IB Economics
HL Price Controls
HL Price Control Calculations
You need to be able to do the following (from your syllabus):
Calculate possible effects from the price ceiling diagram, including the resulting shortage
and the change in consumer expenditure (which is equal to the change in firm revenue)
Calculate the possible effects from the price floor diagram, including the resulting surplus,
the change in producer revenue and government expenditure to purchase the surplus.
A maximum price of Pmax is imposed
Using the numbers 1 to 6 identify the following:
Consumer surplus before the max price
Consumer surplus after the max price
What happened to consumer surplus?
Producer surplus before the max price
Producer surplus after the max price
What happened to producer surplus?
What is the welfare loss to society?
1
IB Economics
HL Price Controls
Calculations: Maximum Price
Example 1
Assume the demand and supply for olive oil can be expressed using the following equations:
QD= 480- 6P
QS= 120+ 3P
Assume quantities (units) are in thousands of kilograms (kg). The Gov then set a maximum price of €30
per kg.
1. What is the free market price and quantity?
480- 6P = 120+ 3P
Equilibrium price= € 40
Equilibrium quantity= 240,000 kg
2. What is the shortage created?
Substitute the maximum price into the supply and the demand formula
QD= 480- (6 X 30)
QS= 120 + (3 X 30)
QD= 300,000 kgs
QS= 210,000 kgs
Shortage= QD- QS= -90,000 kg
3. What level of subsidy would be needed to eliminate the shortage?
To eliminate the shortage of 90 units, supply would need to increase by 90 units (shift to the
right by 90 units)
So QS+ subsidy= 120+ 3P + 90
QS+subsidy= 210 + 3P
Substitute in max price of €30
QS+subsidy= 300, 000kg
Thus QS now= QD at the max price of €30
We now need to calculate the price at which suppliers would have been willing to supply 300 units
without a subsidy, so we need to substitute 300 into our original supply equation:
300= 120+ 3P
3P=300- 120
P=€ 60
So we need to increase the price by €30 per kg for the producer to supply the ‘correct’ quantity
and eliminate the shortage.
Therefore the subsidy needed = €30 per kg.
2
IB Economics
HL Price Controls
Calculations: Minimum Price
Example 2
Assume the demand and supply for olive oil can be expressed using the following equations:
QD= 600-5P
QS= 120+ 3P
Assume quantities are in thousands units. The Gov then set a minimum price of €75 per unit.
1. What is the free market price and quantity?
600-5P = 120+ 3P
Equilibrium price= € 60
Equilibrium quantity= 300, 000 units
2. What is the surplus created?
Substitute the minimum price into the supply and the demand formulas
QD= 600-(5 x 75)
QD= 225, 000 units
QS= 120 + (3 X 75)
QS= 345, 000 units
Surplus= QD- QS= 120, 000 units
3. What must the government spend to support this price (buying up the surplus)
€75 x 120, 000= €9, 000, 000
4. What TR will the producer collect as a result of the minimum price?
345, 000 units x €75 = €25, 875, 000
Note: €9, 000, 000 from Gov. €16, 875 from consumers
5. What subsidy would be necessary for producers to gain the same TR as they do with a
minimum price?
Substitute in 345 to the demand curve
345= 600- 5P
P= €51
So if the price were €51, consumers would buy the 345,000 units
3
IB Economics
HL Price Controls
Therefore producers would receive €51 per unit from the market, but need an extra €24 per unit to
make it up to the ‘price’ of €75 per unit. The subsidy of €24 per unit would give the producers the
same level of revenue as the minimum price.
Which is cheaper? Minimum price or subsidy?
Minimum price cost the gov €9,000,000 to support
The subsidy would cost €24 x 345, 000 = €8, 280, 000
So the minimum price would be a more expensive method for the government. A saving of €720, 000.
Activity 1.
Assume the demand for apartments is given by QD= 4800- 35P while the supply by
qs= 160+ 5p
where the price is in euros and the quantity in thousands of units.
Assume the government introduces a rent control policy which makes it illegal for landlords to ask for
rents above €100 per apartment.
1.
How much would apartments rent for in the absence of rent controls?
2.
What is the size of the shortage of apartments as a result of the rent control policy?
3.
Calculate the necessary subsidy that would remove the shortage of apartments
Activity 2
Assume the demand for a good is given by QD= 800- 4P while supply is QS= 200 + 2P, where the price
is isn RM and the quantity in thousands of units. Lets say the government introduce a minimum price of
RM120 per unit.
4
1.
Calculate the equilibrium price and quantity before the minimum price
2.
What is the resulting surplus?
3.
How much did total consumer expenditure change by as a result of the minimum price?
4.
What does this suggest about the PED?
5.
Calculate the PED
6.
How much did TR for producers change by?
7.
How much would this policy cost the taxpayer?
8.
What is the size of the subsidy necessary to guarantee producers the same revenue?
9.
Which option is cheaper?