've gotten responses from myself and DTNF. I'm not sure where the confusion lies. I made the mistake of using graphs the first time I did this problem. My results made no sense, as I had the same graph as you did with the lower demand curve. So I threw out the idea of graphs. The don't always work.

If you want to think of it another way, just think of "equilibrium price" as price paid by the demander. Then it works out fine. The demander pays the same price, regardless of the tax. So equilibrium price doesn't change.

[palatka]

i understand everyones point, and wasn't claiming your reasonings were wrong. i agree with them. i guess to put it simply i was confused by the use of "equilibrium" price and was hoping someone would agree with me that whoever wrote the question should have been more specific (or maybe im just unaware that equilibrium price is always referring to the price the demander pays) . if you go by landsburg's examples, new equilibrium price after sales tax is price to suppliers, while for an excise tax, new equilibrium price is price to demanders. the drawings are definitely correct and you can use them to prove the answer (as long as you know if they are asking about change in price to demanders or suppliers) i just thought that they should have specified price to demander instead. anyways thanks for the input.

[Bama Gambler]

i attended the neas seminar in chicago. according to gary blumsohn (he taught the economics part) this question is defective. in other words, none of the answers are correct.

bama gambler

[Dr T Non-Fan]

Your second set of graphs is correct. The cost of the good increases at all quantities. That means the supply curve shifts upward (or leftward).

[WQN]

The SOA exam person agreed with me just after the exam that this question is technically defective however C is the best answer of the five and therefore a student could get credit for it so they did not remove it from the exam. The other four are outright wrong however C is half right so it is the solution. This is how students were treated in May 2000.

[Macroman]

The SOA exam person agreed with me just after the exam that this question is technically defective however C is the best answer of the five and therefore a student could get credit for it so they did not remove it from the exam. The other four are outright wrong however C is half right so it is the solution. This is how students were treated in May 2000.

Sorry, but the question is in no way defective. As a student of economics I can tell you that answer C. is entirely consistent with economic theory. You may find it confusing because you don't understand it, but that does not make it defective, A couple definitions to help you out.

Equilibrium: that combination of sales price and quantity which causes the market to clear. This means that all product sellers wish to sell (at equilibrium price) and all purchasers wish to buy (again at the equilibrium price) would be traded.

Perfectly elastic demand means that consumers will not adjust the price they pay regardless of supply situation. The consumers will buy as much product as is offerred at the chosen price, but will not pay any more. If for some reason suppliers did not want to produce at the one price, the market would dry up.

Perfectly elastic demand would be a good model for the situation faced by an individual firm in a competitive market. The product with perfectly elastic demand has become a commodity like gasoline or grain.

The perfectly elastic demand model would not hold for a market or industry, but would represent the typical situation for a firm well.

[Dr T Non-Fan]

If the SOA can write defective questions, it can also be defective in identifying them.

[Bama Gambler]

[Macroman wrote]Sorry, but the question is in no way defective. As a student of economics I can tell you that answer C. is entirely consistent with economic theory. You may find it confusing because you don't understand it, but that does not make it defective, A couple definitions to help you out.

Equilibrium: that combination of sales price and quantity which causes the market to clear. This means that all product sellers wish to sell (at equilibrium price) and all purchasers wish to buy (again at the equilibrium price) would be traded.

Perfectly elastic demand means that consumers will not adjust the price they pay regardless of supply situation. The consumers will buy as much product as is offerred at the chosen price, but will not pay any more. If for some reason suppliers did not want to produce at the one price, the market would dry up.

Perfectly elastic demand would be a good model for the situation faced by an individual firm in a competitive market. The product with perfectly elastic demand has become a commodity like gasoline or grain.

The perfectly elastic demand model would not hold for a market or industry, but would represent the typical situation for a firm well.


[/quote]

First of all according to Landsburg a sales tax shifts the demand curve down by the amount of the tax. This obviously changes the equilibrium price thus eliminating answer C. You might want to reread Price Theory. Second of all, I mentioned in an earlier post Dr. Gary Blumsohn, FCAS (with his PhD in Economics) also claimed this is a defective question. I tend to agree with a Phd of economics vs. a "student" of economics. The correct answer (using the Price Theory Textbook) is the equilibrium quantity and price decreases and the economic incidence is on the seller (the legal incidence is on the buyer).

Bama Gambler

[Macroman]

Okay Bama,

I see your point now...sorry being a little rough and authoritarian there. I was looking at net price, which I think is a valuable simplification. I think that the text does in fact specify that legal incidence of sales tax is on the buyer so that the demand curve will shift to maintain a constant net price. Under that scenario the price and quantity will fall and the supply curve will not shift.

I think it is worth noting that the real world sales tax legal incidence is not necessarily on the buyer. In most states it is perfectly legal far the sellar to quote prices post-tax and remit the appropriate percentage to the taxing authority. If we really want to get rid of pennies, everyone could do this.

[Bama Gambler]

I totally agree, but the exam comittee should follow the text books. :D

[steven]

So "equilibrium price" is the money collected by the producer? (Isn't that what all the confusion over this question is about?)

[Macroman]

according to the definitions used in the textbook, the equilibrium price would be the price consumers are willing to pay. This problem actually has two equilibrium prices, one before and another after the sales tax is imposed.

Suppose we put some numbers to it to make it more understandable:

P0 = amt consumers are willing to pay = $1.10

Suppose the government imposes a 10% sales tax. Consumers will still pay only $1.10, but now $.10 goes to sales tax. A new equlibrium is established at a price of $1.00.

Result, producers now only sell the quantity that they wish to sell at a price of $1.00. The demand curve shifts downwar by $.10, the quantity supplied moves along the supply curve to a new equilibrium point. Equilibrium price and quantity therefore both decline (as stated earlier), but the total price paid by the consumer (payment to supplier plus sales tax) remains constant.