Homework 3-
1. In Surburbia the demand and supply curves for gasoline are given by the following equations where P is the price per gallon and Q is the quantity of gasoline in gallons:
Market Demand: Q = 10,000 - 1000P
Market Supply: Q = 2000P + 4000
a. What is the slope of the demand curve? What is the slope of the supply curve?
b. What is the equilibrium price and equilibrium quantity of gasoline in Surburbia? Show your work in finding these answers.
c. What is the value of consumer surplus (CS) in this market? What is the value of producer surplus (PS) in this market? Show your work in finding these answers. In your answer be sure to include the units of measurement throughout your work.
d. Suppose that the government of Surburbia decides that less gasoline should be consumed in Surburbia due to concerns about climate change. The government decides to enact an excise tax so that the total consumption of gasoline falls by 3000 gallons from its equilibrium quantity. The government has asked you to advise them as to the size of the excise tax that will be necessary in order to achieve this goal. Assume that the only thing that changes in this market is the excise tax and also assume that this excise tax is levied on producers of gasoline.
e. Given the excise tax you calculated in (d): [Hint: you may find it helpful to do step (vii) before you tackle the rest of the steps!]
i. What is the total tax revenue that will be collected from this excise tax?
ii. What is the consumer tax incidence (CTI) equal to given this excise tax?
iii. What is the producer tax incidence (PTI) equal to given this excise tax?
iv. What is the deadweight loss (DWL) from this excise tax?
v. What is the change in consumer surplus due to this excise tax?
vi. What is the change in producer surplus due to this excise tax?
vii. Draw a diagram of the market for gasoline illustrating this excise tax. Make sure your graph is completely and carefully labelled!
f. Instead of the excise tax described in (d), suppose the government of Surburbia decides to approach the problem of too much gasoline being produced and consumed in Surburbia by targeting a particular price for gasoline. Suppose the government mandates that the price per gallon of gasoline must be $8 per gallon. How big must the excise tax be in order for the government of Surburbia to achieve their goal of the price of gasoline being $8 per gallon?
g. Given the excise tax you calculated in (f): [Hint: you may find it helpful to do step (vii) before you tackle the rest of the steps!]
i. What is the total tax revenue that will be collected from this excise tax?
ii. What is the consumer tax incidence (CTI) equal to given this excise tax?
iii. What is the producer tax incidence (PTI) equal to given this excise tax?
iv. What is the deadweight loss (DWL) from this excise tax?
v. What is the new consumer surplus given this excise tax?
vi. What is the new producer surplus given this excise tax?
vii. Draw a diagram of the market for gasoline illustrating this excise tax. Make sure your graph is completely and carefully labelled!
2. Consider the small country of Beachville. It currently has a closed fruit juice market, but its government is considering opening this market to trade. Currently the domestic demand and supply curves for fruit juice in Beachville are given by the following equations where P is the price per gallon of fruit juice and Q is the number of gallons of fruit juice in hundreds:
Domestic Demand for Fruit Juice: Q = 10 - (5/2)P
Domestic Supply of Fruit Juice: Q = (15/2)P
Currently the world price of fruit juice is $2 per gallon of fruit juice.
a. Given the above information, what is the equilibrium quantity and equilibrium price of fruit juice in Beachville? Show how you found your answer.
b. Given the above information, what is the value of consumer surplus (CS)?
c. Given the above information, what is the value of producer surplus (PS)?
d. Given the above information, what would happen to the value of consumer surplus (CS') if this market opened to trade? Provide both a verbal description of the effect of opening this market to trade as well as a numerical value.
e. Given the above information, what would happen to the value of producer surplus (PS') if this market opened to trade? Provide both a verbal description of the effect of opening this market to trade as well as a numerical value.
3. Smurfland is a small, closed economy. In Smurfland the domestic demand and domestic supply of pillows are given by the following equations where P is the price per pillow measured in dollars and Q is the quantity of pillows measured in thousands of pillows:
Domestic Demand for Pillows: P - 20 - Q
Domestic Supply of Pillows: P = 4 + .6Q
The world price of a pillow is $6.
a. What is the equilibrium price and equilibrium quantity of pillows in Smurfland given the above information? Make sure you provide the appropriate units of measurement and not just the numeric values in your answer.
b. If Smurfland opens its pillow market to trade what do you predict will happen? Use a verbal description here and in (c) you can calculate some specific values.
c. Suppose Smurfland opens its pillow market to trade. What will be the quantity of pillows supplied domestically? What will be the quantity of pillows demanded domestically? What will be the level of exports or imports to Smurfland once this market is open to trade? If you get fractional values, don't worry-just round to the nearest hundredth! (Hint: on this question and the next you will likely find it helpful to sketch a graph to guide your calculations.)
d. Suppose that Smurfland opens it pillow market to trade. How much does total surplus in this market increase by because of this decision? Provide all the steps and reasoning that is necessary to get this answer in the answer you provide.
e. Suppose that Smurfland opens its pillow market to trade but in addition it also implements a tariff so that the price of pillows in Smurfland once this market is open is $7.30. (Hint: you will find it helpful to sketch a graph of the market for pillows in Smurfland once this tariff is implemented.)
i. Given this tariff, determine the quantity of pillows domestically demanded in Smurfland.
ii. Given this tariff, determine the quantity of pillows domestically supplied in Smurfland.
iii. Compare the total surplus in the pillow market in Smurfland between the open economy outcome and the outcome with the described tariff.
iv. Given your answer in (iii) what could possibly justify the implementation of this tariff?
v. Calculate the deadweight loss (DWL) from the implementation of this tariff. Describe why there is a deadweight loss from the implementation of the tariff.
4. Cubville is a small economy and its market for sweaters is currently a closed market that can be described by the following domestic demand and domestic supply curves where P is the price per sweater in dollars and Q is the quantity of sweaters:
Domestic Demand Curve for Sweaters: P = 200 - Q
Domestic Supply Curve for Sweaters: P = 50 + (1/2)Q
Currently the world price of sweaters is $60 per sweater.
a. The government of Cubville has decided to open its sweater market to trade, but at the same time it has decided it must either implement a tariff or a quota such that imports into its market are equal to 60 sweaters. The government of Cubville has asked you to determine what level of tariff will be necessary to obtain this goal. The government will also need a thorough explication of how you determined this tariff and the government has also requested that you provide a graph illustrating the sweater market and this tariff.
b. The government of Cubville has requested that you also provide them with an alternative to the tariff. The government needs to know if they choose to use a quota rather than a tariff, how big does the quota need to be? Remember that the government wants these two potential policies to result in the same outcome. The government of Cubville needs a thorough explication of how you determined this quota and they also need a graph illustrating the sweater market with this quota.
c. If the government of Cubville implements the quota you recommend in (b), what is the maximum that a foreign importer of sweaters will be willing to pay for the right to import a sweater? Explain how you found your answer.
5. Tommy recently graduated from college and is now in the process of deciding where he wants to start his career. He has three job offers (!) for similar work and similar future opportunities, but each job offer is in a different city. Tommy has no strong geographic preference and his only goal is to select that job that results in his being financially best off. From his economics class Tommy knows that he needs to be thoughtful when comparing these offers. This is what he knows:
Job Offer #1: is for a job in Toledo that pays $40,000 for his first year of work (for convenience, let's refer to this as year 2015), guarantees him a 10% increase in his nominal salary for the second year (2016), and a 10% increase in his nominal salary for the third year (2017). After that his nominal salary will be adjusted so that his real salary stays constant.
Job Offer #2: is for a job in Miami that pays $42,000 for his first year of work (for convenience, let's refer to this as year 2015), guarantees him a 5% increase in his nominal salary for the second year (2016), and a 5% increase in his nominal salary for the third year (2017). After that his nominal salary will be adjusted so that his real salary stays constant.
Job Offer #3: is for a job in St. Paul that pays $48,000 each year for the first and second years (2015 and 2016), and a 3% increase in his nominal salary for the third year (2017). After that his nominal salary will be adjusted so that his real salary stays constant.
a. Let's start by simply analyzing the nominal values of these three job offers. Given the above descriptions fill out the table below so that Tommy can compare the nominal values of the offers he has. Once you fill out the table rank the options in terms of their nominal values. Show in the table how you computed these answers.
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Nominal Wage in 2015
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Nominal Wage in 2016
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Nominal Wage in 2017
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Toledo
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Miami
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St. Paul
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b. Tommy understands from his economics class that he needs to really consider real salaries rather than nominal salaries in making his decision about which offer to accept. Luckily for him we have data about the CPI projections for the next three years for each of these cities. The table below provides our best estimates of what the CPI for 2015, 2016 and 2017 will be in each of these cities.
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Projected CPI 2015
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Projected CPI 2016
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Projected CPI 2017
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Toledo
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100
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120
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130
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Miami
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110
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120
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130
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St. Paul
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120
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125
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130
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Use this information to complete the following table of real salary values for these three job offers. In the table, you should round your answers to the nearest whole number. Show in the table how you computed your answers. Once you fill out the table rank the options in terms of their real values. Which job offer should Tommy accept?
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Projected Real Salary in 2015
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Projected Real Salary in 2016
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Projected Real Salary in 2017
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Toledo
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Miami
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St. Paul
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c. To drive home the difference between the nominal and real values a bit more. Let's complete one more table using the data you have been given. Here is the table: make sure you show your work for how you computed your answers.
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Percentage change in nominal salary from 2015 to 2016
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Percentage change in nominal salary from 2015 to 2016
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Percentage change in real salary from 2015 to 2016
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Percentage change in real salary from 2016 to 2017
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Toledo
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Miami
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St. Paul
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6. Consider the market for a brand of designer jeans for which there are really no close substitutes. Suppose the demand in this market is described by the following equations where P is the price per pair of jeans and Q is the quantity of jeans:
P = 1000 - .8Q for Q less than or equal to 1000 and
P = 250 - .05Q for Q greater than or equal to 1000
What price and quantity should this jean company charge given the above information if the sole goal of the firm is to maximize their revenue? Explain how you found your answer.
7. Suppose you are given the demand curve
P = 100 - 2Q
where P is the price per widget and Q is the quantity of widgets.
a. Using the point elasticity of demand concept find the elasticity of demand when Q = 10. Show your work.
b. Using the point elasticity of demand concept find the elasticity of demand when P = 60. Show your work.
c. What do you predict will be the value of the elasticity of demand when P = 50? Explain your answer.
d. Using the point elasticity of demand concept find the elasticity of demand when P = 50. Show your work.
8. You know that the elasticity of demand using the arc elasticity formula is
and you know that the point elasticity of demand formula is
Point Elasticity of Demand = [-1/slope][P/Q]
See if you can prove that the arc elasticity formula can ultimately be manipulated to give you the point elasticity formula. Show your work.