Surplus and
University of Toronto Department of Economics
ECO100: Introductory Economics Robert Gazzale, PhD
Tutorial Problems: Surplus and Interventions 1. Assume iPad supply is perfectly elastic at P = $500 and demand is initially characterized by M W T P0 (Q) = 1000 − Q. (Important: We have absolutely no reason to believe that iPad supply is perfectly elastic. Making this assumption makes it easier to focus on consumer surplus, the goal of this question.) (a) Assume the improvement in the quality of Samsung tablets increases the implicit cost of an iPad purchase by exactly $100. What is the the new function for iPad demand (i.e., M W T P as a function of quantity)? (Hint: If you were willing to pay $800 before the Samsung quality improvement, how much are you now willing to pay?) (b) Calculate consumer surplus in the iPad market both before and after the Samsung tablet quality improvement. (c) Calculate the consumer surplus from the 100th iPad both before and after the Samsung tablet quality improvement. (Hint: Assume quantities are ordered from most valued to least valued.) (d) True, False, or Uncertain: Because the improvement in Samsung tablets decreases the total surplus in the iPad market (part 1b) and decreases the surplus from any iPad still purchased (part 1c), consumers are worse off after the improvement in Samsung tablets.1 2. Table 1 indicates for each of five consumers their total willingness to pay for pounds of coffee. For example, Ajaz’s total willingness to pay for 4 pounds of coffee is $28, whereas Ernst is willing to pay $28 in total for 2 pounds of coffee. (Hint you will not get on a test: There is a difference between total and marginal.)2 Ajaz Bertha Canice Diego Ernst
WTP(1) 10 8 20 12 16
WTP(2) 18 15 35 21 28
WTP(3) 24 21 45 27 36
WTP(4) 28 26 50 30 40
Table 1: Total Willingness To Pay across consumers. (a) The initial allocation of eight pounds of coffee: Ajaz, Bertha and Canice each get two pounds, everyone else gets one pound. Assuming no costs to providing or producing the coffee, what is the total surplus generated by this initial allocation? (b) Consider the following string of transactions: i. ii. iii. iv.
Ajaz sells his second pound to Bertha for $12. Bertha gives this pound of coffee to Canice, along with Ajaz’s $12. Canice sells this pound of coffee to Diego for $3. Diego sells this pound to Ernst for $42.
1
Hint: We know that the answer to this is false. You knew this before you took ECO100. Translating what you know as a human being (i.e., the answer is false) to this model will help you understand what economists mean by “surplus.” 2 Hint you will definitely not get on a test: Ajaz’s values a second pound at 18-10=8, which is the same as saying his willingness to pay for the second pound (M W T P (2)) is $8.
20131028: Page 1
Surplus and Interventions: Tutorial
University of Toronto Department of Economics
ECO100: Introductory Economics Robert Gazzale, PhD
What is a) the surplus generated by each of the four mini-transactions? and b) the sum of the surplus created by these four mini-transactions? (c) Assume instead Ajaz gives his second pound of coffee to Ernst, no money involved. What is the total surplus generated by this single transaction? (Hint: You should get the same number you just got in part 2b.) (d) What is the allocation of eight pounds of coffee that maximizes Total Surplus? By how many dollars has surplus increased relative to your answer in 2a? (e) Now, let us consider costs. Assume a constant marginal cost of producing coffee. That is, if the cost of producing the first pound is some constant C, the cost of the second pound is C, the cost of the third pound is C . . . . Under assumption BIG, over what range of C is eight the efficient quantity? 3. Assume that the market for theatre tickets in Toronto is perfectly competitive, and you are given the following information about the market: Qd = 180 − P Qs = 2P − 15, where P is the price of a ticket, Qd the quantity demanded and Qs the quantity supplied. (a) Calculate Q∗ and P ∗ , the quantity and price in this perfectly competitive market. 200
A
180
160
140
Price
120
Let "M" be point where CE intersects GF.
ply Sup
100
80
G
B
C 60
E F
D
40
20
0
De
m
0
20
40
60
80
100
J
K120
140
an d
160
180
200
Quantity
Figure 1: The market for tickets with intervention. (b) Suppose that a tax of $9 per ticket is imposed by the city of Toronto. Using the labels in Figure 1: 20131028: Page 2
Surplus and Interventions: Tutorial
University of Toronto Department of Economics
(c)
(d)
(e) (f) (g)
(h) (i) (j)
(k)
ECO100: Introductory Economics Robert Gazzale, PhD
• Identify the effect of this tax on equilibrium price and quantity. • Identify the deadweight loss. • Identify the change in government, producer and consumer surplus resulting from this tax. For both the with and without tax cases, calculate • Government surplus; • Producer surplus; • Consumer surplus; • Total surplus; • Deadweight loss. Using the point elasticity approach (i.e., the “calculus” method using slopes), calculate the own-price elasticity of demand and the elasticity of supply at the perfectly competitive equilibrium. What is the incidence of this tax on consumers and producers? How does your answer to question 3d help explain the distribution of incidence? What is the price ceiling resulting in the same number of transactions as the $9 tax? For the case of this price ceiling, using the labels in Figure 1 identify the change in producer, consumer, government and total surplus that results in a move from perfect competition to the price ceiling. Why might this price ceiling create more deadweight loss than the tax? What is the price floor resulting in the same number of transactions as the $9 tax? For the case of this price floor, using the labels in Figure 1 identify the change in producer, consumer, government and total surplus that results in a move from perfect competition to the price floor. Assume that you are the local planner for Toronto. If you wanted to make sure that your intervention (tax, price ceiling/floor) resulted in the highest consumer surplus, which intervention would you choose? Why?
4. (A question pilfered from Prof. Pesando) A 15 percent tax imposed on the sellers (i.e., sellers pay the tax) of accounting, economics, business and chemistry textbooks resulted in the following price increases. Assume the supply curves for all of these goods have the usual positive slope, and each has the same elasticity of supply at the pre-tax equilibrium price. Textbook: Price Change
Economics 13%
Business 8%
Accounting 2%
Chemistry 0%
Table 3: Changes in price to buyers from a 15% tax paid by sellers. (a) Which good has the most inelastic demand curve? The most elastic demand curve? (b) For which good is the largest portion of the tax paid by sellers? Why? (c) If the demand curve for accounting textbook were perfectly inelastic, what is the increase in the amount of money a buyer must pay (in total) for each textbook? Support your analysis with a carefully drawn graph. (d) Can you spin a “realistic” story which might result in an extremely inelastic demand for a non-used textbook?
20131028: Page 3
Surplus and Interventions: Tutorial
ECO100: Introductory Economics Robert Gazzale, PhD
Tutorial Problems: Surplus and Interventions 1. Assume iPad supply is perfectly elastic at P = $500 and demand is initially characterized by M W T P0 (Q) = 1000 − Q. (Important: We have absolutely no reason to believe that iPad supply is perfectly elastic. Making this assumption makes it easier to focus on consumer surplus, the goal of this question.) (a) Assume the improvement in the quality of Samsung tablets increases the implicit cost of an iPad purchase by exactly $100. What is the the new function for iPad demand (i.e., M W T P as a function of quantity)? (Hint: If you were willing to pay $800 before the Samsung quality improvement, how much are you now willing to pay?) (b) Calculate consumer surplus in the iPad market both before and after the Samsung tablet quality improvement. (c) Calculate the consumer surplus from the 100th iPad both before and after the Samsung tablet quality improvement. (Hint: Assume quantities are ordered from most valued to least valued.) (d) True, False, or Uncertain: Because the improvement in Samsung tablets decreases the total surplus in the iPad market (part 1b) and decreases the surplus from any iPad still purchased (part 1c), consumers are worse off after the improvement in Samsung tablets.1 2. Table 1 indicates for each of five consumers their total willingness to pay for pounds of coffee. For example, Ajaz’s total willingness to pay for 4 pounds of coffee is $28, whereas Ernst is willing to pay $28 in total for 2 pounds of coffee. (Hint you will not get on a test: There is a difference between total and marginal.)2 Ajaz Bertha Canice Diego Ernst
WTP(1) 10 8 20 12 16
WTP(2) 18 15 35 21 28
WTP(3) 24 21 45 27 36
WTP(4) 28 26 50 30 40
Table 1: Total Willingness To Pay across consumers. (a) The initial allocation of eight pounds of coffee: Ajaz, Bertha and Canice each get two pounds, everyone else gets one pound. Assuming no costs to providing or producing the coffee, what is the total surplus generated by this initial allocation? (b) Consider the following string of transactions: i. ii. iii. iv.
Ajaz sells his second pound to Bertha for $12. Bertha gives this pound of coffee to Canice, along with Ajaz’s $12. Canice sells this pound of coffee to Diego for $3. Diego sells this pound to Ernst for $42.
1
Hint: We know that the answer to this is false. You knew this before you took ECO100. Translating what you know as a human being (i.e., the answer is false) to this model will help you understand what economists mean by “surplus.” 2 Hint you will definitely not get on a test: Ajaz’s values a second pound at 18-10=8, which is the same as saying his willingness to pay for the second pound (M W T P (2)) is $8.
20131028: Page 1
Surplus and Interventions: Tutorial
University of Toronto Department of Economics
ECO100: Introductory Economics Robert Gazzale, PhD
What is a) the surplus generated by each of the four mini-transactions? and b) the sum of the surplus created by these four mini-transactions? (c) Assume instead Ajaz gives his second pound of coffee to Ernst, no money involved. What is the total surplus generated by this single transaction? (Hint: You should get the same number you just got in part 2b.) (d) What is the allocation of eight pounds of coffee that maximizes Total Surplus? By how many dollars has surplus increased relative to your answer in 2a? (e) Now, let us consider costs. Assume a constant marginal cost of producing coffee. That is, if the cost of producing the first pound is some constant C, the cost of the second pound is C, the cost of the third pound is C . . . . Under assumption BIG, over what range of C is eight the efficient quantity? 3. Assume that the market for theatre tickets in Toronto is perfectly competitive, and you are given the following information about the market: Qd = 180 − P Qs = 2P − 15, where P is the price of a ticket, Qd the quantity demanded and Qs the quantity supplied. (a) Calculate Q∗ and P ∗ , the quantity and price in this perfectly competitive market. 200
A
180
160
140
Price
120
Let "M" be point where CE intersects GF.
ply Sup
100
80
G
B
C 60
E F
D
40
20
0
De
m
0
20
40
60
80
100
J
K120
140
an d
160
180
200
Quantity
Figure 1: The market for tickets with intervention. (b) Suppose that a tax of $9 per ticket is imposed by the city of Toronto. Using the labels in Figure 1: 20131028: Page 2
Surplus and Interventions: Tutorial
University of Toronto Department of Economics
(c)
(d)
(e) (f) (g)
(h) (i) (j)
(k)
ECO100: Introductory Economics Robert Gazzale, PhD
• Identify the effect of this tax on equilibrium price and quantity. • Identify the deadweight loss. • Identify the change in government, producer and consumer surplus resulting from this tax. For both the with and without tax cases, calculate • Government surplus; • Producer surplus; • Consumer surplus; • Total surplus; • Deadweight loss. Using the point elasticity approach (i.e., the “calculus” method using slopes), calculate the own-price elasticity of demand and the elasticity of supply at the perfectly competitive equilibrium. What is the incidence of this tax on consumers and producers? How does your answer to question 3d help explain the distribution of incidence? What is the price ceiling resulting in the same number of transactions as the $9 tax? For the case of this price ceiling, using the labels in Figure 1 identify the change in producer, consumer, government and total surplus that results in a move from perfect competition to the price ceiling. Why might this price ceiling create more deadweight loss than the tax? What is the price floor resulting in the same number of transactions as the $9 tax? For the case of this price floor, using the labels in Figure 1 identify the change in producer, consumer, government and total surplus that results in a move from perfect competition to the price floor. Assume that you are the local planner for Toronto. If you wanted to make sure that your intervention (tax, price ceiling/floor) resulted in the highest consumer surplus, which intervention would you choose? Why?
4. (A question pilfered from Prof. Pesando) A 15 percent tax imposed on the sellers (i.e., sellers pay the tax) of accounting, economics, business and chemistry textbooks resulted in the following price increases. Assume the supply curves for all of these goods have the usual positive slope, and each has the same elasticity of supply at the pre-tax equilibrium price. Textbook: Price Change
Economics 13%
Business 8%
Accounting 2%
Chemistry 0%
Table 3: Changes in price to buyers from a 15% tax paid by sellers. (a) Which good has the most inelastic demand curve? The most elastic demand curve? (b) For which good is the largest portion of the tax paid by sellers? Why? (c) If the demand curve for accounting textbook were perfectly inelastic, what is the increase in the amount of money a buyer must pay (in total) for each textbook? Support your analysis with a carefully drawn graph. (d) Can you spin a “realistic” story which might result in an extremely inelastic demand for a non-used textbook?
20131028: Page 3
Surplus and Interventions: Tutorial
