Market Demand
Market Equilibrium
The Partial Equilibrium Competitive Model
Lecture 1, ECON 4240 Spring 2017
summary of Snyder et al. (2015)
University of Oslo
17.01.2017
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Partial Equilibrium
Market Demand
Market Equilibrium
Outline
Focus:
Determination of market price of 1 good, while taking the
price of all other goods as "given" (= not explained)
Why we need this?
To study the effect of taxes and price regulations
To study the effect of changes in income levels or income
distribution on market prices and quantity of goods sold
To think about how the gains from trade are divided between
sellers and buyers (maybe to use this information to guide
policies aimed at redistributing wealth among citizens?)
To have a benchmark for comparison to study potential welfare
losses due to lack of competition (oligopolies)
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Market Demand
Market Equilibrium
The Market Demand Curve I
As discussed in ECON 4200 (and in Part 2 of Snyder et al.
(2015)), when there are two goods available (good x and good
y ) the individual demand function for good x is summarized as:
quantity demanded of good x by consumer i: xi (px , py , Ii )
where px ,py are market prices, Ii is consumer i’s monetary
income
If there are n consumers:
market demand for x: X = Σni=1 xi (px , py , Ii )
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Market Demand
Market Equilibrium
The Market Demand Curve II
Note:
1
2
3
We allow different consumers to have different preferences
(how would you write the market demand if consumers had all the
same preferences?)
We allow consumers to have different incomes (how would you
write the market demand if individuals had all the same income?)
We do not allow the prices faced by different consumers to
differ
As a result of 1 and 2: this model can be used to think about
how the distribution of income among consumers affects
demand
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Market Demand
Market Equilibrium
The Market Demand Curve III
Market demand X is a function of 2 prices and n incomes. It is
common to show graphically the relation between X and px ,
for given values of py and I1 ,..,In
Changes in px : shifts along the demand curve - changes in
quantity demanded
Changes in py or some/all Ii : shifts of the curve - changes in
demand
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Market Demand
Market Equilibrium
The Market Demand Curve IV
Alternative partial equilibrium model: focus on one good with
price P but consider the effects on the market for that good of
changes in prices of other goods (prices of all these other
goods measured in vector P 0 )
Demand for good x denoted
QD (P, P 0 , I )
where I is the income of all consumers.
Price elasticity of market demand: eQ,P =
∂ QD (P,P 0 ,I ) P
QD
∂P
∂ QD (P,P 0 ,I ) P 0
Cross-price elasticity of market demand: eQ,P 0 =
QD
∂ P0
∂ QD (P,P 0 ,I ) I
Income elasticity of market demand: eQ,I =
QD
∂I
What are the effects of these elasticities on the shape of the demand curve in
the standard Q-P space?
summary of Snyder et al. (2015)
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Partial Equilibrium
Market Demand
Market Equilibrium
Timing of Supply Response
We look at market equilibrium at 3 different time horizons. The
time horizon determines the supply response to changing demand
conditions:
Very short run: Quantity supplied is fixed
Short run: Number of firms in the industry is fixed, but the
quantity supplied by each firm, and hence the overall quantity
supplied, can vary
Long run: Firms can enter or exit the market
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Market Equilibrium
Pricing in the Very Short Run
Very short run markets:
not very common. Examples: perishable goods - tickets for a
concert/game (auctions have features in common with very
short run markets)
Supply is a vertical line
In this case the only role of price is to ration demand
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Partial Equilibrium
Market Demand
Market Equilibrium
Pricing in the Short Run
Short run: firms can change the quantity supplied, and (for durable
goods), owners of used goods can sell them
Definition In a perfectly competitive market:
1
A large number of firms, producing the same homogeneous
good,
2
Each firm attempts to maximize profits,
3
Each firm is a price-taker
4
Prices are assumed to be known to all market participants
5
Transactions are costless
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Partial Equilibrium
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Market Equilibrium
Short Run Price Determination
Market supply curve: sum of n individual-firms supply curves:
QS (P, v , w ) = Σni=1 qi (P, v , w )
v : price of capital; w : price of labor
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Market Equilibrium
Equilibrium Price Determination
Definition An equilibrium price P ∗ is one price at which quantity
demanded is equal to quantity supplied. At such price, neither
consumers nor suppliers have an incentive to alter their economic
decisions. The equilibrium price solves:
QD (P ∗ , P 0 , I ) = QS (P ∗ , v , w )
In the short run the price has two roles:
1) a way to ration demand
2) a signal to producers informing them of how much to produce
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Partial Equilibrium
Market Demand
Market Equilibrium
Shifts in Demand and Supply Curves
Demand Curve can shift as a result of changes in:
income,
price of substitutes or complements,
preferences
Supply Curve can shift as a result of changes in:
input prices,
number of producers,
technologies
The effect of a shift in the demand or supply curve on P ∗ depends
on the shape of the two curves.
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Market Demand
Market Equilibrium
Mathematical Model of Market Equilibrium
Demand: QD = D(P, α). α: parameter that shifts the
demand curve.
Supply: QS = S(P, β ).
Equilibrium: QD = QS .
This model allows to understand how elasticities of demand
and supply (which can be estimated empirically) can be used
to estimate/predict the effect of a change of external factors
on the equilibrium price
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Partial Equilibrium
Market Demand
Market Equilibrium
Mathematical Model of Market Equilibrium
Effect of small change in α:
∂ D(P,α)
= DP ∂dαP + Dα ,
dα
)
= ∂ S(P,β
= SP ∂∂ Pα
∂α
Equilibrium requires: ∂∂QαD = ∂∂QαS
α
Hence: ∂∂ Pα = SPD−D
P
∂ QD
dα
∂ QS
dα
=
SP > 0 > DP → SP − DP > 0 → sign of
∂P
∂α
= sign of Dα
We can express this remark in terms of elasticities:
eP,α =
Dα αq
eQ,α
Dα α
∂P α
=
=
=
P
P
∂α P
SP − DP P
eS,P − eD,P
SP q − DP q
Look at Example 11.3
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Market Demand
Market Equilibrium
Long Run Analysis
Long run:
Each firm has time to change its input mix optimally: for each
firm short and long run supply curve can be different (see
digression on next slide)
Unless profits are 0, firms enter or exit the market. Profit=0
↔ P = AC .
As in the short run, P = MC from profit maximization
Definition A perfectly competitive market is in long-run
equilibrium if there are no incentives for profit-maximizing firms to
enter or to leave the market. This will occur when (a) the number
of firms is such that P = MC = AC and (b) each firm operates at
the low point of its long-run average cost curve.
(b) is a consequence of (a) and of the (implicit) assumption of
increasing marginal costs.
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Market Demand
Market Equilibrium
Digression: Short VS Long Run Cost Curves
In the short run SOME inputs are fixed (see ch 9, from page
270)
In the long run all inputs are flexible
Hence:
In the short run the Rate of Technical Substitution does not
have to be equal to the ratio of the input prices (Fig. 9.12)
The long run total cost curve is the lower than any short run
total cost curve (any= for any level of the fixed input) (fig
9.13)
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Market Demand
Market Equilibrium
Long Run: Constant Cost
Entry or exit of firms affect the demand for inputs, and hence can
affect their price.
Simplest case: constant prices of inputs (E.g. the industry is a small
fraction of the total demand of inputs)
With constant input prices, the long-run supply curve is horizontal.
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Market Demand
Market Equilibrium
Long Run: Constant Cost
To understand why the long-run supply curve is horizontal: let the
demand increase, then:
The short-run supply is an increasing curve, so the equilibrium
price increases
Firms earn a positive profit
In the long run, new firms enter, causing an increase in supply
and a reduction in price and profit- but - by assumption - no
effect on input prices
Entry continues as long as firms earn positive profits, that is,
as long as the price is above the original one.
Note: in the short-run the supply curve is determined by the
short-run marginal cost curve. In the long run, it is the low point of
the long-run average cost curve that determines the supply curve
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Partial Equilibrium
Market Demand
Market Equilibrium
Long Run: Increasing Cost Curve
Very common case: entry of new firms drives up price of inputs,
hence the long-run supply curve is upward sloping In this case, if
the demand increases, then:
As the short-run supply is increasing, the equilibrium price
increases
Firms earn a positive profit
In the long run, new firms enter, causing an increase in supply
and a reduction in price and profit, and an increase in input
prices
Entry continues as long as firms earn positive profits.
The new long run equilibrium will have: (a) a higher price of
the good, (b) more firms in the market and (c) a higher price
of input (note (a) increases individual firms’ profits, while (c)
decreases them, in the long run equilibrium (a) and (c)
compensate each other)
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Partial Equilibrium
Market Demand
Market Equilibrium
Classification of Long Run Supply Curves
To summarize, an industry supply curve exhibits one of three
shapes.
Constant costs: entry does not affect input costs; the long-run
supply curve is horizontal at the long-run equilibrium price
Increasing Costs: Entry increases input costs; the long run
supply curve is positively sloped
Decreasing Costs: Entry reduces input costs; the long run
supply curve is negatively sloped
Examples of decreasing costs: entry of new firms allows to reach a
"critical size" of the industry sufficient to finance infrastructure
that enhances productivity (either with money from the firms, or
with public funding)
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Market Equilibrium
Producer Surplus in the Long Run
In the short run, producer surplus represents the return to a
firm’s owners in excess of what would be earned if the output
were 0.
Producer surplus = sum of short-run profits + short-run
fixed-costs.
In the long-run:
fixed-costs=0,
profits=0,
firm owners are indifferent to be in an industry or doing other
economic activities
In the long-run , sellers of inputs are NOT indifferent to the
level of production in an industry.
With increasing long-run supply curve, the producer surplus
does not go to firm owners: it goes to input sellers.
Graphically, the producer surplus in the ling run can be found
in the same way as the producer surplus in the short run
summary of Snyder et al. (2015)
Partial Equilibrium
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Market Demand
Market Equilibrium
Limits of Partial Equilibrium Analysis
A partial equilibrium analysis misses some effects of changes in
technologies/preferences, for example:
If overall income or the distribution of income changes, then
demand for substitutes and complements should change, and
with it the price of substitutes/complements, which in turn
affects the demand of the good considered
If supply shifts because of a change in technology the demand
for inputs should change, and with it the price of inputs, which
in turn affect supply
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Partial Equilibrium