Exchange with Taxes

The table below shows the marginal values for product X for five different individuals, A - E. The values are all in dollars. This table will be used to answer questions 1 - 9. For each question, assume that all transaction costs are zero and that when indifferent, sellers will sell and buyers will buy the marginal unit. Read each question carefully and make sure you understand the market conditions before answering. All of the questions are worth 5 points.

TABLE I

1. At the start A has 10 units of X, B has 4, C has 7, D has 9 and E has 2.

a. what will be the equilibrium price? ____________

b. In equilibrium, how many units of X will each person own.? __

2. Start over again. Everything is exactly the same as it was at the start of question 1 except that the government now levies an excise tax on the sellers of X equal to $4 per unit of X sold.

a. What would the market price have to be in order to get A to sell 2 units of X? ____

b. What would the market price have to be in order to get B to buy 2 units of X? ____

c. If there is trade in this market with the government tax on X, what will be the equilibrium price? ____

d. How many units of X will each person own after trade? _____

e. How much of the tax per unit was the seller able to pass on to the buyers? ____

3. Start over again. Everything is exactly the same as it was at the start of question 1 except that the government now levies an excise tax on the buyers of X equal to $4 per unit of X sold.

a. What would the market price have to be in order to get A to sell 2 units of X? ____

b. What would the market price have to be in order to get B to buy 2 units of X? ____

c. If there is trade in this market with the government tax on X, what will be the equilibrium price? ____

d. How many units of X will each person own after trade? _____

e. How much of the tax per unit was the buyer able to pass on to the sellers? ____

f. How much total tax revenue did the government collect? ____

4. Compare the equilibrium in question 2 with the equilibrium in question 3.

a. How much, in total, did the buyers pay for each unit of X when the tax was levied on the buyer? ____

b. How much, in total did the sellers receive and get to keep for each unit of X they sold, when the tax was levied on the buyers? ___

c. How much, in total, did the buyers pay for each unit of X when the tax was levied on the sellers? ___

d. How much, in total, did the sellers receive and get to keep for each unit of X they sold, when the tax was levied on the sellers? ___

Elasticity

5. Consider individual B in the table above. There are no taxes. Assume that B has 0 units of X to start with.

a. What is the price elasticity of B's demand curve between the prices $24 - $22. ______

b. What is the price elasticity of B's demand curve between the prices $16 - $12? ______

c. What happens to B's total expenditure on X when the price goes from $24 to $22? ___

d. What happens to B's total expenditure on X when the price goes from $16 to $12? ____

6. Consider individual A in the table above. There are no taxes. If A has 10 units of X to start with,

a. What is the price elasticity of A's supply curve between the prices $24 - $22? _________

b. What is the price elasticity of A's supply curve between the prices $16 - $12? _________

7. This question concerns the incidence of an excise tax. Suppose that the government levies an excise tax of $1.00 per unit of X on the sellers of product X. Assuming the normal downward sloping demand for X and the upward sloping supply for X, some portion of this tax will be paid by the sellers and some portion by the buyers. Holding other things constant,

a. if the price elasticity of demand increases, the portion of the tax paid by the seller will __________ (increase, decrease, stay the same, not enough information to tell).

b. if the price elasticity of supply increases, the portion of the tax paid by the buyer will __________ (increase, decrease, stay the same, not enough information to tell).

c. if the price elasticity of demand increases, the total revenue the government will get from the tax will __________ (increase, decrease, stay the same, not enough information to tell).

d. if the price elasticity of supply increases, the total revenue the government will get from the tax will __________ (increase, decrease, stay the same, not enough information to tell).

Monopolies, Barriers to Entry and Open Markets

8. The table above shows the demand for product X facing a monopolist and his total labor costs for each quantity produced each year. For now, assume that there are no other costs.

a. Complete the table above and then draw a graph showing this producers average total cost, marginal cost, demand and marginal revenue

b. Assuming that this monopolist produces X, how many units would he choose to produce each year? ___

c. At the output rate chosen in b, what would be his yearly profit? _____

d. What do we know about the coefficient of price elasticity of demand between the output rate of 12 and 13.? ____

e. What is the marginal revenue over the segment of the demand curve in d?

9. This monopolist has a patent which gives him the exclusive right to produce X. This patent can be sold to another producer, who would then have the exclusive rights to product X. Assume that the profit that you calculated in question 1c can be earned each year, the patent protection lasts forever and the interest rate is 5%. There are a number of other producers of X who have the same production costs as our monopolist, however in order to produce and sell product X they will have to purchase the patent from the current monopolist. If they do buy the patent, they will become the monopolist producing and selling product X. (You will find some clues that will help you answer these next questions in the chapter on Alternative Market Structures in the "insight" box on Taxi Medallions.)

a. At what price would the patent sell? _____

b. Suppose that someone, person B, purchases the patent at the price determined in a. What will happen to this producers total cost per year? ______ If it changes, how much will it change? _____

c. What will happen to B's average total cost? ____ If it changes, how much will it change? _____

d. Draw this new average total cost curve in the monopoly graph you drew for 1a Label it.

e. Having just bought the patent, how many units of X will the new monopolist produce each year? _____

f. What price will the new monopolist charge per unit of X? ___

g. Given your answers to 9b, e and f, how much profit will B earn each year? ____

10. There is usually something that keeps potential competitors out of a profitable market. Very often, this "barrier" to entry is created by the government. In our example in question 9, the barrier was a patent. Suppose that this patent only lasts 17 years and then it expires. After this, anyone can enter the market and produce and sell product X.

a. Let us continue from question 9. The patent for X has just expired. There are other potential producers of X who have the same production costs as our monopolist. As these potential producers are attracted into the market by the profit, what happens to the market price of X? ________

b. At some point entry will stop. Describe the market conditions at this point. ____

c. Assuming a large number of competitors have entered the market for X, such that it is now a price takers market, what price would we expect for product X? ______

Property Rights.

There is a gas station that is currently selling gasoline to retail customers along a freeway in northern Indiana. Like most gasoline stations, the owner of this station stores his gas in underground tanks. Unfortunately, one of the tanks has a leak and 12 gallons of gasoline per year are seeping into the water table that empties into a well owned by a nearby resident. The table below shows the number of gallons of gasoline that are leaking each year and the total cost to the station owner of reducing or stopping the leak. For example, to reduce the rate of leakage from 12 to 11gallons per year would cost the station owner $6. To reduce the flow from 12 to 10 gallons would cost $20, and so on. The leaking gasoline creates harmful effects on the nearby resident by polluting his water supply. The table shows the total value of those harmful effects to the resident. For example, one gallon leaked per year imposes $3 in total harm to the resident: two gallons leaked per year imposes $21 in total harm, and so on. Unless told otherwise, assume that transaction costs are zero.

11. a. If nobody owned the exclusive and transferable rights to pollute the underground water, and there were no regulations on gasoline leaks, how many gallons of gasoline would the station owner choose to leak each year? _________

b. Why? ________________

c. What is the total harm that the chosen leak rate imposes on the resident? ____________

12. a. If the government adopted an anti-leak policy designed to minimize the harmful effects imposed upon the station owner and resident by each other's behavior. How many gallons of gasoline would the government allow the station to leak each year? _______

b. How much harm does this impose on the resident? _______________

c. How much harm does this impose on the station owner? _____________

d. What is the total harm this does to both individuals? _________________

13. a. Suppose the government assigns the exclusive, but not transferable, rights to pollute the ( water to the resident. How much gasoline will the station owner be allowed to leak each year?________

b. If the government assigns the exclusive and transferable rights to pollute the water to the resident, how much gasoline will the station owner be allowed to leak each year? __________

c. How much harm will this leaking gasoline cause in total to the station owner and the resident? ____

14. a. Suppose that the government changes its mind and gives to the station owner the exclusive, but not transferable, rights to pollute the water. How much gasoline will the station owner choose to leak each year? ____________

b. If the government gives the station owner the exclusive and transferable rights to pollute the water, how much gasoline will the station owner choose to leak each year? ___

c. How much harm will this leaking gasoline cause in total to the station owner and the resident? ____

Market Exchange and Price Controls

The table below shows the marginal values for product X for five different individuals, A - E. The values are all in dollars. This table will be used to answer questions 1 - 10. For each question, assume that all transaction costs are zero and that when indifferent, sellers will sell and buyers will buy the marginal unit. Read each question carefully and make sure you understand the market conditions before answering.

1. We will start by giving A and C 7 units of X and E will be given 5 units of X. B and D (5) will have zero units of X.

a. What will be the equilibrium price in a market consisting of these five individuals? ___

b. After trading at the equilibrium price, how many units of X will each person own? ____________________

2. Start over again with the same market conditions as in question 1 The government (5) believes that the price of X is too high because the sellers of X are greedy capitalist pigs, exploiting the poor buyers. Therefore the government puts a price ceiling on X at $24 that can be costlessly enforced such that no seller can receive a price greater than $24 for each X sold.

a. At the ceiling price, how many units of X would A, C, and E be willing to sell? _________

b. At the ceiling price, how many units of X would the buyers want to buy?

c. At the ceiling price, will their be a shortage or a surplus in the market for X? _________

3. One way to resolve the problem identified in question 2c is for the sellers of X to require (5) the buyers of X to purchase something else, a unit of Y, that is not price controlled. For each unit of Y that the buyers purchase, they will receive one unit of X at a zero price. Suppose that Y is nothing more than a piece of paper with the sellers "autograph" written on it. Since each unit of X is given away at zero price, this "tying" arrangement is legal.

a. What would be the market price of each autographed piece of paper? _______

b. How many autographs would each individual purchase? _______

c. How does the resulting equilibrium compare to the equilibrium in #1? In answering this, compare the price paid by the buyers of X (prices of X and Y) and the resulting quantities of X that each person owns after the trade.___________

4. Suppose the price control in question 2 can be enforced such that the sellers can receive (10) nothing of value in excess of the $24 per unit of X. The autograph scheme used in 3 is no longer legal. Assume that the government chooses to resolve the rationing problem by issuing 4 "ration coupons." Each coupon would entitle the holder to buy one unit of X at the price of $24. No individual can purchase X without a ration coupon and the coupon can only be used once to buy a unit of X. To start, the government gives the 4 coupons to individual B at no cost to B. The coupons can be bought and sold.

a. What would be the market price of each of the ration coupons? ________

b. At the price in 4a, how many ration coupons would each person purchase? ___

c. How many units of X would each person own after using the ration coupons to purchase X? ____________

d. What is the total price of X (coupon price + ceiling price) that each buyer paid for each unit of X? ___________