Homework 3-
1. You are given the following information about the demand for cars in Surburbia:
P = 1000 - 2Q
where P is the price per car and Q is the quantity of cars.
a. Using the above information fill in the following table:
|
Price
|
Quantity Demanded
|
Total Revenue
|
|
$100
|
|
|
|
$200
|
|
|
|
$300
|
|
|
|
$400
|
|
|
|
$500
|
|
|
|
$600
|
|
|
|
$700
|
|
|
b. If price changes from $250 to $275, total revenue ______ _______.
c. If price changes from $625 to $650, total revenue _________ _______.
d. The range of prices for which demand for automobiles is price elastic is ________________.
e. The range of prices for which demand for automobiles is price inelastic is ___ ____________.
f. If the goal of the car producers in Surburbia is to maximize their revenue, they should sell __________ cars at a price of _____________ per car.
2. You know that the income elasticity of the product you produce is equal to -3.35. You read in the newspaper today that the economy has entered a recession and that incomes have decreased 10%. Describe the impact of this income decrease on the demand for your product. Make sure you describe the nature of your product in your answer.
3. The cross price elasticity of doughnuts and coffee is equal to -1.25. If the price of doughnuts increases from $1 to $1.25 per doughnut, what will be the percentage change in the quantity demanded of coffee?
4. Suppose that you know Sarah consumes 100 units of detergent when the price is $2 per unit. With each dollar increase in the price of detergent Sarah reduces her consumption by 20 units. Assuming that Sarah's demand curve is linear, calculate the price elasticity of demand if the price rises from $2.50 per unit to $3 per unit. Use the arc elasticity formula to make this calculation. Is demand elastic or inelastic in this part of the demand curve? Explain your answer.
5. Using the information given to you in problem (4), calculate the price elasticity of demand when the price of detergent is $3. Use the point elasticity formula to make this calculation. Is demand elastic or inelastic in this part of the demand curve? Explain your answer.
6. Suppose you are given the following information about the CPI , nominal wages, and real wages for five different cities.
|
Cities
|
CPI
|
Nominal Wage
|
Real Wage
|
|
Dallas
|
100
|
|
$50,000
|
|
Washington
|
|
$75,000
|
$50,000
|
|
New York
|
175
|
$87,500
|
|
|
San Francisco
|
140
|
|
$50,000
|
|
Madison
|
|
$40,000
|
$50,000
|
In addition you also know that you would be indifferent from a real wage perspective between working in New York or in Madison.
a. Examining the above table, what city is being used as the base year? That is, which city dollar is being used to measure the real wage?
b. Fill in the missing values in the table.
c. Suppose you live in New York and want your real wage to equal $75,000. What must your nominal wage be for you to earn this real wage?
d. Suppose you live in Madison and want your nominal wage to be $80,000. What is the real value of this nominal wage?
e. Which of the above cities has the lowest cost of living?
7. Use the information below to answer this set of questions.
|
Year
|
CPI
|
Nominal Income
|
Real Income
|
|
2004
|
25
|
$20,000
|
|
|
2005
|
50
|
$40,000
|
|
|
2006
|
80
|
$60,000
|
|
|
2007
|
100
|
$80,000
|
|
|
2008
|
150
|
$100,000
|
|
a. Fill in the missing cells in the above table.
b. From your information in part (a) fill in the table below. After your calculations identify which year provided the greatest increase in percentage terms in nominal income and which year provided the greatest increase in percentage terms in real income.
|
Year
|
% Increase in Nominal Income
|
% Increase in Real Income
|
|
2004
|
---
|
----
|
|
2005
|
|
|
|
2006
|
|
|
|
2007
|
|
|
|
2008
|
|
|
c. What is the base year in the first table? Explain how you picked the base year from the given data.
d. Given the first table complete the following table.
|
Year
|
Rate of Inflation based on initial values for CPI
|
|
2004
|
---
|
|
2005
|
|
|
2006
|
|
|
2007
|
|
|
2008
|
|
e. Fill in the missing values in the table below.
|
Year
|
CPI initial base year
|
CPI base year 2004
|
|
2004
|
25
|
|
|
2005
|
50
|
|
|
2006
|
80
|
|
|
2007
|
100
|
|
|
2008
|
150
|
|
f. Given the information from part (e) fill in the table below.
|
Year
|
Rate of Inflation based on CPI with base year 2004
|
|
2004
|
---
|
|
2005
|
|
|
2006
|
|
|
2007
|
|
|
2008
|
|
g. Compare the rates of inflation you found in parts (d) and (f). Are they different? Explain your answer.
8. Suppose that the market for gasoline is given by the following equations:
Market Demand: Q = 50,000 - 2500P
Market Supply: Q = 10,000P
where P is the price of gasoline per gallon and Q is the number of gallons per day.
a. What is the equilibrium price and quantity in this market?
b. At the equilibrium you found in part (a), what is the value of consumer surplus? What is the value of producer surplus?
c. Suppose that the government thinks that gasoline consumption is too high. Suppose the government wishes to decrease gasoline consumption by 20,000 gallons per day. How big an excise tax would need to be imposed in this market in order for the government to reach its goal?
d. Given the excise tax you calculated in part (c), what is the value of consumer surplus with the excise tax? What is the value of producer surplus with the tax? What is the value of tax revenue with this tax? What is the value of consumer tax incidence with this tax? What is the value of producer tax incidence with this tax? What is the value of the deadweight loss with this tax?