## ECN Homework #4 (Elasticity Only)

ECN 150 - Homework #4 (Elasticity Only) Ryan Safner Spring 2016 Definitions Please answer the following questions briefly (1-2 sentences). 1. Define ...
Author: Joella Reeves
ECN 150 - Homework #4 (Elasticity Only) Ryan Safner Spring 2016

Definitions Please answer the following questions briefly (1-2 sentences). 1. Define price ceiling, price floor, and give an example of each. 2. Define a black market. Describe some of the goods that are typically found in black markets. 3. What is the statutory incidence of a tax? What is the economic incidence of a tax? How can they be different? What ultimately determines who ends up bearing the economic burden of a tax?

Conceptual Questions Please answer the following questions clearly and concisely (2-3 sentences). Use examples and/or give further explanation as necessary. 4. Answer the following questions about elasticity. I am looking for an intuitive answer for each, not a mathematical formula - these are to check your understanding of how and why we use the concept of elasticity. (a) What is the price elasticity of demand? (b) What does it mean for a demand curve to be more elastic? What sorts of things make demand more elastic? (c) What is the income elasticity of demand? Define normal goods and inferior goods in terms of elasticity. (d) What, in general (between two variables X and Y), does elasticity measure? (e) Why is using elasticity a more useful tool compared to drawing demand and supply curves? (f) How does knowing the price elasticity of demand help firms in making decisions about pricing their product? 1

5. For each of the following pairs, which of the two goods is more likely to be inelastically demanded and why? (a) Demand for tangerines vs. demand for fruit (b) Demand for beef next month vs. demand for beef over the next decade (c) Demand for Exxon gasoline at the corner of 7th and Grand vs. demand for gasoline in the entire city (d) Demand for insulin vs. demand for vitamins 6. For each of the following pairs, which of the two goods is more likely to be elastically supplied? (a) Supply of toothpicks or scotch whiskey (b) Supply of construction workers in Binghamton, New York, vs. supply of construction workers in New York State (c) Supply of breakfast cereal vs. supply of food (d) Original Van Gogh paintings or pencils 7. Henry Ford famously mass-produced cars at the beginning of the twentieth century, starting Ford Motor Company. He made millions because mass production made cars cheap to make, and he passed some of the savings to the con- sumer in the form of a low price. Cars became a common sight in the United States thereafter. Keeping total revenue and its relationship with price in mind, do you expect the demand for cars to be elastic or inelastic given the story of Henry Ford? 8. How might elasticities help to explain why people on vacation tend to spend more for food and necessities than the local population? 9. Two drivers, Tom and Jerry, each drive up to a gas station. Before looking at the price, each places an order with the attendant. Tom says, “I’d like 10 gallons of gas.” Jerry says, “I’d like \$10 of gas.” Who has a higher price elasticity of demand for gas? 10. On January 31, 1990, the first McDonalds opened in Moscow, capital of the then Soviet Union. Economists often described the Soviet Union as a “permanent shortage economy,” where the government kept prices permanently low in order to appear “fair.” An American journalist on the scene reported the customers seemed most amazed at the simple sight of polite shop workers...in this nation of commercial boorishness.”’ (Source). Why were most Soviet shop workers “boorish” while the McDonalds workers in Moscow were “polite?” 11. Antibiotics are often given to people with colds (even though they are not useful for that purpose), but they are also used to treat life-threatening infections. If there was a price control on antibiotics, what do you think would happen to the allocation of antibiotics across these two uses? 12. As we saw, taxes depend on elasticity. Decades ago, Washington, D.C., a fairly small city, wanted to raise more revenue by increasing the gas tax. Washington, D.C., shares borders with Maryland and Virginia, and its very easy to cross the

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borders between these states without even really noticing: The suburbs just blend together. (a) How elastic is the demand for gasoline sold at stations within Washington, D.C.? In other words, if the price of gas in D.C., rises, but the price in Maryland and Virginia stays the same, will gasoline sales at D.C., stations fall a little, or will they fall a lot? (b) Take your answer in part a. into account when answering this question. So, when Washington, D.C., increased its gasoline tax, how much revenue did it raise: Did it raise a little bit of revenue, or did it raise a lot of revenue? (c) How would your answer to part b. change if D.C., Maryland, and Virginia all agreed to raise their gas tax simultaneously? These states have heavily populated borders with each other, but they dont have any heavily populated borders with other states. 13. Someone argues that charging higher prices for goods during an emergency, such as a natural disaster, compared to the price before the emergency, is “price-gouging,” and should be illegal. [A diagram may help, but is not necessary to answer the questions.] (a) What are the causes of sellers charging these higher prices? (b) What would happen over time if it were legal to charge any price? (c) What would happen with an anti-gouging law that makes charging high prices illegal? (In effect, this is a price ceiling set at the original, pre-disaster, market price). (d) Why do you think these laws exist? 14. “Governments cannot raise tax revenues. They can only raise tax rates.” Is this true or false? What economic insight does this statement show? 15. If the government determined that it was in serious need of revenue and required a new tax to generate revenue, which is more likely to raise greater revenue – a tax on tablets, or a tax on clothing? 16. Junk food has often been criticized for being unhealthy and too cheap, enticing the poor to adopt unhealthy lifestyles. Suppose that the state of Oklakansas imposes a tax on junk food. (a) What needs to be true for the tax to actually deter people from eating junk food: Should junk food demand be elastic or should it be inelastic? (b) If the Oklakansas government wants to strongly discourage people from eating junk food, when will it need to set a higher tax rate: When junk food demand is elastic or when it is inelastic? (c) But hold on a moment:The supply side matters as well. If junk food supply is highly elastic–perhaps because its not that hard to start selling salads with lowfat dressing instead of mayonnaise- and cheese-laden burgers–does that mean that a junk food tax will have a bigger effect than if supply were inelastic? Or is it the other way around?

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(d) Lets combine these stories now. If a government is hoping that a small tax can actually discourage a lot of junk food purchases, it should hope for an (elastic/inelastic) supply and an (elastic/inelastic) demand. 17. Suppose that Maria is willing to pay \$40 for a haircut, and her stylist Juan is willing to accept as little as \$25 for a haircut. (a) What possible prices for the haircut would be beneficial to both Maria and Juan? How much total surplus (i.e., the sum of consumer and producer surplus) would be generated by this haircut? (b) If the state where Maria and Juan live instituted a tax on services that included a \$5 per haircut tax on stylists and barbers, what happens to the range of haircut prices that benefit both Maria and Juan? Will the haircut still happen? Will this tax alter the total economic benefit of this haircut? (c) What if instead the tax was \$20? 18. The Federal Insurance Contributions Act (FICA) tax for Social Security levies a tax of 12.4% of wages (up to a maximum of \$110,100) to be evenly borne by the employer and employee, each contributing 6.2%. Is the economic burden of this tax truly split between the employer and employee? Why or why not? 19. How do black markets allocate resources under price controls (e.g. a price ceiling on gasoline)? What are some inefficiencies of black markets?

Problems Please answer the following questions. Show all of your work and be sure to fully label all axes, points, and curves on any graphs (if applicable). 20. (a) Calculate the consumer surplus and producer surplus (in monetary value) for the following market, and indicate them on the graph. Which curve is relatively more elastic? Who earns more surplus in this market, consumers or producers? P(\$) 10

S

9 8 7 6 5 4 3 2 1 D 20 40 60 80 100 120 140 160 180 200

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Q t

(b) Now calculate consumer and producer surplus for the following market, with a very elastic demand curve. Who earns more surplus in this market, consumers or producers? P(\$) 10

S

9 8 7 6 5

D

4 3 2 1 20 40 60 80 100 120 140 160 180 200

Q t

(c) What does this show about the relationship between elasticity and surplus?

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21. This problem will demonstrate the relationship between price, quantity, price elasticity of demand, and total revenue. Take the simple demand curve from class (P = 10 − Q). P (\$) 10 9 8 7 6 5 4 3 2 1

A B

C Demand D 1 2 3 4 5 6 7 8 9 10

Q

(a) Calculate the elasticity between the points A (P=8, QD =2) and B (P=6, QD =4). Is this relatively elastic or inelastic? How responsive are consumers to the price change? (b) Calculate the total revenue at a price of \$8, and the total revenue at a price of \$6. Is the total revenue increasing or decreasing as we lower the price from \$8 to \$6? All else equal, is it a good idea for a seller to aim to lower their price in this fashion? (c) Now calculate the elasticity between the points C (P=3, QD =7) and D (P=1, QD =9). Is this portion of the demand curve relatively elastic or inelastic? How responsive are consumers to the price change? (d) Calculate the total revenue at a price of \$3, and the total revenue at a price of \$1. Is the total revenue increasing or decreasing as we lower the price from \$3 to \$1? All else equal, is it a good idea for a seller to aim to lower their price in this fashion? 22. Suppose there are two goods, A and B. As the price of B increases from \$3 to \$4, consumption rises of A from 100 to 120. Using the cross-price elasticity of demand, determine whether these goods are complements or substitutes. How much would consumption of A change if the price of B fell by 50%? 23. In 2013, WMATA raised the maximum fare for riding the DC Metro from \$5.00 to \$5.75. Partially as a result, ridership in 2013 fell from 218 million in 2012 to 209 million in 2013. (a) Estimate the price elasticity of demand for riding the metro. (b) What does your estimate say about the responsiveness of metro-riders to rate changes?

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(c) What does your estimate imply about the revenues of the WMATA when the fare rises? (d) Why might this elasticity be an unreliable guide for metro policy? (e) If you were to create a demand function from the data we have (assume a simple, linear demand function) what would the equation be? (f) Using your new demand equation, how many rides will consumers take when the fare is \$7.00? 24. On the graph below, draw the effects of a price ceiling on efficiency and welfare (consumer & producer surplus). Label all shaded regions, and describe is happening to each. P (\$) S

D

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Q t

25. Consumers have a relatively more inelastic demand for jeans compared to suppliers of jeans (see graph). Market for Jeans Price 20

S

18 16 14 12 10 8 6 4 2 D 0

2

4

6

8

10

12

Jeans (Millions) 14

16

18

20

(a) Calculate the (i) equilibrium price, (ii) equilibrium quantity, (iii) consumer surplus, (iv) producer surplus. (b) Now the government then levies a \$4 tax on Jeans, requiring producers to pay the tax. Draw the new tax, on the graph below. Calculate the new post-tax (i) quantity exchanged, (ii) gross price that buyers pay, (iii) net price that sellers receive, (iv) consumer surplus, (v) producer surplus, (vi) government revenue, (vii) deadweight loss. Show these on the graph. (c) Who bears more of this tax, consumers or producers? Why?

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26. American agricultural policy has drawn sharp criticism, not only from economists, but from other countries due to its negative impacts on international trade (which we will discuss in lesson 8). The 1933 Agricultural Adjustment Act, ruled unconstitutional by the Supreme Court in U.S. v. Butler (1938), paid farmers to destroy crops and livestock in order to raise the market price. After 1938, it was modified to create ”price supports,” which are a sort of hybrid between a price floor and a subsidy: First, the government creates a price floor for crops above the market price. Second, since this price floor creates a surplus of crops, the government purchases the entire surplus from sellers to take it off the market. This roughly constitutes the basis of our Farm bills today. (a) Assume the initial market price for corn is \$5.00 per bushel, and 5 million bushels are being exchanged. Calculate the consumer and producer surplus. Price 10

S

9 8 7 6 5 4 3 2 1 0

1

2

3

4

5

6

7

8

9

D 10

Bushels (millions)

(b) Now the government sets a price floor for corn at \$7 per bushel. Draw this on the graph above. (c) At \$7 per bushel, how many bushels to buyers want to buy, and how many do sellers want to sell? What is the result? (d) Next, the government purchases the entirety of the surplus. How much does the government have to spend? (e) Draw the welfare effects of this policy. Remember, that the government must spend taxpayer money to purchase the surplus. Label all shaded regions, and describe what is happening to each. Think carefully, this will be a little different than what we have seen in class. (f) Calculate the marginal benefit to producers (i.e. the additional producers sur-

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plus gained from this policy) and the marginal cost to consumers (i.e. the loss to consumer surplus from this policy). Compare the marginal cost to taxpayers of this policy with the marginal benefit (to producers). Is this policy worth it?

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