1 of 92

Chapter 10

THE PARTIAL EQUILIBRIUM COMPETITIVE MODEL

2 of 92

Market Demand

Assume that there are only two goods (x and y)

An individual’s demand for x is

Quantity of x demanded = x(p_x,p_y,I)

If we use i to reflect each individual in the market, then the market demand curve is

3 of 92

Market Demand

To construct the market demand curve, P_X is allowed to vary while P_y and the income of each individual are held constant
If each individual’s demand for x is downward sloping, the market demand curve will also be downward sloping

4 of 92

Market Demand

p_x

x₁*

x₂*

p_x*

To derive the market demand curve, we sum the

quantities demanded at every price

x₁

Individual 1’s

demand curve

x₂

Individual 2’s

demand curve

Market demand

curve

x₁* + x₂* = X*

5 of 92

Shifts in the Market�Demand Curve

The market demand summarizes the ceteris paribus relationship between X and p_x

changes in p_x result in movements along the curve (change in quantity demanded)
changes in other determinants of the demand for X cause the demand curve to shift to a new position (change in demand)

6 of 92

Shifts in Market Demand

Suppose that individual 1’s demand for oranges is given by

x₁ = 10 – 2p_x + 0.1I₁ + 0.5p_y

and individual 2’s demand is

x₂ = 17 – p_x + 0.05I₂ + 0.5p_y

The market demand curve is

X = x₁ + x₂ = 27 – 3p_x + 0.1I₁ + 0.05I₂ + p_y

7 of 92

Shifts in Market Demand

To graph the demand curve, we must assume values for p_y, I₁, and I₂

If p_y = 4, I₁ = 40, and I₂ = 20, the market demand curve becomes

X = 27 – 3p_x + 4 + 1 + 4 = 36 – 3p_x

8 of 92

Shifts in Market Demand

If p_y rises to 6, the market demand curve shifts outward to

X = 27 – 3p_x + 4 + 1 + 6 = 38 – 3p_x

note that X and Y are substitutes

If I₁ fell to 30 while I₂ rose to 30, the market demand would shift inward to

X = 27 – 3p_x + 3 + 1.5 + 4 = 35.5 – 3p_x

note that X is a normal good for both buyers

9 of 92

Generalizations

Suppose that there are n goods (x_i, i = 1,n) with prices p_i, i = 1,n.
Assume that there are m individuals in the economy
The j th’s demand for the i th good will depend on all prices and on I_j

x_ij = x_ij(p₁,…,p_n, I_j)

10 of 92

Generalizations

The market demand function for x_i is the sum of each individual’s demand for that good

The market demand function depends on the prices of all goods and the incomes and preferences of all buyers

11 of 92

Elasticity of Market Demand

The price elasticity of market demand is measured by

Market demand is characterized by whether demand is elastic (e_Q,P<-1) or inelastic (0> e_Q_,_P > -1)

12 of 92

Elasticity of Market Demand

The cross-price elasticity of market demand is measured by

The income elasticity of market demand is measured by

13 of 92

Timing of the Supply Response

In the analysis of competitive pricing, the time period under consideration is important

very short run

no supply response (quantity supplied is fixed)

short run

existing firms can alter their quantity supplied, but no new firms can enter the industry

long run

new firms may enter an industry

14 of 92

Pricing in the Very Short Run

In the very short run (or the market period), there is no supply response to changing market conditions

price acts only as a device to ration demand

price will adjust to clear the market

the supply curve is a vertical line

15 of 92

Pricing in the Very Short Run

Quantity

Price

P₁

D’

P₂

When quantity is fixed in the

very short run, price will rise

from P₁ to P₂ when the demand

rises from D to D’

16 of 92

Short-Run Price Determination

The number of firms in an industry is fixed
These firms are able to adjust the quantity they are producing

they can do this by altering the levels of the variable inputs they employ

17 of 92

Perfect Competition

A perfectly competitive industry is one that obeys the following assumptions:

there are a large number of firms, each producing the same homogeneous product
each firm attempts to maximize profits
each firm is a price taker

its actions have no effect on the market price

information is perfect
transactions are costless

18 of 92

Short-Run Market Supply

The quantity of output supplied to the entire market in the short run is the sum of the quantities supplied by each firm

the amount supplied by each firm depends on price

The short-run market supply curve will be upward-sloping because each firm’s short-run supply curve has a positive slope

19 of 92

Short-Run Market Supply Curve

quantity

Quantity

quantity

q₁^A

q₁^B

P₁

To derive the market supply curve, we sum the

quantities supplied at every price

s_A

Firm A’s

supply curve

s_B

Firm B’s

supply curve

Market supply

curve

Q₁

q₁^A + q₁^B = Q₁

20 of 92

Short-Run Market Supply Function

The short-run market supply function shows total quantity supplied by each firm to a market

Firms are assumed to face the same market price and the same prices for inputs

21 of 92

Short-Run Supply Elasticity

The short-run supply elasticity describes the responsiveness of quantity supplied to changes in market price

Because price and quantity supplied are positively related, e_S_,_P > 0

22 of 92

A Short-Run Supply Function

Suppose that there are 100 identical firms each with the following short-run supply curve

q_i (P,v,w) = 10P/3 (i = 1,2,…,100)

This means that the market supply function is given by

23 of 92

A Short-Run Supply Function

In this case, computation of the elasticity of supply shows that it is unit elastic

24 of 92

Equilibrium Price Determination

An equilibrium price is one at which quantity demanded is equal to quantity supplied

neither suppliers nor demanders have an incentive to alter their economic decisions

An equilibrium price (P*) solves the equation:

25 of 92

Equilibrium Price Determination

The equilibrium price depends on many exogenous factors

changes in any of these factors will likely result in a new equilibrium price

26 of 92

Equilibrium Price Determination

Quantity

Price

Q₁

P₁

The interaction between

market demand and market

supply determines the

equilibrium price

27 of 92

Market Reaction to a�Shift in Demand

Quantity

Price

Q₁

P₁

Q₂

P₂

Equilibrium price and

equilibrium quantity will

both rise

If many buyers experience

an increase in their demands,

the market demand curve

will shift to the right

D’

28 of 92

Market Reaction to a�Shift in Demand

Quantity

Price

SMC

q₁

P₁

This is the short-run

supply response to an

increase in market price

q₂

P₂

If the market price rises, firms will increase their level of output

SAC

29 of 92

Shifts in Supply and Demand Curves

Demand curves shift because

incomes change
prices of substitutes or complements change
preferences change

Supply curves shift because

input prices change
technology changes
number of producers change

30 of 92

Shifts in Supply and Demand Curves

When either a supply curve or a demand curve shift, equilibrium price and quantity will change
The relative magnitudes of these changes depends on the shapes of the supply and demand curves

31 of 92

Shifts in Supply

Quantity

Price

S’

P’

Q’

P’

Q’

Elastic Demand

Inelastic Demand

Small increase in price,

large drop in quantity

Large increase in price,

small drop in quantity

32 of 92

Shifts in Demand

Quantity

Price

P’

Q’

P’

Q’

Elastic Supply

Inelastic Supply

Small increase in price,

large rise in quantity

Large increase in price,

small rise in quantity

D’

33 of 92

Changing Short-Run Equilibria

Suppose that the market demand for luxury beach towels is

Q_D = 10,000 – 500P

and the short-run market supply is

Q_S = 1,000P/3

Setting these equal, we find

P* = $12

Q* = 4,000

34 of 92

Changing Short-Run Equilibria

Suppose instead that the demand for luxury towels rises to

Q_D = 12,500 – 500P

Solving for the new equilibrium, we find

P* = $15

Q* = 5,000

Equilibrium price and quantity both rise

35 of 92

Changing Short-Run Equilibria

Suppose that the wage of towel cutters rises so that the short-run market supply becomes

Q_S = 800P/3

Solving for the new equilibrium, we find

P* = $13.04

Q* = 3,480

Equilibrium price rises and quantity falls

36 of 92

Mathematical Model of Supply and Demand

Suppose that the demand function is represented by

Q_D = D(P,α)

α is a parameter that shifts the demand curve

∂D/∂α = D_α can have any sign

∂D/∂P = D_P < 0

37 of 92

Mathematical Model of Supply and Demand

The supply relationship can be shown as

Q_S = S(P,β)

β is a parameter that shifts the supply curve

∂S/∂β = S_β can have any sign

∂S/∂P = S_P > 0

Equilibrium requires that Q_D = Q_S

38 of 92

Mathematical Model of Supply and Demand

To analyze the comparative statics of this model, we need to use the total differentials of the supply and demand functions:

dQ_D = D_PdP + D_αdα

dQ_S = S_PdP + S_βdβ

Maintenance of equilibrium requires that

dQ_D = dQ_S

39 of 92

Mathematical Model of Supply and Demand

Suppose that the demand parameter (α) changed while β remains constant
The equilibrium condition requires that

D_PdP + D_αdα = S_PdP

Because S_P- D_P > 0, ∂P/∂α will have the same sign as D_α

40 of 92

Mathematical Model of Supply and Demand

We can convert our analysis to elasticities

41 of 92

Long-Run Analysis

In the long run, a firm may adapt all of its inputs to fit market conditions

profit-maximization for a price-taking firm implies that price is equal to long-run MC

Firms can also enter and exit an industry in the long run

perfect competition assumes that there are no special costs of entering or exiting an industry

42 of 92

Long-Run Analysis

New firms will be lured into any market for which economic profits are greater than zero

entry of firms will cause the short-run industry supply curve to shift outward
market price and profits will fall
the process will continue until economic profits are zero

43 of 92

Long-Run Analysis

Existing firms will leave any industry for which economic profits are negative

exit of firms will cause the short-run industry supply curve to shift inward
market price will rise and losses will fall
the process will continue until economic profits are zero

44 of 92

Long-Run Competitive Equilibrium

A perfectly competitive industry is in long-run equilibrium if there are no incentives for profit-maximizing firms to enter or to leave the industry

this will occur when the number of firms is such that P = MC = AC and each firm operates at minimum AC

45 of 92

Long-Run Competitive Equilibrium

We will assume that all firms in an industry have identical cost curves

no firm controls any special resources or technology

The equilibrium long-run position requires that each firm earn zero economic profit

46 of 92

Long-Run Equilibrium: Constant-Cost Case

Assume that the entry of new firms in an industry has no effect on the cost of inputs

no matter how many firms enter or leave an industry, a firm’s cost curves will remain unchanged

This is referred to as a constant-cost industry

47 of 92

Long-Run Equilibrium: Constant-Cost Case

A Typical Firm

Total Market

Quantity

SMC

q₁

P₁

Q₁

This is a long-run equilibrium for this industry

P = MC = AC

Price

48 of 92

Long-Run Equilibrium: Constant-Cost Case

A Typical Firm

Total Market

q₁

Quantity

SMC

P₁

Q₁

P₂

Market price rises to P₂

Q₂

Suppose that market demand rises to D’

D’

Price

49 of 92

Long-Run Equilibrium: Constant-Cost Case

A Typical Firm

Total Market

q₁

Quantity

SMC

P₁

Q₁

D’

P₂

Economic profit > 0

Q₂

In the short run, each firm increases output to q₂

q₂

Price

50 of 92

Long-Run Equilibrium: Constant-Cost Case

A Typical Firm

Total Market

q₁

Quantity

SMC

P₁

Q₁

D’

Economic profit will return to 0

Q₃

In the long run, new firms will enter the industry

S’

Price

51 of 92

Long-Run Equilibrium: Constant-Cost Case

A Typical Firm

Total Market

q₁

Quantity

SMC

P₁

Q₁

D’

Q₃

S’

The long-run supply curve will be a horizontal line

(infinitely elastic) at p₁

Price

52 of 92

Infinitely Elastic Long-Run Supply

Suppose that the total cost curve for a typical firm in the bicycle industry is

TC = q³ – 20q² + 100q + 8,000

Demand for bicycles is given by

Q_D = 2,500 – 3P

53 of 92

Infinitely Elastic Long-Run Supply

To find the long-run equilibrium for this market, we must find the low point on the typical firm’s average cost curve

where AC = MC

AC = q² – 20q + 100 + 8,000/q

MC = 3q² – 40q + 100

this occurs where q = 20

If q = 20, AC = MC = $500

this will be the long-run equilibrium price

54 of 92

Shape of the Long-Run Supply Curve

The zero-profit condition is the factor that determines the shape of the long-run cost curve

if average costs are constant as firms enter, long-run supply will be horizontal
if average costs rise as firms enter, long-run supply will have an upward slope
if average costs fall as firms enter, long-run supply will be negatively sloped

55 of 92

Long-Run Equilibrium: Increasing-Cost Industry

The entry of new firms may cause the average costs of all firms to rise

prices of scarce inputs may rise
new firms may impose “external” costs on existing firms
new firms may increase the demand for tax-financed services

56 of 92

Long-Run Equilibrium: Increasing-Cost Industry

A Typical Firm (before entry)

Total Market

q₁

Quantity

SMC

P₁

Q₁

Suppose that we are in long-run equilibrium in this industry

P = MC = AC

Price

57 of 92

Long-Run Equilibrium: Increasing-Cost Industry

A Typical Firm (before entry)

Total Market

q₁

Quantity

SMC

P₁

Q₁

Suppose that market demand rises to D’

D’

P₂

Market price rises to P₂ and firms increase output to q₂

Q₂

q₂

Price

58 of 92

Long-Run Equilibrium: Increasing-Cost Industry

A Typical Firm (after entry)

Total Market

Quantity

SMC’

MC’

AC’

P₁

Q₁

D’

q₃

P₃

Entry of firms causes costs for each firm to rise

Q₃

Positive profits attract new firms and supply shifts out

S’

Price

59 of 92

Long-Run Equilibrium: Increasing-Cost Industry

A Typical Firm (after entry)

Total Market

q₃

Quantity

SMC’

MC’

AC’

p₁

Q₁

D’

p₃

Q₃

S’

The long-run supply curve will be upward-sloping

Price

60 of 92

Long-Run Equilibrium: Decreasing-Cost Industry

The entry of new firms may cause the average costs of all firms to fall

new firms may attract a larger pool of trained labor
entry of new firms may provide a “critical mass” of industrialization

permits the development of more efficient transportation and communications networks

61 of 92

Long-Run Equilibrium: Decreasing-Cost Case

A Typical Firm (before entry)

Total Market

q₁

Quantity

SMC

P₁

Q₁

Suppose that we are in long-run equilibrium in this industry

P = MC = AC

Price

62 of 92

Long-Run Equilibrium: Decreasing-Cost Industry

A Typical Firm (before entry)

Total Market

q₁

Quantity

SMC

P₁

Q₁

Suppose that market demand rises to D’

D’

P₂

Market price rises to P₂ and firms increase output to q₂

Q₂

q₂

Price

63 of 92

Long-Run Equilibrium: Decreasing-Cost Industry

A Typical Firm (before entry)

Total Market

q₁

Quantity

SMC’

MC’

AC’

P₁

Q₁

D’

P₃

Entry of firms causes costs for each firm to fall

Q₃

q₃

Positive profits attract new firms and supply shifts out

S’

Price

64 of 92

Long-Run Equilibrium: Decreasing-Cost Industry

A Typical Firm (before entry)

Total Market

q₁

Quantity

SMC’

MC’

AC’

P₁

Q₁

The long-run industry supply curve will be downward-sloping

D’

P₃

Q₃

q₃

S’

Price

65 of 92

Classification of Long-Run Supply Curves

Constant Cost

entry does not affect input costs
the long-run supply curve is horizontal at the long-run equilibrium price

Increasing Cost

entry increases inputs costs
the long-run supply curve is positively sloped

66 of 92

Classification of Long-Run Supply Curves

Decreasing Cost

entry reduces input costs
the long-run supply curve is negatively sloped

67 of 92

Long-Run Elasticity of Supply

The long-run elasticity of supply (e_LS_,_P) records the proportionate change in long-run industry output to a proportionate change in price

e_LS_,_P can be positive or negative

the sign depends on whether the industry exhibits increasing or decreasing costs

68 of 92

Comparative Statics Analysis of Long-Run Equilibrium

Comparative statics analysis of long-run equilibria can be conducted using estimates of long-run elasticities of supply and demand
Remember that, in the long run, the number of firms in the industry will vary from one long-run equilibrium to another

69 of 92

Comparative Statics Analysis of Long-Run Equilibrium

Assume that we are examining a constant-cost industry
Suppose that the initial long-run equilibrium industry output is Q₀ and the typical firm’s output is q* (where AC is minimized)
The equilibrium number of firms in the industry (n₀) is Q₀/q*

70 of 92

Comparative Statics Analysis of Long-Run Equilibrium

A shift in demand that changes the equilibrium industry output to Q₁ will change the equilibrium number of firms to

n₁ = Q₁/q*

The change in the number of firms is

completely determined by the extent of the demand shift and the optimal output level for the typical firm

71 of 92

Comparative Statics Analysis of Long-Run Equilibrium

The effect of a change in input prices is more complicated

we need to know how much minimum average cost is affected
we need to know how an increase in long-run equilibrium price will affect quantity demanded

72 of 92

Comparative Statics Analysis of Long-Run Equilibrium

The optimal level of output for each firm may also be affected
Therefore, the change in the number of firms becomes

73 of 92

Rising Input Costs and Industry Structure

Suppose that the total cost curve for a typical firm in the bicycle industry is

TC = q³ – 20q² + 100q + 8,000

and then rises to

TC = q³ – 20q² + 100q + 11,616

The optimal scale of each firm rises from 20 to 22 (where MC = AC)

74 of 92

Rising Input Costs and Industry Structure

At q = 22, MC = AC = $672 so the long-run equilibrium price will be $672
If demand can be represented by

Q_D = 2,500 – 3P

then Q_D = 484

This means that the industry will have 22 firms (484 ÷ 22)

75 of 92

Producer Surplus in the Long Run

Short-run producer surplus represents the return to a firm’s owners in excess of what would be earned if output was zero

the sum of short-run profits and fixed costs

76 of 92

Producer Surplus in the Long Run

In the long-run, all profits are zero and there are no fixed costs

owners are indifferent about whether they are in a particular market

they could earn identical returns on their investments elsewhere

Suppliers of inputs may not be indifferent about the level of production in an industry

77 of 92

Producer Surplus in the Long Run

In the constant-cost case, input prices are assumed to be independent of the level of production

inputs can earn the same amount in alternative occupations

In the increasing-cost case, entry will bid up some input prices

suppliers of these inputs will be made better off

78 of 92

Producer Surplus in the Long Run

Long-run producer surplus represents the additional returns to the inputs in an industry in excess of what these inputs would earn if industry output was zero

the area above the long-run supply curve and below the market price

this would equal zero in the case of constant costs

79 of 92

Ricardian Rent

Long-run producer surplus can be most easily illustrated with a situation first described by economist David Ricardo

assume that there are many parcels of land on which a particular crop may be grown

the land ranges from very fertile land (low costs of production) to very poor, dry land (high costs of production)

80 of 92

Ricardian Rent

At low prices only the best land is used
Higher prices lead to an increase in output through the use of higher-cost land

the long-run supply curve is upward-sloping because of the increased costs of using less fertile land

81 of 92

Ricardian Rent

Low-Cost Firm

Total Market

Quantity

The owners of low-cost firms will earn positive profits

Price

82 of 92

Ricardian Rent

Marginal Firm

Total Market

Quantity

The owners of the marginal firm will earn zero profit

Price

83 of 92

Ricardian Rent

Firms with higher costs (than the marginal firm) will stay out of the market

would incur losses at a price of P*

Profits earned by intramarginal firms can persist in the long run

they reflect a return to a unique resource

The sum of these long-run profits constitutes long-run producer surplus

84 of 92

Ricardian Rent

For each firm, P – AC represents

profit per unit of output

Total Market

Quantity

Each point on the supply curve represents minimum average cost for some firm

Total long-run profits can be

computed by summing over all

units of output

Price

85 of 92

Ricardian Rent

The long-run profits for the low-cost firms will often be reflected in the prices of the unique resources owned by those firms

the more fertile the land is, the higher its price

Thus, profits are said to be capitalized inputs’ prices

reflect the present value of all future profits

86 of 92

Ricardian Rent

It is the scarcity of low-cost inputs that creates the possibility of Ricardian rent
In industries with upward-sloping long-run supply curves, increases in output not only raise firms’ costs but also generate factor rents for inputs

87 of 92

Important Points to Note:

In the short run, equilibrium prices are established by the intersection of what demanders are willing to pay (as reflected by the demand curve) and what firms are willing to produce (as reflected by the short-run supply curve)

these prices are treated as fixed in both demanders’ and suppliers’ decision-making processes

88 of 92

Important Points to Note:

A shift in either demand or supply will cause the equilibrium price to change

the extent of such a change will depend on the slopes of the various curves

Firms may earn positive profits in the short run

because fixed costs must always be paid, firms will choose a positive output as long as revenues exceed variable costs

89 of 92

Important Points to Note:

In the long run, the number of firms is variable in response to profit opportunities

the assumption of free entry and exit implies that firms in a competitive industry will earn zero economic profits in the long run (P = AC)
because firms also seek maximum profits, the equality P = AC = MC implies that firms will operate at the low points of their long-run average cost curves

90 of 92

Important Points to Note:

The shape of the long-run supply curve depends on how entry and exit affect firms’ input costs

in the constant-cost case, input prices do not change and the long-run supply curve is horizontal
if entry raises input costs, the long-run supply curve will have a positive slope

91 of 92

Important Points to Note:

Changes in long-run market equilibrium will also change the number of firms

precise predictions about the extent of these changes is made difficult by the possibility that the minimum average cost level of output may be affected by changes in input costs or by technical progress

92 of 92

Important Points to Note:

If changes in the long-run equilibrium in a market change the prices of inputs to that market, the welfare of the suppliers of these inputs will be affected

such changes can be measured by changes in the value of long-run producer surplus