ECO 101H1: Principles of Microeconomics Prof. Freitas, University of Toronto
Problem Set 5: Surplus
Questions and Solutions
1) Consider a perfectly competitive market with no externalities. Market demand is given by QD = 65 − P while
market supply is given by QS = P − 5. Calculate Consumer Surplus, Producer Surplus and Total Surplus.
Solution: We need to first find market quantity and price. We do that by setting
QD = QS
65 − P = P −5
P = 35
⇒Q = 30
To calculate CS we need the intercept of the demand curve on the y-axis, which is 65. This makes CS the area
of the triangle with base = 30 (the quantity), height = 65-35 (the difference between price and the intercept
of the demand curve on the y-axis).
CS = 0.5 ∗ (65 − 35) ∗ 30 = 450
Similarly, for PS we need the intercept of the supply curve on the y-axis, which is 5. This makes PS the area
of the triangle with base = 30 (the quantity), height = 35-5 (the difference between price and the intercept
of the supply curve on the y-axis).
P S = 0.5 ∗ (35 − 5) ∗ 30 = 450
Since we have no externalities, we can use the private benefits to calculate the social benefits. No members
of society are affected by the buying and selling other than the consumers and producers, so we can calculate
total surplus using
T S = CS + P S = 900
Consumer surplus is $450, producer surplus is $450, and total surplus is $900.
2) We have a perfectly competitive market. Market demand is given by QD = 30 − 12 P while market supply is
given by QS = 2P − 5.
2a) Calculate Consumer Surplus and Producer Surplus.
Solution: We proceed the same way as in the question above. We need to first find market quantity and price.
We do that by setting
QD = QS
30 − 12 P = 2P − 5
P = 14
⇒Q = 23
To calculate CS we need the intercept of the demand curve on the y-axis, which is 60. This makes CS the area
of the triangle with base = 23 (the quantity), height = 60-14 (the difference between price and the intercept
of the demand curve on the y-axis).
CS = 0.5 ∗ (60 − 14) ∗ 23 = 529
Similarly, for PS we need the intercept of the supply curve on the y-axis, which is 2.5. This makes PS the area
of the triangle with base = 23 (the quantity), height = 14-2.5 (the difference between price and the intercept
of the supply curve on the y-axis).
P S = 0.5 ∗ (14 − 2.5) ∗ 23 = 132.25
Consumer surplus is $529 and producer surplus is $132.25.
202609 1 of 8 Problem Set 5 Questions and Solutions
, ECO 101H1: Principles of Microeconomics Prof. Freitas, University of Toronto
2b) Can you calculate total surplus?
Solution: Without being told that all benefits and costs accrue only to the parties in the transaction and no one
outside (i.e. no externalities), we couldn’t calculate total surplus. There could be benefits or costs accruing to
people outside the transactions that would need to be counted in total surplus. Another way of saying this is
that social benefit (or cost) could be different from private benefit (or cost). The demand and supply curves
just reflect private costs and benefits. But in this question, since we are told it is a perfectly competitive
market, we know that one of the assumptions is no externalities, so that holds here and we can calculate
it.
Market quantity is 23, and total surplus is the area below the MWTP curve and above the MC curve up to
the market quantity.
T S = 0.5 ∗ 23 ∗ (60 − 2.5) = 661.25
Total surplus is $661.25.
3) A perfectly competitive market consists of 15 individual buyers and 10 individual sellers. Each buyer’s demand
curve is given by p = 30 − 41 q D . Each supplier’s supply curve is given by p = 41 q S + 5. There are no
externalities. (Notation: I’m using small letters for individuals and capital letters for markets to make things
easier to keep track of visually. There is no deeper meaning to it.)
3a) Calculate market Consumer Surplus, market Producer Surplus and Total Surplus.
Solution: Step 1 is to calculate market supply and market demand. Recall that to do that we need to sum
up individual quantities demanded and supplied at a given price. First, we need to rewrite each individual
consumer’s demand in terms of q D (p) which gives us p = 30 − 14 q D ⇒ q D = 120 − 4p. Summing this up over
15 buyers gives us market demand
QD = 15 ∗ (120 − 4p) = 1800 − 60p
Second, we need to rewrite each individual supplier’s supply in terms of q S (p) which gives us p = 41 q S + 5 ⇒
q S = 4p − 20. Summing this up over 10 sellers gives us market supply
QS = 10 ∗ (4p − 20) = 40p − 200
To find market quantity and price we set
QD = QS
1800 − 60p = 40p − 200
P = 20
⇒Q = 600
To calculate CS we need the intercept of the demand curve on the y-axis, which is 30. This makes CS the area
of the triangle with base = 600 (the quantity), height = 30-20 (the difference between price and the intercept
of the demand curve on the y-axis).
CS = 0.5 ∗ (30 − 20) ∗ 600 = 3000
Similarly, for PS we need the intercept of the supply curve on the y-axis, which is 5. This makes PS the area
of the triangle with base = 600 (the quantity), height = 20-5 (the difference between price and the intercept
of the supply curve on the y-axis).
P S = 0.5 ∗ (20 − 5) ∗ 600 = 4500
Since all benefits accrue only to the parties in the transaction and no one outside (i.e. no externalities), we
can calculate total surplus using
T S = CS + P S = 7500
Market CS is $3,000, market PS is $4,500, and total surplus is $7,500.
202609 2 of 8 Problem Set 5 Questions and Solutions
Problem Set 5: Surplus
Questions and Solutions
1) Consider a perfectly competitive market with no externalities. Market demand is given by QD = 65 − P while
market supply is given by QS = P − 5. Calculate Consumer Surplus, Producer Surplus and Total Surplus.
Solution: We need to first find market quantity and price. We do that by setting
QD = QS
65 − P = P −5
P = 35
⇒Q = 30
To calculate CS we need the intercept of the demand curve on the y-axis, which is 65. This makes CS the area
of the triangle with base = 30 (the quantity), height = 65-35 (the difference between price and the intercept
of the demand curve on the y-axis).
CS = 0.5 ∗ (65 − 35) ∗ 30 = 450
Similarly, for PS we need the intercept of the supply curve on the y-axis, which is 5. This makes PS the area
of the triangle with base = 30 (the quantity), height = 35-5 (the difference between price and the intercept
of the supply curve on the y-axis).
P S = 0.5 ∗ (35 − 5) ∗ 30 = 450
Since we have no externalities, we can use the private benefits to calculate the social benefits. No members
of society are affected by the buying and selling other than the consumers and producers, so we can calculate
total surplus using
T S = CS + P S = 900
Consumer surplus is $450, producer surplus is $450, and total surplus is $900.
2) We have a perfectly competitive market. Market demand is given by QD = 30 − 12 P while market supply is
given by QS = 2P − 5.
2a) Calculate Consumer Surplus and Producer Surplus.
Solution: We proceed the same way as in the question above. We need to first find market quantity and price.
We do that by setting
QD = QS
30 − 12 P = 2P − 5
P = 14
⇒Q = 23
To calculate CS we need the intercept of the demand curve on the y-axis, which is 60. This makes CS the area
of the triangle with base = 23 (the quantity), height = 60-14 (the difference between price and the intercept
of the demand curve on the y-axis).
CS = 0.5 ∗ (60 − 14) ∗ 23 = 529
Similarly, for PS we need the intercept of the supply curve on the y-axis, which is 2.5. This makes PS the area
of the triangle with base = 23 (the quantity), height = 14-2.5 (the difference between price and the intercept
of the supply curve on the y-axis).
P S = 0.5 ∗ (14 − 2.5) ∗ 23 = 132.25
Consumer surplus is $529 and producer surplus is $132.25.
202609 1 of 8 Problem Set 5 Questions and Solutions
, ECO 101H1: Principles of Microeconomics Prof. Freitas, University of Toronto
2b) Can you calculate total surplus?
Solution: Without being told that all benefits and costs accrue only to the parties in the transaction and no one
outside (i.e. no externalities), we couldn’t calculate total surplus. There could be benefits or costs accruing to
people outside the transactions that would need to be counted in total surplus. Another way of saying this is
that social benefit (or cost) could be different from private benefit (or cost). The demand and supply curves
just reflect private costs and benefits. But in this question, since we are told it is a perfectly competitive
market, we know that one of the assumptions is no externalities, so that holds here and we can calculate
it.
Market quantity is 23, and total surplus is the area below the MWTP curve and above the MC curve up to
the market quantity.
T S = 0.5 ∗ 23 ∗ (60 − 2.5) = 661.25
Total surplus is $661.25.
3) A perfectly competitive market consists of 15 individual buyers and 10 individual sellers. Each buyer’s demand
curve is given by p = 30 − 41 q D . Each supplier’s supply curve is given by p = 41 q S + 5. There are no
externalities. (Notation: I’m using small letters for individuals and capital letters for markets to make things
easier to keep track of visually. There is no deeper meaning to it.)
3a) Calculate market Consumer Surplus, market Producer Surplus and Total Surplus.
Solution: Step 1 is to calculate market supply and market demand. Recall that to do that we need to sum
up individual quantities demanded and supplied at a given price. First, we need to rewrite each individual
consumer’s demand in terms of q D (p) which gives us p = 30 − 14 q D ⇒ q D = 120 − 4p. Summing this up over
15 buyers gives us market demand
QD = 15 ∗ (120 − 4p) = 1800 − 60p
Second, we need to rewrite each individual supplier’s supply in terms of q S (p) which gives us p = 41 q S + 5 ⇒
q S = 4p − 20. Summing this up over 10 sellers gives us market supply
QS = 10 ∗ (4p − 20) = 40p − 200
To find market quantity and price we set
QD = QS
1800 − 60p = 40p − 200
P = 20
⇒Q = 600
To calculate CS we need the intercept of the demand curve on the y-axis, which is 30. This makes CS the area
of the triangle with base = 600 (the quantity), height = 30-20 (the difference between price and the intercept
of the demand curve on the y-axis).
CS = 0.5 ∗ (30 − 20) ∗ 600 = 3000
Similarly, for PS we need the intercept of the supply curve on the y-axis, which is 5. This makes PS the area
of the triangle with base = 600 (the quantity), height = 20-5 (the difference between price and the intercept
of the supply curve on the y-axis).
P S = 0.5 ∗ (20 − 5) ∗ 600 = 4500
Since all benefits accrue only to the parties in the transaction and no one outside (i.e. no externalities), we
can calculate total surplus using
T S = CS + P S = 7500
Market CS is $3,000, market PS is $4,500, and total surplus is $7,500.
202609 2 of 8 Problem Set 5 Questions and Solutions
