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Chapter 3: Goods Market Equilibrium
In a free market the point at which demand and supply curves intersect is the equilibrium
point. The equilibrium price is the price at which the quantity demanded by consumers equals
the quantity supplied by producers. The market is in balance.
The demand and supply functions for bread (loaves of sour dough bread) are given as
Demand function :Pd  9.5  0.01Q d
(1)
Supply function :Ps  0.5  0.005Q s
(2)
Calculate the equilibrium price and quantity in a free market, the consumer and producer
surplus and the price elasticity of demand.
The government is considering introducing a sales tax and also imposing price controls on
essential food products.
Analyse the effect of a tax of £0.30 per loaf on the equilibrium price and quantity. What
proportion of the tax borne by consumers and producers?
If the government imposes a maximum price (price ceiling) of £2.00 per loaf, analyse the
effect on the quantity supplied, with and without a £0.30 tax. Comment on the role of the
black market.
Compare consumer / producer surplus and price elasticity of demand in the free market and
the market with price controls.
Based on the above analysis, discuss whether the imposition of price controls benefits the
consumer.
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Chapter 3: Goods Market Equilibrium
Equilibrium price and quantity in a free market
Solution
The goods market is in equilibrium when Pd = Ps and Qd = Qs.
9.5 – 0.01Q = 0.5 + 0.005Q
9500 – 10Q = 500 + 5Q
15Q = 9000
Q = 600 equilibrium quantity
Substituting Q = 600 into (1) or (2), P = 3.50 equilibrium price.
The equilibrium quantity and price are 600 units and £3.50 respectively.
Figure 3.1C shows market equilibrium at E0, with equilibrium quantity 600 and
equilibrium price £3.50.
P
9.5
Supply function with tax:
P = 0.8 + 0.005Q
P = 9.5 - 0.01Q
E0: P =3.5 Q = 600
3.5
P = 0.5 + 0.005Q
0.5
Figure 3.1C Equilibrium in the free market
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Chapter 3: Goods Market Equilibrium
Goods market equilibrium: Taxes and their distribution
If the government imposes a tax of 30 pence (£0.30) per loaf,
(i) Calculate the new equilibrium price and quantity.
(ii) What is the distribution of the tax between the consumer and producer?
Solution:
(i) The tax of £0.30 per unit sold means that the effective price received by the producer is
(P – 0.3). The equation of the supply function adjusted for tax is
P – 0.3 = 0.5 + 0.005Q
…(3)
P = 0.8 + 0.005Q
The new equilibrium price and quantity are calculated by equating the original demand
function, equation (1) and the supply function adjusted for tax, equation (3),
9.5  0.01Q  0.8  0.005Q
Q  580
Substitute the new equilibrium quantity, Q = 580, into either equation (1) or equation (3) and
solve for the new equilibrium price
P = 9.5 – 0.01(580) substituting Q = 580 into (1)
P = 3.7
The new market equilibrium with the imposition of a 30 cent tax is 580, 3.70
This is shown as point E1 in Figure 3.2C
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Chapter 3: Goods Market Equilibrium
P
9.5
Supply function with tax:
P = 0.8 + 0.005Q
E1: P = 3.7, Q = 580
P = 9.5 - 0.01Q
P = 0.5 + 0.005Q
E0: P =3.5 Q = 600
0.5
Figure 3.2C Goods market equilibrium with and without taxes
(ii) The relative burden of a tax on the consumer and producer is known as the incidence of a
tax. The consumer pays the new equilibrium price of £3.70, an increase of £0.20 on the
original equilibrium price with no tax, which was £3.50. The consumer pays 2/3 of the tax.
The producer receives the new equilibrium price minus the tax, so the producer receives
£3.70 - £0.30 = £3.40, a reduction of £0.10 on the original equilibrium price of £3.50. The
producer pays 1/3 of the tax.
Note that the introduction of a tax reduces the equilibrium quantity.
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Chapter 3: Goods Market Equilibrium
Goods market equilibrium: Price Ceiling
The government decides to control prices of essential food products and imposes a
maximum price (price ceiling) of £2 per loaf.
Analyse the effect on quantity supplied.
Solution:
The price ceiling of £2 is below the equilibrium price of £3.50. Its effect is analysed by
comparing the levels of quantity demanded and supplied at P = £2.
The quantity demanded at P = 2 is,
Pd  9.5  0.01Q d
The quantity supplied at P = 2 is,
Ps  0.5  0.005Q s
(1)...
2  9.5  0.01Q d ...substituting P  2
0.01Q d  9.5  2
...(2)
2  0.5  0.005Q s ...substituting P  2
0.005Q s  1.5
Q d  750
Q s  300
Since the quantity demanded ( Q d = 750) is greater than the quantity supplied ( Q s = 300),
there is an excess demand (XD) of: XD  Q d  Q s  750  300  450 . This is also referred
to as a shortage in the market. It is illustrated in Figure 3.3C
With only 300 units supplied:
Pd = 9.5 – 0.01Q
Pd = 9.5 – 0.01(300)
Pd = 6.5
Consumers would be willing to pay £6.50 per unit.
The existence of price ceilings often leads to the establishment of black markets where goods
are sold illegally at prices above the legal maximum. Black marketers would buy as many
loaves as possible at the controlled price of £2, and sell them for £6.50, making a profit of
£4.50 per unit.
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Chapter 3: Goods Market Equilibrium
P
P = 9.5 - 0.01Q
PD = 6.5
E0: P =3.5 Q = 600
P = 0.5 + 0.005Q
PC = 2
Excess Demand
Q
QS = 300
QD = 750
Figure 3.3C Price ceiling, P = £2
Price ceiling and government tax
Analyse the effect on quantity supplied and black market profit when a tax of 30 pence
(£0.30) per loaf is imposed together with a price ceiling of £2.00.
Solution:
The supply function (adjusted for tax) for loaves of bread is given by
Ps = 0.8 + 0.005Qs
2 = 0.8 + 0.005Qs
0.005 Qs = 1.2
Qs = 240
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Chapter 3: Goods Market Equilibrium
Since the quantity demanded ( Q d = 750) is greater than the quantity supplied ( Q s = 240),
there is an excess demand (XD) of: XD  Q d  Q s  750  240  510 . It is illustrated in
Figure 3.3C
With only 240 units supplied:
Pd = 9.5 – 0.01Qd
Pd = 9.5 – 0.01(240)
Pd = 9.5 – 2.4
Pd = 7.1
Consumers would be willing to pay £7.10 per unit.
Black marketers would buy as many loaves as possible at the controlled price of £2, and sell
them for £7.10, making a profit of £5.10 per unit.
The imposition of the tax reduces the quantity supplied, increases the amount consumers
would be willing to pay, and increases the black market profit from £4.50 to £5.10 per loaf.
Price ceilings may require the government to introduce some form of rationing, to ensure
people can purchase a quantity of the good at the controlled price.
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Chapter 3: Goods Market Equilibrium
P
P = 9.5 - 0.01Q
PD = 7.1
With Tax: P = 0.8 + 0.005Q
P = 0.5 + 0.005Q
PC = 2
Excess Demand
Q
QS = 240
QD = 750
Figure 3.4C Price ceiling with tax
Calculate Consumer and Producer surplus in a Free Market
Solution:
The demand and supply functions in the free market are
Demand function :Pd  9.5  0.01Q d
(1)
Supply function :Ps  0.5  0.005Q s
(2)
The equilibrium price and quantity in the free market were £3.50 and 600 loaves respectively.
Consumer surplus is the difference between the price paid by the consumer and the highest
price which the consumer would be prepared to pay.
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Chapter 3: Goods Market Equilibrium
Producer surplus is the difference between the price received by the producer and the lowest
price at which the good would have been supplied.
Consumer and producer surplus at market equilibrium are calculated as follows:
At P = 3.5, Q = 600
CS = triangle AP0 E 0 = 0.5  (9.5 – 3.5)  600 = 1800
At P = 3.5, Q = 600
PS = triangle BP0 E 0 = 0.5  (3.5 – 0.5)  600 = 900
Total surplus is the sum of consumer and producer surplus; therefore,
TS = CS + PS = 1800 + 900 = 2700
P
A = 9.5
P = 9.5 + 0.01Q
CS
E0: Pe = 3.5, Qe = 600
Pe = 3.5
P = 0.5 - 0.001Q
PS
D = 0.5
Figure 3.5C Consumer and producer surplus in the free market
Calculate Consumer and Producer surplus with price ceiling of £2
The price ceiling of £2 is below the equilibrium price of £3.5.
As shown above, the quantity supplied at P = 2 is
Ps = 0.5 + 0.005Qs
2 = 0.5 + 0.005Qs
0.005Qs = 1.5
Qs = 300
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Chapter 3: Goods Market Equilibrium
With only 300 units supplied:
Pd = 9.5 – 0.01Q
Pd = 9.5 – 0.01(300)
Pd = 6.5
Consumers would be willing to pay £6.50 per unit.
Consumer and producer surplus at equilibrium with a price ceiling of £2.00 are calculated as
follows:
CS = rectangle BCEF + triangle ABF
= 300  4.5 + 0.5 × 300 × 3
= 1350 + 450 = 1800
PS = triangle CED = 0.5  300 × 1.5 = 225
Total surplus is the sum of consumer and producer surplus; therefore,
TS = CS + PS = 1800 + 225 = 2025
P
A = 9.5
P = 9.5 + 0.01Q
B = 6.5
F
CS
E0: Pe = 3.5, Qe = 600
Pe = 3.5
P = 0.5 - 0.001Q
C=2
E
PS
D = 0.5
300
Figure 3.6C Consumer and producer surplus with price ceiling
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Chapter 3: Goods Market Equilibrium
Compared to the free market when the price is £3.5 per loaf, the controlled market with a
price ceiling of £2 per loaf has left consumer surplus unchanged (in this case) but has reduced
producer surplus from 900 to 225. The imposition of a price ceiling below the free market
equilibrium will always reduce producer surplus.
Calculate the price elasticity of demand in
(i) the free market
(ii) the market when price controls are imposed and no tax is charged.
Solution:
Price elasticity of demand measures the responsiveness of quantity demanded to changes in
price. As an increase in price results in a reduction in quantity demanded and vice versa, price
elasticity of demand is a negative number. (See Chapter 2.6)
When price elasticity of demand is more negative than -1 (or the absolute value, excluding
the negative sign, is greater than 1) the good is said to be elastic.
When price elasticity of demand is between -1 and 0, the good is said to be inelastic.
Price elasticity becomes more inelastic as you move down the demand curve.
ed 
dQ dP

Q
P
ed 
dQ P

Q dP
ed 
dQ P

dP Q
The demand function for loaves is P = 9.5 – 0.01Q
P = 9.5 – 0.01Q
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Chapter 3: Goods Market Equilibrium
0.01Q = 9.5 - P
Q = 950 – 100P
dQ
 100
dP
(i) In the free market P = 3.5 and Q = 600
ed = (-100) x 3.5/600 = -0.5833
(ii) when a price ceiling of €2 per loaf is imposed, P = 2 and quantity demanded , Q = 750 .
ed = (-100) x 2/750 = - 0.2667.
The price is more inelastic at the lower price.
Price elasticity can be calculated from the demand function without using calculus.
P = 9.5 – 0.01Q
When P = 3.5, Q = 600.
If the price is increased by 1%, P becomes 3.535. Substituting in the demand function we get
3.535 = 9.5 – 0.01Q
0.01Q = 9.5 – 3.535
0.01Q = 5.965
Q = 596.5
Quantity demanded has decreased from 600 to 596.5, a decrease of 0.5833%
An increase in price of 1% leads to a decrease in demand of 0.583%.
Price elasticity of demand can be expressed as
% change in Quantity  0.583

% cahnge in Price
1
= -0.583, as above.
When the price of a good is in the inelastic section of the demand curve, an increase in price
leads to an increase in Total Revenue. The reduction in quantity demanded is more than
offset by the increase in price.
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