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Behavior and Choice: EC 102

Andrew Monaco

Exercises 1.7 Practice Problems

Subsection 1.7.1 Constructing demand

  1. Is a consumer’s willingness to pay (WTP) the maximum price she would pay for a good or service, or her minimum price she would be willing to pay for a good or service? Explain in words, and support your answer with an example.
  2. Give your willingness to pay for each of the following single items: a ticket to a Seattle Seahawks game; a cup of coffee; rent for a two-bedroom apartment in Tacoma. For each, describe the factors which influence your willingness to pay.
  3. Imagine you are grocery shopping, planning to buy some apples. What is the quantity of apples you demand when the price per apple is $3.50? $2.50? $2.00? $1.25? $0.75? Express your demand in a demand schedule, and draw your demand curve for apples.
  4. Consider Kevin, a consumer looking to purchase a new truck. He is only willing to buy a truck if the price of the truck is less than or equal to $24,000.
    1. What is Kevin’s WTP for the truck?
    2. Construct a demand schedule which identifies Kevin’s quantity demanded at prices of $30,000, $26,000, $22,000, $18,000, and $14,000.
    3. Draw Kevin’s demand curve given the above WTP.
    4. If the price in the market is $29,000, how many trucks will Kevin buy? [Extra from 1.4: What is Kevin’s consumer surplus?]
    5. If the price in the market is $21,000, how many trucks will Kevin buy? [Extra from 1.4: What is Kevin’s consumer surplus?]
  5. Consider Rosie, a consumer looking to purchase notebooks. She is only willing to buy one book if the price of the book is less than or equal to $15. Additionally, she is willing to purchase two books if the price of a book is less than or equal to $5.
    1. What is Rosie’s WTP for the first book? The second book?
    2. Construct a demand schedule which identifies Rosie’s quantity demanded at prices of $21, $16, $11, $6, and $1.
    3. Draw Rosie’s demand curve given the above WTP.
    4. If the price in the market is $12, how many books will Rosie buy? [Extra from 1.4: What is Rosie’s consumer surplus?]
    5. If the price in the market is $3, how many books will Rosie buy? [Extra from 1.4: What is Rosie’s consumer surplus?]
  6. Consider Alicia, a consumer looking to purchase notebooks. She is only willing to buy one book if the price of the book is less than or equal to $20. Additionally, she is willing to purchase two books if the price of a book is less than or equal to $10.
    1. What is Alicia’s WTP for the first book? The second book?
    2. Construct a demand schedule which identifies Alicia’s quantity demanded at prices of $27, $22, $17, $12, and $7.
    3. Draw Alicia’s demand curve given the above WTP.
    4. If the price in the market is $15, how many books will Alicia buy? [Extra from 1.4: What is Alicia’s consumer surplus?]
    5. If the price in the market is $8, how many books will Alicia buy? [Extra from 1.4: What is Alicia’s consumer surplus?]

Subsection 1.7.2 Individual demand to market demand

  1. Consider Alicia and Sadie, two consumers looking to purchase the newest Harry Potter book. Each consumer is only willing to purchase at most one copy of the book. Alicia is willing to purchase a book if the price is less than or equal to $25. Sadie is willing to purchase a book if the price is less than or equal to $19.
    1. Construct a demand schedule which identifies Alicia’s quantity demanded at prices of $30, $26, $22, $18, and $14.
    2. Construct a demand schedule which identifies Sadie’s quantity demanded at prices of $30, $26, $22, $18, and $14.
    3. Combining the two, construct a market demand schedule.
    4. On separate graphs, draw Alicia’s demand curve and Sadie’s demand curve.
    5. Combining the two, draw the market demand curve.
  2. Consider Alicia and Sadie, two consumers looking to purchase books. Alicia is only willing to buy one book if the price of the book is less than or equal to $20. Additionally, Alicia is willing to purchase two books if the price of a book is less than or equal to $10. Sadie is only willing to buy one book if the price of the book is less than or equal to $15. Additionally, Sadie is willing to purchase two books if the price of a book is less than or equal to $10.
    1. Construct a demand schedule which identifies Alicia’s quantity demanded at prices of $27, $22, $17, $12, and $7.
    2. Construct a demand schedule which identifies Sadie’s quantity demanded at prices of $27, $22, $17, $12, and $7.
    3. Combining the two, construct a market demand schedule.
    4. On separate graphs, draw Alicia’s demand curve and Sadie’s demand curve.
    5. Combining the two, draw the market demand curve.
  3. You are given the willingness to pay for a new pair of jeans for each of 5 consumers below. Given this data,
    \(WTP\)
    James $30
    Ben $55
    Eric $28
    Jody $10
    Spencer $40
    1. Construct a demand schedule given the prices: $45, $35, $25, $15.
    2. Draw the demand curve for jeans for these 5 consumers.
  4. EXPERIMENT: Can you think about demand by collecting willingness to pay data from a group of friends or family? Choose a good or service, and take a survey. Consider asking a few of these questions:
    • “What is your willingness to pay for this good or service?”
    • “What factors influence your willingness to pay?”
    • Come up with a change in the scenario or circumstances, and ask “What is your new willingness to pay?” Inquire why it has changed.
    With this data, you should be able to construct a demand schedule or demand curve! Summarize any patterns you identify in the quantitative data, and provide a recap of some of the demand parameters which influence demand for the good or service you have chosen.
  5. Consider a market with many buyers, where the demand function is given by \(Q_D = 400 - 10P\text{.}\)
    1. How many units are demanded at a price of \(P = 5\text{?}\) At a price of \(P = 20\text{?}\)
    2. Does the Law of Demand hold for this demand function? What mathematical sign in the demand function equation supports your answer?
    3. Carefully graph the demand function. What is its slope?
    4. d.).
      [Extra from 1.3: What if the demand function in this question shifted to \(Q_D = 450 - 10P\text{?}\) Carefully graph this new demand function. Is this a demand increase or decrease? What kind of demand parameter changes could bring about this shift? Give two examples.]
  6. Consider a market with many buyers, where the demand function is given by \(Q_D = 250 - 5P\text{.}\)
    1. How many units are demanded at a price of \(P = 10\text{?}\) At a price of \(P = 50\text{?}\)
    2. Does the Law of Demand hold for this demand function? What mathematical sign in the demand function equation supports your answer?
    3. Carefully graph the demand function. What is its slope?
    4. [Extra from 1.3: What if the demand function in this question shifted to \(Q_D = 150 - 10P\text{?}\) Carefully graph this new demand function. Is this a demand increase or decrease? What kind of demand parameter changes could bring about this shift? Give two examples.]
  7. Under what conditions (or assumption) would a stepwise demand curve be most appropriate to model a group of consumers? A smooth demand curve? Describe this distinction in words, and use two graphs to highlight the distinction.
  8. \(^{***}\)Consider the demand functions for three consumers: Andrew, Bart, and Claire. Andrew’s demand function is \(Q_A = 10 - P\text{;}\) Bart’s demand function is \(Q_B = 10 - P\text{,}\) and Claire’s demand function is \(Q_C = 10 - 2P\text{.}\)
    1. How many units does each consumer demand at a price of 4?
    2. Form the demand function for Andrew and Bart, \(Q_{AB}\text{,}\) by adding their demand functions together. When the price is 4, how many units do Andrew and Bart demand combined?
    3. Form the demand function for Andrew, Bart, and Claire, \(Q_{ABC}\text{,}\) by adding their demand functions together. When the price is 4, how many units do the three consumers demand combined?
    4. Calculate three inverse demand functions (solve for P as a function of Q): one for \(Q_A\text{,}\) one for \(Q_{AB}\text{,}\) and one for \(Q_{ABC}\text{.}\)
    5. Graph the three inverse demand functions. What happens to the shape of the demand curve as more consumers are incorporated?

Subsection 1.7.3 The Law of Demand and demand shifts

  1. Give the Law of Demand. How can the Law of Demand be observed in a demand schedule? On a demand curve? In a demand function?
  2. Name four different demand parameters. For each, describe the interaction between the demand parameter and any shift in demand.
  3. Consider a market with demand function \(Q_D = 100 - 4P\text{.}\)
    1. Carefully graph the demand function.
    2. What is the slope of the demand function?
  4. Consider a market with many buyers, where the demand function is given by \(Q_D = 300 - 10P\text{.}\)
    1. How many units are demanded at a price of \(P = 5\text{?}\) At a price of \(P = 20\text{?}\)
    2. Does the Law of Demand hold for this demand function? What mathematical sign in the demand function equation supports your answer?
    3. Carefully graph the demand function. What is its slope?
    4. What if the demand function in this question shifted to \(Q_D = 350 - 10P\text{?}\) Carefully graph this new demand function. Is this a demand increase or decrease? What kind of demand parameter changes could bring about this shift? Give two examples.
  5. Consider a market with demand function \(Q_D = 200 - 2P - P_R\text{,}\) where \(P_R\) is the price of a related good.
    1. How does an increase in the price of a related good shift the demand curve of a good?
    2. On one graph, draw the demand function above when \(P_R = 20\) and label it \(D_{20}\text{.}\) Make sure axes and intercepts are labeled.
    3. On the same graph, draw the demand function above when \(P_R = 30\) and label it \(D_{30}\text{.}\) Make sure axes and intercepts are labeled.
    4. What is the quantity demanded when \(P = 35\) and \(P_R = 20\text{?}\) When \(P = 35\) and \(P_R = 30\text{?}\)
    5. What does your graph tell you about the relationship between the two goods?
  6. Consider a market with demand function \(Q_D = 150 - 2P + P_R\text{,}\) where \(P_R\) is the price of a related good.
    1. How does an increase in the price of a related good shift the demand curve of a good?
    2. On one graph, draw the demand function above when \(P_R = 20\) and label it \(D_{20}\text{.}\) Make sure axes and intercepts are labeled.
    3. On the same graph, draw the demand function above when \(P_R = 30\) and label it \(D_{30}\text{.}\) Make sure axes and intercepts are labeled.
    4. What is the quantity demanded when \(P = 35\) and \(P_R = 20\text{?}\) When \(P = 35\) and \(P_R = 30\text{?}\)
    5. What does your graph tell you about the relationship between the two goods?
  7. For the demand curve \(Q_D = 50 - 5P + I\text{,}\) let \(I\) stand for income.
    1. What is the quantity demanded when \(I = 40\) and price is 5?
    2. Graph the demand curve when \(I = 40\text{.}\)
    3. What is the quantity demanded when \(I = 50\) and price is 5?
    4. Graph the demand curve when \(I = 50\text{.}\)
    5. Does a change in income shift the demand curve? If yes, what type of good is represented by this demand curve?

Subsection 1.7.4 Consumer surplus

  1. You are given the willingness to pay for a new pair of jeans for each of 5 consumers below. Given this data,
    \(WTP\)
    James $30
    Ben $55
    Eric $28
    Jody $10
    Spencer $40
    1. Draw the demand curve for jeans for these 5 consumers.
    2. How much consumer surplus is generated when the price is $35? Calculate and indicate consumer surplus on the graph.
    3. How much consumer surplus is generated when the price is $15? Calculate and indicate consumer surplus on the graph.
  2. Consider the demand function \(Q_D = 200 - 2P\text{.}\)
    1. Graph the demand function. What is the quantity demanded when \(P = 70\text{?}\)
    2. How much consumer surplus is generated when \(P = 70\text{?}\) Calculate numerically and illustrate on your graph.
    3. What is the quantity demanded when \(P = 20\text{?}\)
    4. How much consumer surplus is generated when \(P = 20\text{?}\) Calculate numerically and illustrate on your graph.

Subsection 1.7.5 Price elasticity of demand

  1. Give the definition of price elasticity of demand, \(\epsilon_D\text{,}\) in two ways: (1) using percentage changes; (2) using change in \(Q_D\) over change in \(P\) (\(\frac{\Delta Q_D}{\Delta P}\)).
  2. Does \(\epsilon_D\) have a positive sign or negative sign? Explain your reasoning.
  3. Compute the following numerical responses.
    1. If a 4% decrease in the price of potato chips generates a 12% increase in the quantity demanded, what is the price elasticity of demand for potato chips?
    2. If the price elasticity of demand for corn is -2, and there is a 5% increase in the price of corn, how will the quantity demanded change?
    3. If the price elasticity of demand for salt is -0.2, what size decrease in the price of salt would be needed to generate a 50% increase in the quantity demanded for salt?
  4. Whole Foods has decided to cut prices on many products, especially produce, after its acquisition by Amazon. For example, in its Austin, TX stores, it has cut the price of organic baby kale from $4 to $3, and the price of organic rotisserie chicken from $10 to $8. Source: \url{https://www.eater.com/2017/8/28/16214528/amazon-whole-foods-price-cuts}
    1. What is the percentage change in the price in baby kale? What is the percentage change in the price of rotisserie chicken?
    2. While quantity data hasn’t been reported yet, suppose the sale of baby kale in Austin Whole Foods stores increase from 1000 units to 1800 units. What is the percentage change in quantity demanded?
    3. Given your above answers, what is the price elasticity of demand for baby kale? How would you characterize demand for baby kale?
    4. Similarly, suppose the sale of rotisserie chicken in Austin Whole Foods stores increase from 200 units to 300 units. What is the percentage change in quantity demanded?
    5. Given your above answers, what is the price elasticity of demand for rotisserie chicken? How would you characterize demand for rotisserie chicken?
  5. Suppose the price elasticity of demand of eggs is -0.4.
    1. How would you characterize the elasticity of demand for eggs? Relatively elastic? Or relatively inelastic? Explain in words, and give at least one additional example of a good which would fall in this same category.
    2. If the price of eggs decreased by \(20\%\text{,}\) what would you anticipate to happen to the quantity demanded of eggs? Give a precise numerical answer.
    3. Now you notice that in response to the \(20\%\) price decrease for eggs, the quantity demanded of ham increases by \(25\%\text{.}\) What is the cross-price elasticity of ham and eggs?
    4. Additionally, you notice that in response to the \(20\%\) price decrease for eggs, the quantity demanded of bacon increases by \(15\%\text{.}\) What is the cross-price elasticity of bacon and eggs?
    5. What is the relationship between ham and eggs? Bacon and eggs? Is one relationship stronger than another? Explain using elasticity.
  6. Suppose demand is given by the function \(Q_D = 100 - 20P\text{.}\)
    1. Graph the demand function. What is its slope?
    2. What is the value of \(\frac{\Delta Q_D}{\Delta P}\text{?}\) Is this equal to the slope of the demand function?
    3. Substitute in your answer from b). What is the formula for \(\epsilon_D\text{?}\)
    4. Is \(\epsilon_D\) constant? Justify your answer by choosing two different points on the demand curve, and calculating the value for \(\epsilon_D\) at those points.
  7. Suppose demand is given by the function \(Q_D = 200 - 2P\text{.}\)
    1. What is the price elasticity of demand when \(P = 20\text{?}\)
    2. What is the price elasticity of demand when \(P = 60\text{?}\)
    3. What is the price elasticity of demand when \(P = 50\text{?}\)
    4. In general, what can be said about the price elasticity of demand when \(P > 50\text{?}\) When \(P \lt 50\text{?}\)
    5. Describe in words why price elasticity of demand varies from the top of the demand curve to the bottom. Be careful!

Subsection 1.7.6 Application: Price elasticity of demand and total revenue

  1. Define a firm’s total revenue with an equation. What does this represent?
  2. Does a firm generate more revenue when it increases its price? Explain.
  3. Does a firm generate more revenue when it lowers its price? Explain.
  4. What is the relationship between price elasticity of demand and the impact of price changes on total revenue?
  5. What is the relationship between price elasticity of demand and the maximum amount of total revenue a seller can make?
  6. If demand in a market is \(Q_D = 240 - 10P\) ...
    1. How much revenue is generated when the price in the market is \(P = 10\text{?}\) What is \(\epsilon_D\) at this point?
    2. How much revenue is generated when the price in the market is \(P = 15\text{?}\) What is \(\epsilon_D\) at this point?
    3. Graph the demand curve, and indicate the total revenue at \(P = 10\) and \(P = 15\) on this graph.
    4. Compute the equation of the total revenue curve, and graph this curve on a separate graph with \(TR\) on the vertical axis and \(Q\) on the horizontal axis.
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