part 1 - microeconomics(1)
TRANSCRIPT
TOPIC 1 : DEMAND AND SUPPLY
X and Y are positively related if ↑X → ↑Y.
X and Y are negatively(inversely) related if ↑X → ↓Y.
Substitutes/complements.
Substitutes goods are goods that can be used in place of another good.
If good X and Y are substitutes. E.g. butter and margarine are substitutes
goods.
Complements : are goods that are used in conjunction with each other.
E.g. CD player and CD.
(A) DEMAND
Quantity demanded of X is the amount of a commodity that households
wish to purchase. It is a desired quantity, not actual quantity purchased.
Determinants of Quantity Demanded : The demand function :
- +
Dx = f (Px, Py, I ) where
Px = Price of the good X.
Py = Price of another good Y.
I = Income of household.
Px : A fall in Px will lead to an increase in quantity demanded.
PY : An increase in PY will lead to an increase in the demand for X if X and
Y are substitutes.
I : An increase in income will lead to an increase in the demand for X if X
is a normal good, but a fall if X is an inferior good.
2
2
Demand curve or Demand schedule.
The Law of demand shows the negative relationship between price and
quantity demanded: Quantity demanded increases when the price of a
commodity fall, and vice versa. Hence, the demand schedule is
downward-sloping.
A fall in prices will lead to an increase in quantity demanded which
is represented by a movement along the demand curve.
P
P0 a
↓Px → X↑
P1 b
D (PY , I )
X0 X1 Quantity, X
Market Demand curve
The market demand curve is the horizontal sum of the individual demand
curve of all households in the market.
Household A Household B Market : A + B
P P P
•
•
• •
• • •
• $2 2 2 A A A
B B B $1 $1 $1
DA + DB DB
DA
1 2 x 2 3 x 3 5 X
3
3
Shifts in Demand curve.
↑I will ↑Dx or ↑Py will ↑Dx if X and Y are substitutes.
An increase in demand shifts the entire demand curve to the right,
and vice versa. This means that, at each price level, more X is now
being demanded.
P
$1 A A”
D0 D1
3 4 X
(B) Supply
Quantity Supplied is the amount of a commodity that firms are able and
willing to sell. It is a desired sale, not actual sale.
Determinants of Quantity supplied: The supply function
+ + - -
Sx = f (Px, Tech, W, r ).
Px = Price of commodity
Tech = state of technology
W = wages.
r = interest rates
Px : An increase in Px will lead to an increase in quantity supplied.
Technology: An improvement in technology means that more output could
be produced with the same inputs. Hence, supply will increase.
W and r : An increase in W or r will lead to an increase in the cost of
production, causing firms to produce and supply less.
• •
4
4
Supply curve or Supply schedule
The Law of supply postulates that the quantity supplied will increase as
prices rise, and vice versa. Therefore, the supply curve has a positive
slope.
A rise in prices will lead to an increase in quantity supplied, which is
represented by a movement along the supply curve.
P
P1
P0 ↑Px → X↑
Market Supply curve
The market supply curve is the horizontal sum of the supply curve of all
firms in the market.
Firm A Firm B Market : A + B
P P P
•A
•B
•
•
• •
• •
X0 X1 Quantity, X
$2 $2 $2
S ( W, r )
SA SB SA + SB
B B B
A A A
1 2 x 2 3 x 3 5 X
$1 $1 $1
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5
Shifts of the supply curve
An increase in supply shifts the supply curve to the right, and vice
versa. This means that, at each price level, more quantity will be
supplied.
P
↑↑↑↑S →→→→ S→→→→
↑↑↑↑D →→→→ D→→→→
(C) The determination of prices
Price is determined by the interaction of demand and supply forces.
Equilibrium price and quantity occur at the point where demand = supply.
This occurs at the intersection of the demand curve and the supply curve.
P0, X0 = Equilibrium price and equilibrium quantity.
Above equilibrium price, we have excess supply: P will fall.
Below equilibrium price, we have excess demand: P will rise.
P
Excess S(producers, sellers, firms)
Supply
P2
Excess Demand
10 Xo 15 X
• •
•
D(buyers,consumers)
A
P1
P0
So S1
X0 X1 Quantity, X
P0
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6
(D) Effect of shifts on equilibrium price and quantity
E.g. ↑↑↑↑I for a normal good.
P
↑↑↑↑I→→→→ ↑↑↑↑D
Hence, P↑↑↑↑ and X↑↑↑↑.
E.g. If X and Y are complements, then an ↑↑↑↑PY
Px So
P0
P1
↑↑↑↑ PY →→→→ ↓↓↓↓DY ↓↓↓↓D
X. Hence,
P↓↓↓↓ and X↓↓↓↓.
E.g. ↑↑↑↑wages(w) of workers producing X.
↑↑↑↑w →→→→ ↑↑↑↑ costs of production →→→→ ↓↓↓↓S →→→→ S ←←←← .
P
P1
a
Do(Py, I)
X1 X0 X
P0
•
•
•
•
•
•
Xo X1 X
b
a
Do ( PY , Io)
So
P1
P0
D1 ( PY , I1 )
D0 (PY0 , I )
D1, (PY1 , I )
X1 Xo X
S1 (w1, ro)
So (wo, ro)
Hence, ↑↑↑↑P and ↓↓↓↓X b
b
a
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7
(E) (Demand) Elasticity
Elasticity measures the responsiveness(sensitivity) of demand to changes in prices, income, prices of substitutes or complements, etc.
Price elasticity of demand measures the responsiveness (sensitivity) of
quantity demanded with respect to a percent change in price.
ηηηηP = Price elasticity of demand = percentage change in demand for X
percentage change in Price
ηηηηP = % X = - 2 ∴↑P by 1% → X↓ by 2%.
% P
Note that the sign is always negative for a negative slope demand curve.
The demand for a good is more price elastic(sensitive) when there more substitutes in the market.
ηηηηI = Income elasticity of demand = percentage change in demand for X
percentage change in Income
ηηηηI = %X = 3 ∴↑I → X↑.
% I
Hence, when the income elasticity is positive, good X is a normal good.
ηηηηPy = Cross price elasticity of demand
= percentage change in demand for X
percentage change in the price of another good Y
= % X = +3 ∴↑PY → X↑.
% PY
Hence, when the cross price elasticity is positive, good X and Y are substitutes.
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Price Elasticity of Demand
Elastic :ηP> 1. For every 1% change in P, X changes by more than 1%
(responsive or sensitive or elastic).
Hence ↓↓↓↓Ρ→ ↑↑↑↑TR = P * X and vice versa.
|ηηηηP| = % X = 2
% P
Inelastic :ηP < 1. For every 1% change in P, X changes by less than
1% (not responsive or inelastic).
Hence ↑↑↑↑Ρ→ ↑↑↑↑TR = P * X and vice versa.
|ηηηηP| = % X = 0.2
% P
Unit Elasticity means ηP = 1. For every 1% change in P, X change by
the same 1% (unit elastic).
If demand is elastic ηp > 1
P
At P0, quantity demanded=Xo
At P1, quantity demanded=X1
P Elastic demand P Inelastic demand
D
D
X X
•
• P0 A
B
0 X0 X1 X
P1
D D
B •
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9
Perfectly elastic demand: |η= ∞ Perfectly inelastic demand:η|=0
P P
D
D
X X
Supply elasticity :
Price elasticity of supply measures the responsiveness(sensitivity) of
quantity supply with respect to a one percent change in price.
Perfectly or completely Perfectly or completely
elastic supply inelastic supply
P P
S
SF
X X
Topic 2
(A)The Production Possibility Frontier (PPF)
It shows the maximum combination of goods that can be produced given
the amount of resources and the state of technology in the economy.
Consider an economy producing two goods, X and Y with labour as the
only means of production. Assume that labours are equally suitable in the
production of X and Y.
One unit of labour can produce either 2 units of Y or 1 unit of X. There are
100 units of labour. 100L , 1L 2Y
1X
The PPF or the labour constraint can be expressed as Y = 200 – 2X.
dY = 2Y
dX 1X
1X
2
Opportunity cost The 'cost' which society pays for its choices is called the opportunity cost. The opportunity cost of a unit of X is 2 units of Y per unit of X The opportunity cost of producing 25 units of X is 2 units of Y per X.
Efficiency Every point on the PPF is a productive-efficient point because
it is not possible to increase the output of one good without reducing the
output of another good. Hence, goods produced on the PPF have
opportunity costs.
Bundle “A” is an efficient allocation as producing more X requires giving
up some Y. Bundle “B” is an inefficient allocation as there is no
opportunity cost associated with the production of an extra unit of any
good. Bundle “C” is an unattainable combinations (illustrates scarcity).
•
•
•
•
2Y
•
26 25 100
200
A 150
C
• B
Good X
D
Good Y
L
2
2
(B) The shape of the PPF with two constraints. Let us now suppose that labour is not the only means of production. We need capital (say machines), as well as labour, to produce both X and Y. One unit of capital produces either 1 unit of Y or 2 units of X. Assume a total of 100 machine hours is available. One unit of labour produces either 1 unit of X or 2 units of Y, and there are 100 labour hours available. The L-constraint : Y = 200 – 2X. The K-constraint : Y = 100 – ½ X. As both labour and machines are needed for the production process of both X and Y, both constraints have to be satisfied simultaneously. This means that a pair of X and Y will be feasible only if both constraints are satisfied. Y Use both K and L to produce X & Y
2
At point A, the combination of 150Y and 25X satisfies the labour constraint because there are enough units of labour to produce it. But it does not satisfy the capital constraint. So if we insist on producing 25 units of X, we will have to reduce our production of Y in order to make it feasible. This means that we will have to reduce Y until we reach the binding limit imposed by the capital constraint. This is given by point E
•
200 L
150
100
A
• E
K
25 70 100 200 X ½
100L , 1L 2Y 100K , 1K 1Y 1X 2X
3
3
(D) Specialization and trade.
Countries will be able to have more of everything once they specialize and trade. Countries 1 can produce, and consume, either 6 units of C or 2 units of F, or any convex combination of these two extremes. Countries 2 can produce, and consume, either 6 units of C or 6 units of F, or any convex combination of these two extremes. Clothes(C) Clothes(C)
Sell C Sell F
6 Country 1 6 Country 2
dC = 3C
3 A dF 1F 3 B
OC1 = 3 units of C OC2 = 1 unit of C 1unit of F 1unit of F Country 2 has a comparative advantage in the production of F. Produce F and sell F. Country 1 has a comparative advantage in the production of C. Produce C and sell C.
3 1
1 2 Food(F) 3 6 F •
•
4
4
If the international price of X is 2 units of Y per unit of X, then each country can specialise in the production of one good, and trade with each other. Both countries can become better off. Feasible sets after specialization and trade, with an agreed price of 2C per F. (2C / 1F) Clothes(C) Sell C Clothes(C) Sell F
6 Country 1 6 Country 2
3 A 3
Both countries now have consumption opportunities which they did not have before. They could now consume outside their initial PPF. Evidently, both households are better off (assuming that having more of all goods is indeed equivalent to being better off) after specialising and trading.
•
1 2 2 3
• • B •
1 1.5 2 Food(F) 3 4.5 6 F
•
•
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Tutorial 2
1) An economy produces two goods, X and Y. It uses two means of production, labour and capital. A unit of labour can produce either 1 unit of X or 4 units of Y (or any linear combination of the two). A unit of capital can produce either 4 units of X or 1 unit of Y (or any linear combination of the two). There are 100 units of each means of production. a) Draw the production possibility frontier of the economy when the two goods can only be produced by a mixture of both factors. b) What will be the opportunity cost of X if the economy produces 50 units of X? c) Given that the production technology is linear, will the opportunity cost of X remain unchanged when we produce 90 units of it ?
100L , 1L 1X 100K , 1K 4X
4Y 1Y
a) Y
400 L-constraint
100
80
4 ¼
The PPF is given by the heavy line as both capital and labour are required for the production of each unit of X and Y. b) When the economy produces 50 units of X, we are to the left of point A above. The binding constraint is that of capital. Hence, the opportunity cost is ¼ unit of Y per X. c) When we produce 90 units of X, we are to the right of point A above. Hence, the opportunity cost of X is 4 units of Y per X.
• A
•
•
Labour constraint: Y = 400 – 4 X or X = 100 – ¼ Y Capital constraint Y = 100 – ¼ X Y = 100 – ¼ (100 – ¼ Y)
∴ Y = 80 X = 80. K-constraint
50 80 90 100 400 X
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6
2) To produce one unit of commodity X requires half a unit of labour( no capital is needed). Each unit of X needs storage space during the production process which is limited up to 180 units of X. Commodity Y, on the other hand, requires a quarter of a unit of labour and half a unit of capital for the production of one unit. There are 100 units of labour and100 units of capital.
a) Draw the production possibility frontier. b) What will be the opportunity cost of Y when we produce 30 units of it. c) What will be the opportunity cost of X when we produce 80 units of it. d) Had we produce 120 units of X efficiently and the international price of X was 1Y per X, what would now be produced in this economy?
1X ½ L, 1S 180X, 1Y ¼ L ½ K
100L, 1L 2X 100K, 1K 2Y 1S 180X
4Y
a)
b) When 30 units of Y are produced, 180 units of X can be produced. The opportunity cost of producing 30 units of Y is 0 unit of X. c) When 80 units of X are produced, 200 units of Y can be produced. The opportunity cost of producing 80 units of X is 0 unit of Y. d) At 120 units of X, the opportunity cost of a unit of X is 2 units of Y per
X. Since the international price of X was 1Y per X, it means foreigners can produce X at a lower opportunity cost. It also means this economy has a comparative advantage in producing Y and hence, it is likely to specialise and produce at point A. It will then sell Y to buy X and hence, can become better off by consuming beyond their original PPF.
A
L : Y = 400 – 2X K : Y = 200 At point A, 400 – 2X = 200
∴ X = 100 and ∴ Y = 200 L: Y = 400 – 2X or X = 200 – ½Y S: X = 180 At point B, 200 – ½Y = 180
∴ Y = 40 and ∴ X = 180
K
200
400
120
L
Y
X
200
2
•
S
90 B
40
180 100
• • 30
80
•
•
1
1
TOPIC 3
Indifference Preference Theory
A) Budget Line :
The Budget Line shows the maximum combinations of good X and Y that
a consumer can buy with his income.
Budget line equation: PX X + PY Y = I
Slope of budget line, dY/dX = (Io/PY0 ) / (Io/PX
0 ) = PX
0 / PY
0 units of Y
per unit of X. It gives the market rate of exchange.
Suppose Io = $1,000, PX0 = $50, PY
0 = $10
Y Peter
Pt A: 5 PX0
+ 75 PY0
= Io
PX0
PY0
X
Every point on the same BL has the same PX0, PY
0, and Io
75 •A
•B
=20
=100
6 5 Io PX
0
Io PY
0
5
1
2
Shifts of the Budget Line
If Px falls, the budget line will rotate right along pivot (Io/PY0).
If Py falls, the budget line will rotate upward along pivot(Io/PX0).
If Income increases, the budget line shifts parallel outward as more of X
and Y can now be bought, and vice versa.
Y
↑↑↑↑
↑↑↑↑ X
B Utility Theory
Utility is the satisfaction a consumer gets from consuming a good.
Total Utility is the total satisfaction from the total consumption of a good.
It rises as more of X and Y are consumed.
Marginal Utility is the additional satisfaction one derived from consuming
1 more unit of a good. It diminishes as consumers consume more and
more of a good.
Thus, although total utility rises, marginal utility declines as a consumer
consumes more and more of a good.
•A
↓↓↓↓
↓↓↓↓
•B
•B •A
PX1
PY0
•A •B
•H
The further the budget line from the origin, the higher the income.
Io PX
1
Io PX
0
Io PY
0
Io PX
0
Io PY
0
Io PY
1
X
X
PX0
PY0
PX0
PY0
PX0
PY0
I1 PX
0 Io PX
0
Io PY
0
I1 PY
0
Y Y ↓↓↓↓Px ↓↓↓↓ PY
↑↑↑↑I
3
C) Indifference Curve(IC) or Utility Curve(U)
An utility curve shows the combinations of goods X and Y that give the
household equal utility or satisfaction. Therefore every point on an utility
curve has the same utility.
Y
Y0
Y1
Deriving the slope of the indifference curve. If we give up some units of good Y, the total loss in utility = dY ∗ MUY. If we increase the consumption of good X, the total gain in utility = dX ∗ MUX. Along the same utilty curve, the loss of utility from Y = gain in utility from X for utility to remain the same. Hence, dY ∗ MUY = dX ∗ MUx dY = MUx dX MUY
∴ the slope of the utility curve = MUx MUY
An Indifference map is a set of indifference curves or utility curves (U).
Properties of the Indifference maps:
1) Every point on the same utility curve has the same level of
satisfaction or utility. ( see point A and B)
2) Utility curves that are further away from the origin have higher utility.
3) Utility curves cannot intersect each other. (parallel)
Y
U2 = 50 utils
U1 = 20 utils
Uo = 10 utils
X
X0 X1 X
•
•
B =10
A =10
Uo =10 units of utility
•C
•B
•A
•
4
D) The equilibrium of a household
Utility maximisation:
Consumer is maximising utility at point A where the budget line is tangent
to the utility curve. At the point of tangency, the slope of the budget line
(Px/PY) equals the slope of the utility curve (MUx/MUY),
i.e. Px/PY = (MUx/MUY).
Utility is not maximised at point B as one can consume at A with Io to get
a higher Uo. It is only at A where utility cannot be further increased.
Y
Io
PY0
Y0
Uo
X0 Io X
PX0
Y
Io
PY0
Y0
Uo
U1
X0 Io X
PX0
• A is the utility-maximising bundle.
•
• B
A is the utility-maximising bundle.
PX0
PY0
5
F) Demand Curve
Income increases → Normal goods: buy more. E.g. Houses.
Inferior goods: buy less. E.g. black and white TV.
The Substitution Effect (SE) and the Income Effect (IE) Px falls.
1) Substitution effect (SE)
When consumers will have more incentive to buy more X because it is
now relatively cheaper, i.e. ↓Px→↑X and vice versa. It is a movement
along the same utility curve.
For all goods, the SE is such that a ↓Px→↑X.
2) Income effect (IE)
When Px falls, consumers will feel wealthier because their real
income( I / PX ) increases. It is a movement to another utility curve.
↓PX → ↑real income( I / PX ).
For normal goods, the IE is such that ↑real income → ↑X.
For inferior goods, the IE is such that an ↑real income → ↓X.
3) The Total Effect ↓Px→TE = SE + IE.
For inferior goods, SE > IE: (SE dominates)
Y
A
X
•
Uo
BN
I1 PX
0 Io PX
0
•
BI •
•
•
I2 PX
0
BN
BI
5 8 3
U1
6
(G) Hicksian versus Slutsky definition of real income.
Hicksian :
Based on Hicksian’s definition of real income, real income is measured by
utility. The higher the utility, the higher the real income.
Hence, every point on the same utility curve has the same real income.
The real income at point C is higher than that at point A.
Y
C
A U1
Uo
X
Slutsky : the original bundle of goods, bundle A(Xo,Yo) is used as the
reference point for real income.
Example ↑↑↑↑Px
Y
Io
PY
0
↑↑↑↑Px : The individual’s real income becomes lower based on both Hicksian’s and
Slutsky’s definition of real income.
•
B
•
•
A ••••
U0 U1
••••
X
Io PX
0
Io PX
1
BN
7
SE and IE
If Px↓↓↓↓, show the SE and IE for X which is a normal good.
1) The consumer initially consumes bundle A to maximise utility, Uo.
2) ↓Px will cause the budget line to rotate out as more X can now be
purchased. He will now choose bundle B and beomes richer because
his utility(U1) or real income based on Hick’s definition of real income
is higher.
3) To find the SE, shifts the new budget line parallel until it is tangent to
the original indifference curve, Uo at point C on the dotted budget line.
At point C, his his utility(Uo) or real income remains the same as
before(point A). Hence, the IE had been successfully removed.
Example ↓↓↓↓Px
Y
Io
PY
0
Example ↑↑↑↑Px
Y
Io
PY0
C
A ••••
U0 U1
••••A
••••
•••• Uo
IE
Io PX
1
SE
X2
X1
X0
••••C
Io PX
0
••••
IE
SE
X
X
Io PX
0
X0
Io PX
1
X1
BN
U1
BN
X2
TE = SE + IE
Notice that when X is a normal good, the SE and IE always move in the same direction.
8
Normal and inferior goods Income When the price of X has fallen from PX
0 to PX
1, the substitution effect
suggests that the individual will move from point A to point C. This is always true, regardless of whether the good is inferior or normal. Y X inferior X normal
Io
PY0
The move from the dotted line at C to the new budget line requires a
parallel shift, which is equivalent to an increase in nominal income. This,
therefore, is the income effect.
There are now two main possibilities: 1. If X is a normal good, consumption increases with income. Hence,
the individual will choose point BN which must be on the right of point C.
2. If X is an inferior good, consumption decreases with income.
Hence, the individual will choose point BI which must be on the left of point C
C ••••
••••
BI
IEI
A
IEN SE
Io PX
0
Io PX
1
U1
Uo
X2N X1 X0 X
BN
••••
••••
X2I
9
Complements and gross substitutes When the consumption of Y increases as the price of X falls, we say X and Y are complements. Examples of such goods are cars and fuel. As the price of fuel falls, there will be greater use of private cars and greater consumption of fuel. In a case where the consumption of Y falls as the price of X falls, we say that X and Y are gross substitutes. Again, a fall in the price of X will lead to more consumption of X. A typical example can be the use of private cars and public transport. When the price of public transport drops, people will tend to use car less and travel more on public transport. Y
A
Y Example Px↑↑↑↑
BS
BC
•
•
•
•
•
•
U0
Io PX
1
Io PX
0
X0
X
Io PY
0
Example ↓↓↓↓Px
Io PX
0
Io PX
1
X
A
BC
BS
Complements
Gross substitutes
Gross substitutes
Complements
Y0
Y0
U0
10
What is rationality? The economic concept of rationality involves two assumptions: Assumption 1 People know their desires and know the consequences of each choice of means. Assumption 2 People will behave in a consistent manner. By this we mean that if people have two feasible options available and choose one over the other, they should not, at a later date, choose the other option if both are still feasible. Option A or B: Choose A. Later if A and B are still feasible : if choose A: rational.
11
Tutorial 2
1) In a world of two goods, will the fact that one of the goods is normal have any
implication regarding whether the two goods are gross substitutes or complements?
X is normal. Are X and Y substitutes?
Yo
2) In a world of two goods, when the demand elasticity of good X is greater than unity, X and Y must be gross substitutes and X is more likely to be a normal good. True or false? Explain.
Yo
↓↓↓↓Px → demand is elastic → Total spending on X will rise. As nominal income is
unchanged, total spending on Y must fall. As the price of Y remains unchanged, the quantity demanded of Y must fall.
Y↓↓↓↓
Hence, X and Y must be gross substitutes. From the diagram, they lie on the right of C. Therefore, X is a normal good.
c
BNC
• •
Io PX
0
Io PX
1
U0
A
X
•
• BN
S
X1
Gross substitutes
X0
Complements
Io PY
0
X normal
Y
c •
•
Io PX
0
Io PX
1
U0
A
X X1
Gross substitutes
X0
Complements
Io PY
0
X normal
SE
Y
12
3) In a world of two goods, if the price of x decreases at the same time that the price of y increases in such a way that the real income under Slutsky’s definition remains unchanged, individuals will be worse off. True or false, explain.
↓↓↓↓Px and PY↑↑↑↑ such that Slutsky real income remains unchanged.
Indiv worse off?
The individual becomes better off
B
Io PY
0
Io PX
0
• A
U0
•
Y
U1
X Io PX
1
Io PY
1
13
4) You observe a consumer in two different market situations:
(i) earning $100 and spending it on 5 units of x at the price of $10 each and 10 units of y at the price of $5 each;
(ii) earning $175 and buying 3 units of x at the price of $15 and 13 units of y at the price of $10.
Is the consumer rational ?
Io = 100, Px0 = 10, Py
0 = 5. Choose A(5X,10Y)
I1 = 175, Px1 = 15, Py
1 = 10. Choose B(3X,13Y). Is he rational?
17.5
We begin at point A where the following budget line applies:
Px0 Xo + Py
0 Yo = Io.
10 ∗ 5 + 5 ∗ 10 = 100
Now, we have a new budget line and a new choice B:
Px1 X1 + Py
1 Y1 = I1
15 ∗ 3 + 10 ∗ 13 = 175
Is A(5X, 10Y) is on the new budget line?
••••
•••• B
3 5 10 11.67 X I1 = 175 Px
1 15
A
13
10
20 2) He chose B when A is still feasible.
1) He choose A when B is feasible.
Y
14
5) A good is a normal good whenever the substitution and income effects work in the same direction. True or false? Explain.
Y
When an individual receives income in kind of X units of X, the SE and IE can move in the opposite direction even if the good is a normal good.
C •••• •••• A
SE
Uo
X1 X0 X
X inferior X normal
PX0 X
PY0
PX1 X
PY0
X
↓↓↓↓Px
•••• BN
X2
IE
15
6) "It is better to give the poor a subsidy for food rather than an income supplement which they are likely to spend on other goods and alcohol." Suppose individuals consume only two goods, X, which is food and Y, which is other goods (including alcohol), and that they have an income of I. a) Show the effects on consumption of paying income supplement of S; b) Show the effects on consumption of paying a subsidy of s per unit of X consumed; c) Compare the effects of the two schemes assuming that government spending on each individual is the same in both cases (this means that if under the subsidy scheme the individual chooses Xs then sXs = S); 6(a,b)
c)
P.U. BL : (Px0- s
)X2 + PY
0 Y2 = I0 or Px
0 X2 + PY
0 Y2 = I0 + sX2
Lump BL : Px0 X2 + PY
0 Y2 = I0 + S
• •
Io + S PX
0
Io PX
0 Io PX
0 Io PX
0 - s
Io PY
0
Io PY
0
X
X
PX0
PY0
Y Income supplement(S)
Y
Io + S PY
0
U0
A • B
U1 • A B
U1 U0
Per-unit subsidy(s)
Xo
Yo
• • • A
B
U0 U1
U2
C
Io PX
0 Io PX
0 - s
Io + S PX
0
X
X2
Y2
Io PY
0
Io + S PY
0
Y
PX0
PY0
X2
16
7. A beauty parlour “Drop Dead Gorgeous” (DDG) wishes to create an exclusive and discerning clientele for its beauty treatments. To get the type of clients it hopes for, the parlour sets the price per treatment above the market rate. To get the exclusive attentions of its clients, it only accepts people who normally take more than a certain number of treatments per period (say B). These first B visits are part of a joining fee(F) package. a) Describe the budget constraint facing consumers. What are the conditions for the proposal to attract some customers? b) Will all consumers join DDG? c) Could joining the clientele of DDG mean a reduction in one’s visits to the beauty parlour? If so, would this mean that beauty treatment is an inferior good?
To capture some customers, the new budget line must be at least tangent to the original Uo. b) Will all consumers join DDG?
Io - F PY
0
Io PY
0
Io PX
0
X
Y
B + Io - F PX
1
• A
•
•
• A
A
A
Io - F PY
0
Io PY
0
Io PX
0
X
Y
B + Io - F PX
1
• B
Uo
Px1
PY0
Px0
PY0
B
B
17
c) Could joining DDG mean fewer visits. Would this mean that X is an inferior good?
Ending up with fewer visits does not necessarily mean that X is an inferior good.
Io - F PY
0
Io PY
0
Io PX
0
X
Y
•
A •
B
Uo
• C
U1
X0 X2 X1
Normal good Inferior good
1
Ting Mun Kwong TOPIC 4 : Production and the Behaviour of the Firm.
(A) Output (X)
The Production function: X = f(L, K) relates output(X) to two factors of
production, labour (L) and capital (K).
Inputs (L,K) → Technology → Output(X)
1) Product definition
Total Product (TP) = total output = X .
Average Product of labour (APL) or average output = X / L = output per
worker.
Marginal Product of labour (MPL) = dX/dL is the extra product(output)
produced by one extra labour.
Marginal Cost (MC) = dC/dX is the extra cost of producing one extra
output.
2) Cost definitions
Total Cost = Fixed Costs + Variable Costs.
C = FC + VC
FC does not vary with output (cost of building a factory).
VC increases with output, eg. wages, utility bills.
C = FC + VC
X X X
AC = AFC + AVC
Average cost AC = Average FC + Average VC
Average cost (AC) varies inversely with average product (AP).
↓AC = C / X↑ = $100 / 10TVs = $10 / 1TV
Marginal cost (MC) varies inversely with marginal product (MP).
When AP per worker is rising, AC falls as each new worker adds the
same amount to cost, but a greater amount to output, thereby lowering
the average cost per unit of output. Whenever marginal product is rising,
the cost of an extra unit (the marginal cost) will be decreasing. Hence,
when AP↑ → AC↓ and when MP↑→ MC↓ and vice versa.
2
(B) The SHORT RUN
Short run : At least one input (factor of production) is fixed, eg
capital, which implies diminishing returns to factor of production.
Initially, MP rises due to specialisation. Eventually, MP falls due to
diminishing returns to a factor of production because one inputs is fixed.
1) Initially, the increase in MP leads to a corresponding fall in MC.
2) Up to a certain level of output, diminishing returns sets in, causing MP
to fall and MC to rise. The Law of Diminishing Returns states that if
increasing quantities of a variable factor (e.g. labour) are applied to a
given quantity of fixed factor (e.g. capital), the MP of the variable factor(L)
will eventually decrease. This will lead to a corresponding increase in MC.
The fixed factor limits the amount of additional output that can be realised
by adding more of the variable factor(L).
Therefore the law of diminishing returns (that MP will eventually fall)
implies eventually increasing MC.
To sum up: ↑MP→ ↓MC and vice versa.
Therefore, all short-run cost (SRC) curves are the mirror (opposite)
image of the short-run product curves due to diminishing returns to factor
of production(L).
3
(C) The LONG RUN Returns to Scale
Long run : All inputs or factors of productions are variable. This
implies returns to scale. Again all long-run cost curves are the mirror
(opposite) image of the product curves due to returns to scale.
Scale refers to the size of operation.
Returns to a Factor(SR) Versus Returns to Scale(LR)
a) Returns to factor (marginal product) refer to the marginal product of
one factor while keeping the other factor inputs constant(K). SR
b) Returns to scale refer to situation when all input levels increase by the
same proportion.
Increasing returns to scale (IRS) or economies of scale could
originate from managerial and labour specialisation or more efficient use
of capital.
Here output increases at a faster rate than inputs(costs).↓↓↓↓AC = C / X
Decreasing returns to scale (DRS) or Diseconomies of scale could be
due to management problems or access to skilled labour as the business
becomes bigger and more complex.
Here output increases at a slower rate than inputs(costs).↑↑↑↑AC = C / X
Constant returns to scale (CRS): output increases at same rate as
inputs. AC is Constant.
4
D) Short-run cost curve
All short-run cost (SRC) curves are the mirror (opposite) image of the short-run product curves due to diminishing returns to factor. The Marginal Product (MP) of Capital or Labour defines the increase in output for one-unit increase of a particular input, keeping the other one constant. We typically assume that the marginal product is increasing for low levels of an input, but decreasing for high levels. This is referred to as increasing and diminishing returns to a factor, respectively. This assumption yields a graph which depicts the level of output attainable for every level of one input (labour), keeping the level of the other input (capital) constant.
X
↓MP TP
XA
↑MP
L1 L
C
MC↓↓↓↓
$
C
M
A
•
• •
•
• • M
C A
ACB ACC
ACM
ACA
ACC
ACA
AC is minimum at pt M or XM
MC↑↑↑↑ Tangent ray
XA XM XC X
XA XM XC X
SRC
SRAC
5
C
$
C
M
A
•
• •
•
• • M
C
•
A
ACB ACC
ACM
ACA
ACC
ACA
•CM
MC = AC where AC is minimum.
MCM
MCM
MC = AC where AC is minimum. A
M
XA XM XC X
XA XM XC X
SRMC
SRAC
SRC
6
E) Long-run Cost curve(LRC)
The general form of the cost function in the two inputs model is C (K, L) = wL + rK. Assume the production function initially exhibits IRS follows by DRS.
IRS: output increases faster than inputs.
DRS: output increases slower than inputs.
X
XA
V(K,L)
C
IRS
0
$
C
M
XA XM XC X
A
•
• •
•
• • M
C A
ACB ACC
ACM
ACA
ACC
ACA
AC is minimum at pt M or XM
DRS
Tangent ray
•
TP
LRC
XA XM XC X
LRAC
A
7
C
IRS
0
$
C
M
A
•
• •
•
• • M
C
•
A
ACB ACC
ACM
ACA
ACC
ACA
•CM
MC = AC where AC is minimum.
MCM
MCM
MC = AC where AC is minimum. A
M
LRC
LRAC
LRMC
XA XM XC X
XA XM XC X
8
F) Long Run Average Cost (LRAC ) and Short run average cost (SRAC)
The LRAC shows the lowest cost of producing any output when all inputs are variable.
Input prices (W0 and r0) and technology are assumed to be fixed.
$
XM X
AC
SRAC
SRAC (Ko)
SRAC (K1) SRAC
The LRAC shows the lowest average cost to produce each level of output
in the long run.
M
•
•
• •
•
•
• •
•
•
• SRAC(K2)
LRAC
SRAC SRAC(K3)
IRS:AC↓↓↓↓ DRS: AC↑↑↑↑
LRAC(W0, r0)
X0 X1 X2 XM X
SRAC
9
G) Isoquants and Isocosts
A) Isoquant (equal quantity) shows the combination of two inputs,
labour (L) and capital (K) that will produce the same quantity of output (X).
Thus, all points on an isoquant curve have the same output. Isoquant
analysis helps us to understand how the firm determines the least cost
method of production.
K
K0
K1
L0 L1 L
The slope of the isoquant is defined as dK/dL when X is unchanged. If we
reduce K by dK, output will fall by dK ∗ MPK. In the same way, if we
increase L by dL, output will rise by dL ∗ MPL. Along the isoquant, the fall
in output as a result of a fall in K has to equal to the rise in output as a
result of a rise in L.
Hence, dK ∗∗∗∗ MPk = dL ∗∗∗∗ MPL or dK/dL = MPL / MPk Therefore, slope of isoquant = MPL / MPk
Properties
a) Every point on the same isoquant has the same level of output (X).
b) Isoquants that are further away from the origin represents higher
output (X).
c) Isoquants cannot intersect each other. (parallel)
K
X2 = 70
X1 = 30
Xo = 10
L
•
• 1L
• B 10X
Xo = 10
A 10X
3K
10
H) Isocost (equal cost) shows the combinations of two inputs (L,K) that
can be hired with budgets, Co and for given prices of labour (Wo) and
capital (ro). Cost (Co) is constant along an isocost.
Slope of isocost = w / r
Slope = (Co / ro) / (Co / Wo) = Wo / ro Y
K
C0
r0
PK Xo Uo
Isocost
Shifts of Isocost.
↓Wo causes the isocost to rotate out along pivot Co/ro ,and vice versa.
↓ro causes the isocost to rotate out along pivot Co/Wo ,and vice versa.
↑Co shifts the isocost out parallel to the right, and vice versa, as more L
and K can now be purchased.
K K
C0 C0
r0
↓↓↓↓W r1 ↓↓↓↓r
C0
r0
w0 w1
r0 r0
Co Co L Co L
w0 w1
w0
K
↑↑↑↑C
C1/ r0
C0/ r0
A B
w0 w0
r0 r0
C0 / w0 C1 / w0 L
Io/PY0
Io/PX0 X
Peter Firm
C0 / w0 PL L
w0 r0
• •
• •
11
C) Combining Isocost and Isoquant.
The cost-minimising output is found at the point of tangency between the isocost
and the isoquant.
K
Co
r0
Tangent pt A is the output-maximising pt
A
Co L
Wo
The tangent point (A) represents the maximum output that can be produced for a
given cost (Co).
Expansion path:
K
LR expansion path
Co
r0
K1
SR:K0 A SR expansion path( K is fixed)
X1
L0 L1 C0 C1 CS L
w0 w0 w0
Short-run expansion path Along the short-run expansion path, the level of capital is fixed and the
only way to increase output is through increases in labour inputs.
Long-run expansion path
The long-run expansion path depicts the firm's growth of output when all
inputs are increased by the same proportion, along the ray through the
origin.
•
• • BS
•
Xo
Xo
BL
12
Tutorial 4
1) The minimum average cost is always at the point where it equals marginal cost. True or false? Explain. 2) Suppose that a long run cost function displays increasing returns to scale and then decreasing returns to scale. What does this imply for the shape of the long run average and marginal cost curves. 3) An increase in wages means that the new optimal choice of input mix will contain much less expensive labour which will be substituted by the cheaper capital. Therefore, the same level of output could be produced at exactly the same level of cost as before the change. Also the optimal input mix falls. True or false? Explain. 4) Explain why short run average cost is never less than long run average cost. 5) If long run marginal cost equals short run marginal cost at the point where neither of
them equals their average costs, the short run optimal input mix will not be the same as the long run optimal mix for that level of output. True or false? Explain.
6) The short-run marginal cost will always equal the long-run marginal cost at the point of minimum short-run average cost when there are increasing returns to scale. True or false? Explain. 7) a) Under which conditions will the long-run average cost and marginal cost be the same?
b) Will the short-run average cost be the same as the long-run average cost? c) Will the short-run marginal cost be the same as the short-run average cost?
8) The short-run marginal cost will always equal the long-run marginal cost at the point
of minimum short-run average cost when there are constant returns to scale. True or false? Explain.
13
Tutorial 4
1) True, refer to lecture. Derive.
2) Same as pg 6. IRS, then DRS imply that LRAC and LRMC are
U-shape. Derive.
3)
↑↑↑↑W : the same X can be produced with the same costs. T/F.
False, as at pt B, the cost is the same(Co), but less output is produced.
Capital to labour ratio or input mix, K/L↑
K
Co
r0
A •
L1
• K1 B
X1
C0 / w1 L0 C0 / w0 L
K0
X0
K
L
14
4) Why SRAC ≥≥≥≥ LRAC ?
K To produce Xo, SR & LR : pt A. ∴ SRC = LRC = Co ⇒ SRAC = LRAC.
LR expansion path
Co
ro
K1
K0 A SR expansion path
L0 L1 C0 CL CS L
W0 w0 w0
C SRC(Ko) LRC
$ LRAC
SRAC(Ko)
LRMC
• BL
•
• BS
Xo X1
•
•
•
M BS
•
• •
M
•
A
A
A SRMC=LRMC
X0 X1 XM X
SRMC(Ko)
X0 X1 XM X
BL •
BS
C0
K
L
CL
CS
SRAC=LRAC
15
5. False. If SRMC = LRMC⇒ pt A or Xo : SR K/L = LR K/L
6. False.
7. a) Under which conditions will the long-run average cost and marginal cost be the same? Under Constant returns to scale.
b) Will the short-run average cost be the same as the long-run average cost? No. 8. The short-run marginal cost will always equal the long-run marginal cost at the point of minimum short-run average cost when there are constant returns to scale. True or false? Explain. True
•
•
• • LRAC = LRMC A
A
B
B
Xo X1
X1 Xo
LRC SRC
LRACA
SRMC SRAC SRAC
• C
With CRS: At min SRAC :
SRMC
LRMCB
At pt B or X1 : SRC = LRC SRAC = LRAC
1
TOPIC 5 Perfect Competition(PC)
PERFECT COMPETITION (PC)
A) Characteristics
1) Many agents (buyers and sellers) - both are price takers.
2) Homogenous products.
3) Free entry and exist - low barrier to entry/exit.
LR profit = 0.
4) Perfect information - both buyers/sellers know the market price.
5) Free mobility of factors of production - low barrier to entry/exit of factors
of production.
There are two immediate conclusions:
a) All agents are price takers. As there are a large number of agents,
none of the agents can, on their own, change the market price.
b) There will be a single price in the market due to perfect information.
B) Demand curve and Revenue curve
As the firm is a price-taker, its demand curve is perfectly elastic.
In a perfectly competitive market, the firm's demand curve is horizontal as
price is fixed, whereas the industry's demand curve is the usual
downward sloping demand curve.
Single firm Market or Industry
$ P
So
6
5= P0
D=P=MR
5= P0
Do
1 2 x0 x X0 X
A •
2
C) Rules for profit-max in a perfectly competitive(PC) market.
Rule (1) Short run : Produce only if P ≥ AVC as part of the revenue
(P - AVC) X can be used to cover fixed cost. Long run : Produce only if
P ≥ AC in the long run.
AC = AFC + AVC TC = TFC + TVC
14 = 10 + 4. If P = $7, the firm should still produce.
Rule (2) To maximise profit(π), PC firm will produce up to the output
where MR = MC or as P = MR ∴Produce until P=MC to maximise π
$
Economic profit(π)
π = TR – TC
π = PX - AC(X)
π = (P – AC) X
When P > AC, firms are making economic profit.
When P < AC, firms are making economic losses.
When P = AC, economic profit = 0. Normal profit.
MR = P=D P ••••
x 1 3 2
MC
••••
••••
•••• ••••
MR
MC
4
••••
•••• A
3
D) Supply curve of a PC Firm = MC.
Firm’s short-run supply curve Firm’s long-run supply curve
$ $ MC = S
MC=S AC
P1 AVC
P0
P*
P*
X0 X1 X X
1) The supply curve in the short run is the part of MC above AVC. The
reason is that in the short run if P < AVC, firms will shut down.,
2) The supply curve in the long run is the part of MC above AC. The
reason is that in the long run, if P < AC, firms will shut down.
E) Short-Run Supply curve of a perfectly competitive industry.
The industry supply curve is the horizontal sum of the supply curve of
each firm in the industry.
Firm A Firm B Market : A + B
P P P
B
A
B
A A
B $2
$1
$2
•
•
•
•
• • • $2
S
S
• • •
SA + SB or MCA + MCB MCA=SA MCB=SB
1 2 x 2 3 x 3 5 X
$1 $1
4
F) Long-Run Equilibrium for a perfectly competitive firm.
1) In the long-run, all PC firms will only earn zero economic profit.
Otherwise profit/losses will lead to entry/exit of firms which will cause a
corresponding shift in the supply schedule until economic profit or
losses = 0.
$ Firm Industry
Do
x0 x X0 X
• • A
A P0
AC(wo, ro) MC(wo, ro) P
So(wo, ro)
P0
5
Effect of taxation.
$ $
AC0
AC0
t
x0 x x0 x1 x
ACt = ACo + t
MCt = MCo + t
Effect of subsidy.
Per-unit subsidy(s) Lump sum Subsidy(S)
$ MC0
MC0 - s MC0 AC0
AC0
AC0-s
s
x0 x x0 x1 x
ACS = ACo - s AC
S = AC - S
MCS = MCo - s x
•
•
•
•
Lump sum Tax(T) Per-unit tax(t) on firms: MC0
ACo + T /X
ACo – S x
Per unit: Both MC and AC shift parallel:
Lump change in costs
MC0 + t
MC0 AC0+t
ACT = AC + T
x
CT = C + T
6
Consumer Surplus(CS) and Producer Surplus(PS)
Consumer Surplus (CS) is the net benefit to consumers of being able to
buy units of a good more cheaply than the amount they will willing to pay.
Producer Surplus (PS) is the net benefit a producer gets by obtaining a
higher price for any unit than the additional cost incurred in producing that
unit.
P
S0
9
Do (willingness to pay)
0 1 2 X
P Output XPC.
S0
9
Do
0 1 2 X
• A
3
8
2
CS
PS
• A
3
8
2
5 = P0
5 = P0
•
•
•
•
•
•
XPC
= 3
XPC
= 3
7
Allocative efficiency
Allocative efficiency occurs when it is impossible to change the allocation
of resources in such a way as to make someone better off without making
someone else worse off.
This condition is satisfied in a perfect competitive market where the
demand curve intersects the supply curve.
P S0 = MC
Do ( willingness to pay)
0 Xm X
By producing more X from Xm to XPC , CS + PS can be further increased
by area 1 + area 2. At XPC , CS + PS are maximised. It is clear, we can
increase neither consumer nor producer surpluses without reducing the
other. In that sense, the perfectly competitive solution is allocative
efficient.
• A
5 = P0
XPC
= 2
3
•
•
•
1
2
3
4
8
Tutorial 5 Perfect Competition
1. An increase in demand for a good in a perfectly competitive industry
will in the long run bring about an increase in the number of firms in the
industry although each firm will produce as much as before the change.
True or false? Explain.
2. "In the long-run, a lump sum tax will be completely transferred onto
consumers. Therefore, one can safely say that in competition, with
free entry and exit, consumers always carry the full burden of taxation.
Discuss.
3. "If a lump-sum subsidy is granted to every firm in a competitive
industry, the output of each of the original firms will fall in the long-run".
Discuss (a) when only the original firms qualify for the subsidy;
(b) when all firms qualify.
9
Tutorial 5
1. ↑↑↑↑D →→→→ ↑↑↑↑ # of firms; x unchanged. T/F .
Firm Industry
$ MC P S0
AC
x
Firm Industry
$ MC P S0
AC
Π
x
Firm Industry
$ MC P S0
AC S1
Π
P0
1
x
•
•
•
• B
A
A
B P1 P1
X0 X1
•
•
• •
• B
A = C
A
B
•
P1
P2, C AC
P1
x2 X0 X1 X2
•
•
•
• B
A
A
B
•
P1
AC
P1
X0 X1
x0 x1 X
Do
D1
Do
x0 x1
X
X
x0 x1
P0 P0
P0
1
Do
1 D1
D1
2
10
Short Run :
An increase in demand shifts the demand curve to the right causing
market price and industry output to increase to P1 and X1 respectively. At
P1, firms will produce x1 where P1 = MC to maximise profit. Each firm now
makes economic profit. Firm’s output and industry output increase; P↑.
Long Run :
Economic profit will attract new firms to enter the industry. As more
outputs are produced and supplied, the market supply schedule will shift
to the right and price will fall until there is no more economic profit.
The market is now at equilibrium.
Firm’s output(x) unchanged; Industry output(X)↑; price unchanged;
more firms in the industry.
11
2. $ Lump-sum Tax(T) P
MC0
AC0 + T
AC0
$ P
MC0
AC0
SR: AC shifts up. As cost of production goes up, firms make economic losses.
LR: Losses will cause some firms to close down and market supply falls and shifts to
the left until economic losses is zero at point B(P=min AC). Hence, X↓, P↑, x↑.
Consumers bear the full burden of the tax. Allocative efficient as P = MC.
A Losses
•
• •
x
D
A P0
S0
B B
A Losses
•
•
•
•
AC0 + T x
D
SLR
P1
A P0
S0
•
P0
AC1
x1 Xo X1 x0 X
Xo x0 X x
x
T
x1
12
3. When only existing firms qualify for the lump sum subsidy, S
$ P
MC0
AC0
SR: AC shifts down. Economic profit. LR :
When all firms qualify for the lump sum subsidy, S
$ P
SR: AC shifts down. Firms make economic profit.
LR: Profit: new firms will enter and market supply will shift to pt B(P = min AC)
Hence, X↑, P↓, x↓.
S0
B
B
A
•
•
•
D
P0 A
P1
SLR
•
• ∏
Xo X1 X x0 x1 x
P1
AC0 - S x
MC0 AC0
A •
D
S0
P0 A •
•
Xo X x0 x
P0
AC1
AC0 - S x
∏
P0
1
Topic 6 MONOPOLY (MP)
A) Characteristics of a monopoly
1) One single producer (seller).
2) Very strong barriers to entry: may be due to economies of scale or
patents.
3) Perfect information and mobility.
4) Homogeneous good.
Firm's demand curve is the market demand curve (sole producer) and is downward-
sloping.
B) The Demand function and Marginal Revenue function.
Revenue, R = P X
Marginal Revenue (MR) is defined as dR/dX.
MR = dR = P dX + X dP
dX dX dX
MR = dR = P + dP X
dX dX
MR = P 1 + dP X
dX P
As η = dX P , hence 1 = dP X
dP X η dX P
∴ MR = P 1 + 1
η
∴ MR = P 1 - 1
|η|
MR is a function of the current price and the demand elasticity.
2
C) Linear demand and demand elasticity.
A monopolist will never produce along the inelastic part of the demand schedule.
Example: Assume a linear demand function: P = a – bX.
Revenue R = PX = aX – bX2 . Hence dR / dX = MR = a – 2bX
P
a
demand elastic : |ηηηη| > 1
demand inelastic : |ηηηη| < 1
MR b D
MR
• Unit elastic : |η| = 1
0 20 40 X
2b
3
D) Profit maximization for the monopolist.
1. How much to produce to maximise profit? Set MR = MC
To maximise profits, the monopolist will produce up to the output where MR = MC.
2. Whether to produce?Produce as long as: P ≥ AC.
The final market configuration of the monopolist is shown below.
1) Produce the output where MR = MC to maximise profit.
Project a vertical line from the equilibrium output to the demand curve and read the
price on the vertical axis.
(D) Monopolistic Power
Monopolistic power, P / MC refers to the producer’s ability to keep price above
marginal cost: the greater is the gap, the greater is the firm’s power to exploit the
market.
When P = MC, P / MC = 1 ( no monopolistic power)
Monopolist produces where MR=MC
P 1 - 1 = MC
ηηηη
P = 1 If ηηηη , P
MC 1 - 1 MC
ηηηη
The greater the price elasticity of demand,ηηηη, the smaller the degree of monopolistic
power. For the case where ηηηη = ∞∞∞∞ as in perfect competition, the firm has no power.
P / MC = 1
•
•
•
AC
A
MC
AC
PM
MC =MR
MR
D
XM
5
10
X
P
π
4
(E) The inefficiency of the monopolist
The demand schedule represents individuals' willingness to pay.
Under perfect competition, the triangle A-C-Pc depicts what we called the consumer
surplus in the sense that this is part of what the consumer was willing to pay, but
ended up paying less ( the market price Pc).
Similarly, the marginal cost schedule represents the seller's willingness to sell. The
difference between the prices he gets for each unit and the price for which he, or she,
was willing to sell is called producer surplus (triangle Pc -C-F).
We interpret both surpluses to be the benefits generated by the market.
D
If we now compare the two equilibria, M( under monopoly) and PC ( under perfect
competition), we can clearly see the way in which the monopolistic market structure is
inefficient.
In the case of the monopolist, we see that by moving from point M or output XM (which is the
monopolist allocation) to XPC , both consumer and producer surpluses can be increased.
Hence, the monopolist solution is inefficient in the sense that we can have more of one thing
(benefits of either consumers or producers) without giving up another (benefits to the other
group).
The loss of consumer surplus and producer surplus associated with a monopolist is given by
the shaded triangle B-C-M. This is called the deadweight loss, which is a net loss to
society. Hence, a monopolist is inefficient as it leads to deadweight loss.
MR
MC = S(PC)
C •
•
M
XPC XM
•
1 2
•
•
•
CS
PS
PM
PC •
•
•
Deadweight loss
A
F
B
P
X
5
Tutorial 6 Monopoly
1. Monopolist always produces in the inelastic portion of its demand schedule.
T/F
Revenue, R = P X
MR = dR = P dX + X dP
dX dX dX
MR = dR = P + dP X
dX dX
MR = P 1 + dP X
dX P
As η = dX P , hence 1 = dP X
dP X η dX P
∴ MR = P 1 + 1
η
MR = P 1 - 1
η
False, a monopolist will never produce in the inelastic portion of its demand schedule
as MR is negative.
2. Can one say that the greater is the price elasticity of demand, the less power will the monopolist enjoy. ↑↑↑↑ηηηη →→→→ monopolistic power ↓↓↓↓. T/F
Monopolist produces where MR=MC
P 1 - 1 = MC
ηηηη
P = 1 If ηηηη↑↑↑↑, P ↓↓↓↓
MC 1 - 1 MC
ηηηη
6
3. Analyse the effects of a lump-sum tax on a monopolist. Will such a tax help in rectifying the monopolist's inefficiencies?
P
The lump-sum tax would constitute a fixed increase in costs and would therefore
affect AC, but not MC. AC shifts up by T/X which means that the new AC would be
asymptotic to the original one as the quantity produced increases. As marginal costs
remain unchanged, the monopolist would not change its profit maximising output
where MR=MC at point A. However, profits is now lower as AC is higher.
Hence, X and P unchanged, profit ↓.
As the tax does not affect the equilibrium condition in the monopolist market and in
this respect, it does not alter the inefficiency created by the monopolist.
The lump-sum tax would not change the deadweight loss which would still be triangle
M-C-A. However, if members of society have different weightage in the social welfare
function, it is possible to re-distribute the tax to the more needy group. In other words,
the policy can fuel a social improvement. Hence, some of the inefficiency may be
compensated through an appropriate use of the tax revenue.
4. An increase in the fixed cost will have no effect on the equilibrium price and output of a monopolist. True or false, explain.
An increase in the fixed cost by $F would constitute a fixed increase in costs and
would therefore affect AC, but not MC. AC shifts up by F/X which means that the new
AC would be asymptotic to the original one as the quantity produced increases.
•
• • A
Π0
Xo X
AC1= AC0 + T X AC0
D
MC0
MR
P0
AC
M P1
X1
•
XPC
C
7
5. Analyse the effects of a unit subsidy on a monopolist. Will such a subsidy provide
any improvement? 1999 ZB 4b.
P
The subsidy will shift AC and MC parallel down, resulting in a higher level of output.
This means that the subsidy is effective in bringing the output closer to the allocative
efficient output.
X↑↑↑↑, P↓↓↓↓, profit ↑↑↑↑.
6. An effective imposition of a maximum price will necessarily cause a monopoly to
reduce its output. T/F, explain.
P
P0
Pmax
D1
8
X↑, P = Pmax.
•
•
• •
•
P1
A
P0
MC0-s
AC0
MC0
AC0-s
X0X1 X
MR
D B
XPC
•
• A
B
MR0
X0 X1 X
MC0
AC0
•
8
7. A famous gallery which houses a large exhibition of rare impressionistic paintings
faces demand from tourists as well as locals. The tourists’ demand schedule
begins at a higher price and its price elasticity of demand is more inelastic than that
of the locals.
a) Draw the demand and the marginal revenue curves facing the monopolist.
b) Determine the output and price if the firm cannot price-discriminate.
b) Cannot price discriminate.
Will produce X1 and sell to both tourists and locals at P1
MR1
P
P
P
x
X
x
D1
D2
D1 +2
D1
MR2
Tourists
Locals
Monopolist
P
DT
MRT
Constant MC
•
• a
T
d
b
H •
X0
X1
z • •
P1
•
X
T
P2
MRT
P1
P*
P*
P*
5
5
XL
• • •
1
Topic 7 MONOPOLISTIC COMPETITION
Monopolistic competition is the market structure where there are many sellers producing differentiated product.
Sellers are price-makers. Therefore, it faces a downward sloping demand curve which means it can change the price at which it sells its own output.
A) Characteristics: same as perfect competition except product is differentiated.
1) Differentiated product.
2) Freedom of entry and exit.
3) Large number of firms.
4) Perfect information and mobility.
Firm’s demand curve is downward sloping.
Product differentiation can take the form of non-price competition such as advertising and providing better services. There are, apart from advertising, many methods which firms can adopt to create differentiation. The following list contain a few examples: Packaging Product Design Types of services Location
2
B) The Monopolistic Competitive model :
Short-run equilibrium
Firms set output such that MR = MC to maximise profits. Equilibrium output is given by XSR and the price charged is PSR. This is the situation in which each firm earns economic profits.
Long-run equilibrium
In the long run, economic profit will attract new firms to the industry. With more substitutes and greater competition, the demand for each firm will fall and become more elastic until it is tangent to the average cost curve. Firm will produce at the tangent point. P P X
A•
•
PSR
Π •
DS
XSR
MR
AC
MC
AC
A•
•
PSR
Π •
DS
XSR
MR
AC
MC
AC
DLR
XLR
• PLR B
3
Long-run equilibrium Π = 0 XLR X
• A
MC
AC
P
DLR
AC =PLR
•
4
Tutorial 7 Monopolistic Competition 1) How will a lump-sum tax on firms in monopolistic competition affect their long-run output? ”It is good of the government to tax the industry in such way as it forces the
long-run equilibrium to be nearer to the point of minimum average cost. Hence, with proper calculation of the lump-sum tax, the government can restore allocative efficiency in the economy and reduce the monopolistic power of the firm”. Comment on this statement.
B SR: Lump-sum tax ↑↑↑↑AC and leads to economic losses. LR: Losses cause some firms to close down. With lesser competition, the demand for each firm’s output will rise and become less elastic. Hence, the demand schedule will shift up and become steeper until it is tangent to AC. Hence, X↑↑↑↑ closer to the point of minimum average cost. The industry becomes less inefficient. X↑↑↑↑↓↓↓↓ or unchanged. P↑↑↑↑
Firms produce where MR=MC to maximise profits.
P 1 - 1 = MC
ηηηη
P = 1
MC 1 - 1
ηηηη
2) An increase in fixed cost will have no effect on the equilibrium price and output of a
firm in monopolistic competition. It will also not affect its inefficiency. True or false, explain.
↑↑↑↑ in fixed costs by $F: New cost = Cost + F : AC converged up.
•
A•
Losses
• P
P1
D1
AC0
AC1
P0
XLR
MC0
D0
X XAE Xpc
X1
•
AC1
MR0
•
5
3) An increase in annual license fees will have no effect on the long-run equilibrium of firms in monopolistic competition. True or false, explain. ↑↑↑↑ in annual license fee by $L: New cost = Cost + L : AC converged up.
1
Topic 8 Factors Market
(A) The demand for factors
The demand for factors of production comes from the firm, the producing agent. It can
be derived as a result of the desire of the firm to maximize profits.
Remember that the profit function is:
Π = R(X) - C(X) = Px X - wL - rK
where L stands for labour and K for capital goods.
Price of labour is wages (w) and the price of capital is the interest rate (r). The aim of
the firm is to maximize profits. We must now inquire what that would mean for the
choice of inputs.
(B) The Demand for Labour (MRPL )
Marginal product of labour, MPL is the extra product produced by one extra labour.
Marginal Revenue Product of Labour, MRPL = MPL . MR. It is the money value of the
marginal product.
Assume there is only 1 variable input labour (L) with unit cost w. The question is how
much labour should the firm demand if its objective is to maximise profit.
The competitive firm’s objective is to choose labour to maximise profit, i.e.
Max (π)= PX(L) – wL where p is the price per unit of output. L
dπ = P dX - w = 0
dL dL
∴ MPL P = w
MPL is the extra product produced by one extra labour.
Therefore, to maximise π, firm would hire labour up to the point where MPL P = w,
where the money value of the marginal product (or the Marginal Revenue Product of
Labour) equals the nominal wages. The diagrams is shown below:
Labour Demand Curve Real Labour Demand Curve
W
W0
• •
MRPL = P X MPL MPL
SL SL
L0 L L0 L
DL
1 2
•
•
ω = W
PX0
ω0 = W0
PX0
2
Optimality in consumption- leisure space.
The individual will want to choose the most preferred combination of consumption and
leisure. Given the shape of indifference curves and the fact that utility is increasing
with an increase in both leisure and consumption, such an optimal point is captured in
the following diagram.
Formally, this problem takes the form of:
Maximising U(X, Le) s.t. Px X = w ( Ĺ - Le) and its solution is exactly point A.
X
ĽWo
Px0
U0
•
Wo Px
0
Xo A
Le0
Ľ Le
3
Deriving the Supply of labour
Upward-sloping part of Ls (pt A to pt B)
An increase in wage from Wo to W1.
At the lower end of wage levels, income is very low. Labours will more likely to
respond to the increase in the wage level by working more.
From A to B, when w↑→ work↑ or Ls↑(labour supply).
↑↑↑↑w→→→→ SE →→→→ ↑↑↑↑Ls
→→→→ IE →→→→ ↓↓↓↓Ls
Backward-bending part of Ls (pt B to pt C)
An increase in wage from W1 to W2 .
At the other end, when your hourly wage is enormous, you are unlikely to be
impressed by a proposed increase in your hourly wage. You are more likely to work
less and have more fun. You are more likely to think to yourself, “If I am paid more, I'd
better spend more time at the golf course so that other people can see that I am a
high flyer.”
From B to C, when w↑→ work↓ or Ls↓(labour supply).
↑↑↑↑w→→→→ SE →→→→ ↑↑↑↑Ls
→→→→ IE →→→→ ↓↓↓↓Ls
IE>SE
SE>IE
U2
•
•
•
•
• •
C B
A
C
U1
U0
B
A
LsA Ls
B Ls
C Ls
Labour Supply
LeA Le
B Le
C Le
Leisure Ľ
LsA
= Ĺ - LeA
LsB
= Ĺ – LeB
16 10 13 8
W0 Ľ PX
0
W1 Ľ
PX0
W2 Ľ
PX0
ω1 = W1
PX0
ω2 = W2
PX0
ω0 = W0
PX0
ω0 = W
PX0
Xo
X SL
4
Market equilibrium
Consider the aggregate demand for labour based on the marginal product of labour
and the supply of labour which is based on the simple horizontal summation of
individuals' supply curves:
ω
Pt A is the equilibrium point.
SL
A • ωe
L
DL
5
Tutorial 8
1) Derive the supply curve of labour and explain why it may be backward bending?
See lecture notes.
2) Is leisure a normal good or inferior good?
X
C
A
U0
On the upward part, ↑w→ ↑Ls → ↓Le. Leisure can be a normal or an inferior good.
On the backward part, ↑w→ ↓Ls → ↑Le. Leisure must be a normal good.
3) When labour supply is upward-sloping, leisure cannot be inferior. True or false,
explain. False.
4) The backward bending part of labour supply can only be a result of leisure being a
normal good. True or false, explain. True.
5) The backward bending supply curve of labour means that leisure is an inferior good.
True or false, explain. False.
•
•
• •
Xo •
•
•
Le0
Ľ =24 Le
BU
I
BBACK
BUP
BU
N
BB
N
W0 Ľ
PX0
W1 Ľ
PX0
le normal le inf
LeC
11
SE
16
6
6) Consider an individual who treats leisure as an inferior good. Would he work more
hours when nominal wages increase?
7) Suppose that a labourer has chosen to work Lo hours at the going real wage of ω0
and ω0= w/p. He is now offered the following:
i) an increase in their real wage to ω1 per hour,
ii) an increase of B pounds per hour (which is greater than the increase in the first
option, B > ω1 - ω0 ) but only for overtime (the hours above Lo);
a) What will happen to the labour supplied by this individual under each of these
proposals assuming that his choice is in the upward region of his labour supply ?
b) Will your answer be different if he is at the backward bending region of his
labour supply ?
c) Is it possible that the labourer might be indifferent between the two schemes?
A •
W0Ľ
PX0
•
Inferior
ω0
LsA
BI
LeA
•
C
ω1
W1Ľ
PX0
U0
LeC
9
U1
Ľ Le LeB
X
7
7
7(a,b)
Option 1: ↑ W0 to W1 per hour. (W1 > W0)
Option 2: Same W0 for the first normal Ls0
hours, but pay overtime pay of W2 per hour
thereafter. W2 > W1
X Option 1 X Option 2
W1L BUP
BBACK
PX0
W0L W0L
PX0 PX
0
U1
U0 U0
Upward part of Ls: ↑Ls Here, Ls always ↑
Backward part of Ls: ↓Ls.
7(c) It is possible for him to be indifferent to the two schemes.
X
W1 L
PX0
B2
W0 L B1
PX0
A •
• •
•
•
A
B
W0 PX
0
BU
W1 PX
0
W2 PX
0
•
U1
•
W0 PX
0
W1 PX
0
Le1 Le
0 L Le
Ls0
BB
Le0
L Le
Ls0
Le0
L Le