978-1259723223 Chapter 4 Part 2

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Chapter 04 – Market Failures: Public Goods and Externalities

4-12

Feedback: Consider the following tables as an example:

If Bob buys a unit of the good from Carlos, then the economic surplus is the difference

between Bob’s “maximum price willing to pay” and Carlos’s the “minimum acceptable

Chapter 04 – Market Failures: Public Goods and Externalities

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4. ADVANCED ANALYSIS Assume the following values for Figures 4.4a and 4.4b. Q1 = 20

bags. Q2 = 15 bags. Q3 = 27 bags. The market equilibrium price is $45 per bag. The price at a is

$85 per bag. The price at c is $5 per bag. The price at f is $59 per bag. The price at g is $31 per

bag. Apply the formula for the area of a triangle (Area = ½ x Base x Height) to answer the

following questions. LO2

a. What is the dollar value of the total surplus (producer surplus plus consumer surplus) when the

allocatively efficient output level is being produced? How large is the dollar value of the

consumer surplus at that output level?

b. What is the dollar value of the deadweight loss when output level Q2 is being produced? What

is the total surplus when output level Q2 is being produced?

c. What is the dollar value of the deadweight loss when output level Q3 is produced? What is the

dollar value of the total surplus when output level Q3 is produced?

Answers:

Feedback: To answer this question, let us first find the mathematical representation of

the supply and demand schedules. To help us accomplish this objective we us the

following figures.

Chapter 04 – Market Failures: Public Goods and Externalities

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Now consider the following values as an example. Assume the following values for

Figures 5.4a and 5.4b: The equilibrium quantity Q1 = 20, the market equilibrium price is

$45 per bag, the price at a is $85 per bag, the price at c is $5 per bag.

To derive the demand schedule (inverse demand schedule), we use the following ordered

pairs: (20,45) equilibrium and (0,85) point a.

We know the form of the demand schedule will be P=C1 + C2Q where C1 and C2 are

unknown constants. The intercept, C1, can be found by setting Q equal to zero. This is

point a, so C1 equals 85. To find the slope, C2, we divide the change in quantity by the

change in price using our two ordered pairs above (rise-over-run). This implies C2 equals

(20 – 0) / (45 – 85) = –2.

Thus, we have the following demand schedule: P = 85 – 2Q

To derive the supply schedule (inverse supply schedule), we use the following ordered

pairs: (20,45) equilibrium and (0,5) point c.

Chapter 04 – Market Failures: Public Goods and Externalities

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With these schedules we can now answer the following questions:

Part (a): What is the dollar value of the total surplus (producer surplus plus consumer

surplus) when the allocatively efficient output level is being produced? How large is the

dollar value of the consumer surplus at that output level?

To calculate total surplus we use the following formula for the area of a triangle (Area =

½ (Base x Height)).

The area between the demand schedule P = 85 – 2Q and the supply schedule P = 5 + 2Q

Part (b): What is the dollar value of the deadweight loss when output level Q2 is being

produced? What is the total surplus when output level Q2 is being produced?

The total surplus can be found by subtracting the deadweight loss from the original total

surplus that maximized efficiency. This is 800 (maximum total surplus) – 50 (deadweight

loss) = 750.

Part (c): What is the dollar value of the deadweight loss when output level Q3 is

produced? What is the dollar value of the total surplus when output level Q3 is produced?

Here we follow the same procedure. We are given the price at point f is $59 and the price

at point g is $31 (we do not need to calculate these prices using the demand and supply

Chapter 04 – Market Failures: Public Goods and Externalities

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5. On the basis of the three individual demand schedules below, and assuming these three people

are the only ones in the society, determine (a) the market demand schedule on the assumption that

the good is a private good and (b) the collective demand schedule on the assumption that the good

is a public good. LO3

Chapter 04 – Market Failures: Public Goods and Externalities

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Feedback: Consider the following table:

Part (a): Derive the market demand schedule on the assumption that the good is a private

good. To accomplish we use the principle of horizontal summation. That is, we fix price

Chapter 04 – Market Failures: Public Goods and Externalities

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Part (b): Derive the collective demand schedule on the assumption that the good is a

public good. To accomplish we use the principle of vertical summation. That is, we fix

quantity and add up the price (willingness to pay) for the individuals. The logic here is

that the individuals (society) can pool resources to purchase a given quantity because this

good will be shared (public good).

6. Use your demand schedule for a public good, determined in problem 5, and the following

supply schedule to ascertain the optimal quantity of this public good. LO3

Chapter 04 – Market Failures: Public Goods and Externalities

Feedback: From the example table in problem 5, we calculated the collective demand

schedule from the individual demand schedules:

Collective Demand Schedule:

Quantity

Price Society is

Willing to Pay

$19

$16

$13

$10

Combining this collective demand schedule with the following supply schedule, we can

determine the optimal provision (quantity) of the public good.

The optimal quantity can be found by finding the price where the willingness to pay

equals price required by the firm to supply that last unit (basically the price that clears the

market). For example, at $19 society demands one unit but firms are willing to supply 10

units. At $16 society demands 2 units but firms are willing to supply 8 units. This

continues until we reach the price of $10 where society demands 4 units and firms are

willing to supply 4 units. Thus, the optimal quantity is 4 units.

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7. Look at Tables 4.1 and 4.2, which show, respectively, the willingness to pay and willingness to

accept of buyers and seller of bags of oranges. For the following questions, assume that the

equilibrium price and quantity will depend on the indicated changes in supply and demand.

Assume that the only market participants are those listed by name in the two tables. LO4

a. What are the equilibrium price and quantity for the data displayed in the two tables?

b. What if instead of bags of oranges, the data in the two tables dealt with a public good like

fireworks displays. If all the buyers free ride, what will be the quantity supplied by private

sellers?

c. Assume that we are back to talking about bags of oranges (a private good), but that the

government has decided that tossed orange peels impose a negative externality on the public that

must be rectified by imposing a $2-per-bag tax on sellers. What is the new equilibrium price and

quantity? If the new equilibrium quantity is the optimal quantity, by how many bags were oranges

being overproduced before?

Feedback: Here we consider the tables from Problems 1 and 2.

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Part (a): To determine the equilibrium price of oranges, we begin by comparing the

highest willingness to pay with the lowest minimum acceptable price. Bob is willing to

pay $13 and Carlos is willing to accept at minimum $3. This trade is made because Bob

Part (c): If the government decides that tossed orange peels impose a negative externality

on the public that must be rectified by imposing a $2-per-bag tax on sellers, then the

“minimum acceptable price” will increase by the amount of the tax. The reason is that the

Bob is willing to pay $13 and Carlos is willing to accept at minimum $5. This trade is

made because Bob is willing to pay more than Carlos requires for the sale. We then move

on to the trade between Barb and Courtney. This trade is also made because Barb is