Download Consumer and Producer Surplus

Consumer Surplus
Consumer and Producer Surplus
Bill Gibson
EC 11, Spring 2011
Bill Gibson
University of Vermont
Consumer Surplus
Why are demand curves downward sloping
First answer: substitution
Bill Gibson
University of Vermont
Consumer Surplus
Why are demand curves downward sloping
First answer: substitution
Second answer: when price is high resource will only be
allocated to high value uses
Bill Gibson
University of Vermont
Consumer Surplus
Why are demand curves downward sloping
First answer: substitution
Second answer: when price is high resource will only be
allocated to high value uses
When price is low, resource will also be allocated to some low
value uses
Bill Gibson
University of Vermont
Consumer Surplus
Why are demand curves downward sloping
First answer: substitution
Second answer: when price is high resource will only be
allocated to high value uses
When price is low, resource will also be allocated to some low
value uses
High value uses is just another way of saying: high marginal
benefit
Bill Gibson
University of Vermont
Consumer Surplus
Why are demand curves downward sloping
First answer: substitution
Second answer: when price is high resource will only be
allocated to high value uses
When price is low, resource will also be allocated to some low
value uses
High value uses is just another way of saying: high marginal
benefit
When price is low those with high marginal benefit enjoy the
low price more than those with low marginal benefit
Bill Gibson
University of Vermont
Consumer Surplus
Why are demand curves downward sloping
First answer: substitution
Second answer: when price is high resource will only be
allocated to high value uses
When price is low, resource will also be allocated to some low
value uses
High value uses is just another way of saying: high marginal
benefit
When price is low those with high marginal benefit enjoy the
low price more than those with low marginal benefit
Marginal benefit is same thing as “willingness to pay”
Bill Gibson
University of Vermont
Consumer Surplus
Why are demand curves downward sloping
First answer: substitution
Second answer: when price is high resource will only be
allocated to high value uses
When price is low, resource will also be allocated to some low
value uses
High value uses is just another way of saying: high marginal
benefit
When price is low those with high marginal benefit enjoy the
low price more than those with low marginal benefit
Marginal benefit is same thing as “willingness to pay”
Example
What do we call the extra kick that those with high marginal
benefit receive?
Bill Gibson
University of Vermont
Consumer Surplus
Why are demand curves downward sloping
First answer: substitution
Second answer: when price is high resource will only be
allocated to high value uses
When price is low, resource will also be allocated to some low
value uses
High value uses is just another way of saying: high marginal
benefit
When price is low those with high marginal benefit enjoy the
low price more than those with low marginal benefit
Marginal benefit is same thing as “willingness to pay”
Example
What do we call the extra kick that those with high marginal
benefit receive?
Answer: Consumer surplus
Bill Gibson
University of Vermont
Consumer Surplus
Consumer surplus
Area under demand curve and above price
Bill Gibson
University of Vermont
Consumer Surplus
Consumer surplus
Area under demand curve and above price
If demand curve linear use area of triangle A = bh/2
Bill Gibson
University of Vermont
Consumer Surplus
Consumer surplus
Area under demand curve and above price
If demand curve linear use area of triangle A = bh/2
Rp
If not linear must integrate p max Qd (p )dp
Bill Gibson
University of Vermont
Consumer Surplus
Consumer surplus
Area under demand curve and above price
If demand curve linear use area of triangle A = bh/2
Rp
If not linear must integrate p max Qd (p )dp
Sum of CS for all consumers
Bill Gibson
University of Vermont
Consumer Surplus
Consumer surplus
Area under demand curve and above price
If demand curve linear use area of triangle A = bh/2
Rp
If not linear must integrate p max Qd (p )dp
Sum of CS for all consumers
Example
Can CS ever be zero?
Bill Gibson
University of Vermont
Consumer Surplus
Consumer surplus
Area under demand curve and above price
If demand curve linear use area of triangle A = bh/2
Rp
If not linear must integrate p max Qd (p )dp
Sum of CS for all consumers
Example
Can CS ever be zero?
Answer: Yes...but only when demand curve is flat
Bill Gibson
University of Vermont
Consumer Surplus
Producer surplus
Area below the price and above the supply curve.
Bill Gibson
University of Vermont
Consumer Surplus
Producer surplus
Area below the price and above the supply curve.
Add to CS to get total potential gains from trade
Bill Gibson
University of Vermont
Consumer Surplus
Producer surplus
Area below the price and above the supply curve.
Add to CS to get total potential gains from trade
If supply curve linear use area of triangle A = bh/2
Bill Gibson
University of Vermont
Consumer Surplus
Producer surplus
Area below the price and above the supply curve.
Add to CS to get total potential gains from trade
If supply curve linear use area of triangle A = bh/2
Rp
If not linear must integrate pmin Qs (p )dp
Bill Gibson
University of Vermont
Consumer Surplus
Producer surplus
Area below the price and above the supply curve.
Add to CS to get total potential gains from trade
If supply curve linear use area of triangle A = bh/2
Rp
If not linear must integrate pmin Qs (p )dp
Sum of PS for all firms
Bill Gibson
University of Vermont
Consumer Surplus
Producer surplus
Area below the price and above the supply curve.
Add to CS to get total potential gains from trade
If supply curve linear use area of triangle A = bh/2
Rp
If not linear must integrate pmin Qs (p )dp
Sum of PS for all firms
Example
Can PS ever be zero?
Bill Gibson
University of Vermont
Consumer Surplus
Producer surplus
Area below the price and above the supply curve.
Add to CS to get total potential gains from trade
If supply curve linear use area of triangle A = bh/2
Rp
If not linear must integrate pmin Qs (p )dp
Sum of PS for all firms
Example
Can PS ever be zero?
Answer: Yes...but only when supply curve is flat
Bill Gibson
University of Vermont
!"#$%&'()$%(*+%$),!-.)
Consumer Surplus
Consumer surplus
Area beneath the demand curve and above the price
P
CS for consumer with highest marginal benefit
80
Lower MB so CS is less
20
Demand
CS =(80-20)90/2 =2,700
90
Note: recall that area of a triangle is !(base x height)
Bill Gibson
University of Vermont
Q
11
Consumer Surplus
At Q=24, there are buyers who value buying the good more than sellers value
selling the good (there are unexploited gains from trade up until 65 units)
Unexploited Gains and Wasteful Trade
Price of Oil
per Barrel
Satisfied Wants
$57
P*
Supply Curve
Unsatisfied Wants
Unexploited
gains from
trade
MC < MB
$30
Wasteful trades
MC>MB
$15
Demand Curve
Quantity of Oil
(MBD)
24
Q* = 65
Q = 100
Equilibrium
Quantity
Bill Gibson
14
University of Vermont
Consumer Surplus
Calculations
Example
What are equilibrium P and Q
Qd = 90 − P
Qs = −150 + 3P
Bill Gibson
University of Vermont
Consumer Surplus
Calculations
Example
What are equilibrium P and Q
Qd = 90 − P
Qs = −150 + 3P
Answer: Set
Qd = Qs → 90 − P = −150 + 3P → P = 60Q = 30;
Bill Gibson
University of Vermont
Consumer Surplus
Calculate maximum gains from trade
Example
Add producer and consumer surplus
Bill Gibson
University of Vermont
Consumer Surplus
Calculate maximum gains from trade
Example
Add producer and consumer surplus
Answer:
Bill Gibson
University of Vermont
Consumer Surplus
Calculate maximum gains from trade
Example
Add producer and consumer surplus
Answer:
Use formula for triangle 1/2 base × height
Bill Gibson
University of Vermont
Consumer Surplus
Calculate maximum gains from trade
Example
Add producer and consumer surplus
Answer:
Use formula for triangle 1/2 base × height
Base is 90-50 = 40
Bill Gibson
University of Vermont
Consumer Surplus
Calculate maximum gains from trade
Example
Add producer and consumer surplus
Answer:
Use formula for triangle 1/2 base × height
Base is 90-50 = 40
Height is 30
Bill Gibson
University of Vermont
Consumer Surplus
Calculate maximum gains from trade
Example
Add producer and consumer surplus
Answer:
Use formula for triangle 1/2 base × height
Base is 90-50 = 40
Height is 30
Maximum gains from trade (1/2)(40)(30) = 600
Bill Gibson
University of Vermont
Consumer Surplus
Market equilibrium
When Qs = Qd at a given P, the market is in equilibrium
Bill Gibson
University of Vermont
Consumer Surplus
Market equilibrium
When Qs = Qd at a given P, the market is in equilibrium
Amount consumers would purchase at this price is matched
exactly by the amount producers wish to sell
Bill Gibson
University of Vermont
Consumer Surplus
Market equilibrium
When Qs = Qd at a given P, the market is in equilibrium
Amount consumers would purchase at this price is matched
exactly by the amount producers wish to sell
Solving model is finding P, Q combination s.t. Qs = Qd
Bill Gibson
University of Vermont
Consumer Surplus
Market equilibrium
When Qs = Qd at a given P, the market is in equilibrium
Amount consumers would purchase at this price is matched
exactly by the amount producers wish to sell
Solving model is finding P, Q combination s.t. Qs = Qd
No shortages–excess demand
Bill Gibson
University of Vermont
Consumer Surplus
Market equilibrium
When Qs = Qd at a given P, the market is in equilibrium
Amount consumers would purchase at this price is matched
exactly by the amount producers wish to sell
Solving model is finding P, Q combination s.t. Qs = Qd
No shortages–excess demand
No surpluses–excess supply
Bill Gibson
University of Vermont
Consumer Surplus
Market equilibrium
When Qs = Qd at a given P, the market is in equilibrium
Amount consumers would purchase at this price is matched
exactly by the amount producers wish to sell
Solving model is finding P, Q combination s.t. Qs = Qd
No shortages–excess demand
No surpluses–excess supply
Example
How does price change?
Bill Gibson
University of Vermont
Consumer Surplus
Market equilibrium
When Qs = Qd at a given P, the market is in equilibrium
Amount consumers would purchase at this price is matched
exactly by the amount producers wish to sell
Solving model is finding P, Q combination s.t. Qs = Qd
No shortages–excess demand
No surpluses–excess supply
Example
How does price change?
Answer: Have ∆P
∆t = f (ED ) which means price rises with
excess demand and falls with excess supply
Bill Gibson
University of Vermont
Consumer Surplus
Click to download the Excel spreadsheet
Demand and supply curves are fully determined by their slope
and intercept.
Bill Gibson
University of Vermont
Consumer Surplus
Click to download the Excel spreadsheet
Demand and supply curves are fully determined by their slope
and intercept.
Must be careful here: price (P) is on the vertical axis but
really should be on horizontal.
Bill Gibson
University of Vermont
Consumer Surplus
Click to download the Excel spreadsheet
Demand and supply curves are fully determined by their slope
and intercept.
Must be careful here: price (P) is on the vertical axis but
really should be on horizontal.
If problem is given in form Q = a − bP must solve for P
before plotting.
Bill Gibson
University of Vermont
Consumer Surplus
Click to download the Excel spreadsheet
Demand and supply curves are fully determined by their slope
and intercept.
Must be careful here: price (P) is on the vertical axis but
really should be on horizontal.
If problem is given in form Q = a − bP must solve for P
before plotting.
This gives: P = a/b − Q/b so the slope is 1/b and intercept
is Q/b.
Bill Gibson
University of Vermont
Consumer Surplus
Click to download the Excel spreadsheet
Demand and supply curves are fully determined by their slope
and intercept.
Must be careful here: price (P) is on the vertical axis but
really should be on horizontal.
If problem is given in form Q = a − bP must solve for P
before plotting.
This gives: P = a/b − Q/b so the slope is 1/b and intercept
is Q/b.
True for both supply and demand curves.
Bill Gibson
University of Vermont
Consumer Surplus
Click to download the Excel spreadsheet
Demand and supply curves are fully determined by their slope
and intercept.
Must be careful here: price (P) is on the vertical axis but
really should be on horizontal.
If problem is given in form Q = a − bP must solve for P
before plotting.
This gives: P = a/b − Q/b so the slope is 1/b and intercept
is Q/b.
True for both supply and demand curves.
Example
Let demand be P = 10 − 5Q and supply be P = 1 + 4Q.
Calculate the the equilibrium price and quantity.
Bill Gibson
University of Vermont
Consumer Surplus
Click to download the Excel spreadsheet
Demand and supply curves are fully determined by their slope
and intercept.
Must be careful here: price (P) is on the vertical axis but
really should be on horizontal.
If problem is given in form Q = a − bP must solve for P
before plotting.
This gives: P = a/b − Q/b so the slope is 1/b and intercept
is Q/b.
True for both supply and demand curves.
Example
Let demand be P = 10 − 5Q and supply be P = 1 + 4Q.
Calculate the the equilibrium price and quantity.
Answer: Set Ps equal: 10 − 5Q = 1 + 4P or 9 = 9Q gives
Q = 1 and so P = 5.
Bill Gibson
University of Vermont
Consumer Surplus
What if the price ceiling were P = 2 ?
Producers would like to charge a higher price but cannot.
Bill Gibson
University of Vermont
Consumer Surplus
What if the price ceiling were P = 2 ?
Producers would like to charge a higher price but cannot.
Calculate deadweight loss: at P = 2 supply is only
1/4 = 0.25.
Bill Gibson
University of Vermont
Consumer Surplus
What if the price ceiling were P = 2 ?
Producers would like to charge a higher price but cannot.
Calculate deadweight loss: at P = 2 supply is only
1/4 = 0.25.
The willingness to pay at this quantity is
= 10 − 5(1/4) = 8.75
Bill Gibson
University of Vermont
Consumer Surplus
What if the price ceiling were P = 2 ?
Producers would like to charge a higher price but cannot.
Calculate deadweight loss: at P = 2 supply is only
1/4 = 0.25.
The willingness to pay at this quantity is
= 10 − 5(1/4) = 8.75
Deadweight loss is 1/2base × height
Bill Gibson
University of Vermont
Consumer Surplus
What if the price ceiling were P = 2 ?
Producers would like to charge a higher price but cannot.
Calculate deadweight loss: at P = 2 supply is only
1/4 = 0.25.
The willingness to pay at this quantity is
= 10 − 5(1/4) = 8.75
Deadweight loss is 1/2base × height
= (1/2)(8.75 − 2)(1 − 0.25) = 2.53
Bill Gibson
University of Vermont
Consumer Surplus
What if the price ceiling were P = 2 ?
Producers would like to charge a higher price but cannot.
Calculate deadweight loss: at P = 2 supply is only
1/4 = 0.25.
The willingness to pay at this quantity is
= 10 − 5(1/4) = 8.75
Deadweight loss is 1/2base × height
= (1/2)(8.75 − 2)(1 − 0.25) = 2.53
Example
What is value of lost time?
Bill Gibson
University of Vermont
Consumer Surplus
What if the price ceiling were P = 2 ?
Producers would like to charge a higher price but cannot.
Calculate deadweight loss: at P = 2 supply is only
1/4 = 0.25.
The willingness to pay at this quantity is
= 10 − 5(1/4) = 8.75
Deadweight loss is 1/2base × height
= (1/2)(8.75 − 2)(1 − 0.25) = 2.53
Example
What is value of lost time?
Answer: = (8.75 − 2)0.25 = 1.6875 as can be confirmed from
the spreadsheet.
Bill Gibson
University of Vermont
Consumer Surplus
What if the price floor were P = 7?
Producers would like to charge a lower price but cannot.
Bill Gibson
University of Vermont
Consumer Surplus
What if the price floor were P = 7?
Producers would like to charge a lower price but cannot.
Calculate deadweight loss: at P = 7 demand is only
3/5 = 0.6.
Bill Gibson
University of Vermont
Consumer Surplus
What if the price floor were P = 7?
Producers would like to charge a lower price but cannot.
Calculate deadweight loss: at P = 7 demand is only
3/5 = 0.6.
The supply price this quantity is 1 + 4(0.6) = 3.4
Bill Gibson
University of Vermont
Consumer Surplus
What if the price floor were P = 7?
Producers would like to charge a lower price but cannot.
Calculate deadweight loss: at P = 7 demand is only
3/5 = 0.6.
The supply price this quantity is 1 + 4(0.6) = 3.4
Deadweight loss is 1/2base × height
Bill Gibson
University of Vermont
Consumer Surplus
What if the price floor were P = 7?
Producers would like to charge a lower price but cannot.
Calculate deadweight loss: at P = 7 demand is only
3/5 = 0.6.
The supply price this quantity is 1 + 4(0.6) = 3.4
Deadweight loss is 1/2base × height
= (1/2)(7 − 3.4)(1 − 0.6) = 0.72
Bill Gibson
University of Vermont
Consumer Surplus
What if the price floor were P = 7?
Producers would like to charge a lower price but cannot.
Calculate deadweight loss: at P = 7 demand is only
3/5 = 0.6.
The supply price this quantity is 1 + 4(0.6) = 3.4
Deadweight loss is 1/2base × height
= (1/2)(7 − 3.4)(1 − 0.6) = 0.72
Example
What is value wasted quality?
Bill Gibson
University of Vermont
Consumer Surplus
What if the price floor were P = 7?
Producers would like to charge a lower price but cannot.
Calculate deadweight loss: at P = 7 demand is only
3/5 = 0.6.
The supply price this quantity is 1 + 4(0.6) = 3.4
Deadweight loss is 1/2base × height
= (1/2)(7 − 3.4)(1 − 0.6) = 0.72
Example
What is value wasted quality?
Answer: = (7 − 3.4)0.6 = 2.16 as can be confirmed from the
spreadsheet.
Bill Gibson
University of Vermont