GEOGRAPHICAL ECONOMICS

GEOGRAPHICAL ECONOMICS

Sponsored by a Grant TÁMOP-4.1.2-08/2/A/KMR-2009-0041 Course Material Developed by Department of Economics, Faculty of Social Sciences, Eötvös Loránd University Budapest (ELTE)

Department of Economics, Eötvös Loránd University Budapest Institute of Economics, Hungarian Academy of Sciences

Balassi Kiadó, Budapest

Authors: Gábor Békés, Sarolta Rózsás Supervised by Gábor Békés

June 2011

ELTE Faculty of Social Sciences, Department of Economics

GEOGRAPHICAL ECONOMICS

week 6

Monopolistic competition and the Dixit-Stiglitz model

Gábor Békés, Sarolta Rózsás

1 Monopolistic competition: Introduction

NEG market structure

The nuts and bolts of Geographical Economics

• Market structure - monopolistic competition (mixing the elements of perfect competition and monopoly)

• Dixit, A - J. Stiglitz 1977 “Monopolistic competition, and the optimum product diversity,” AER (top 20)

• Necessary to understand the (later) core model Topics for today

• Basics: theory and reality

• Model: demand

• Model: supply

Industrial Organization

Market structure - hing on the market power of the firms

• Perfect competition

• Oligopoly (Bertrand / Cournot)

• Monopoly

• Monopolistic competition (mixing the elements of perfect competition and monopoly)

– Firms determine the prices of their products in part as a monopoly, – but the competition is close to the perfectly competitive model

– There may arise economic profit (disappear when there are plenty of firms)

Product varieties

• (Product) differentiation – each firm produces a variety which is different in some aspects from the products of the other firms

– Product varieties are near but imperfect substitutes varieties

– Price-elastic demand: when price goes up, the quantity demanded decreases

• Rational for competition – difference, quality

• = design, reliability, services, marketing, etc.

• Differentiating products decrease the price elasticity

Product differentiation

The features of product differentiation

• Material difference

• Convenience

• Feeling

• Reputation

• Vanity, snobbery

• Fear and desire

• Private services

• The place and circumstances of shopping

Competition

Monopolistic competition in reality

• A lot but not too much competitors

• Innovation – differentiating products

• Low concentration level

• Concentration is measurable

– Market share of the first three or four largest companies – Hirschmann-Herfindahl index (0-100)

– : HHI:

∑

sh²/100

– USA: lower than 10 = competitive market; higher than 18 = enquiry of the Competition Au- thority

• Distinguishable

– Almost competitive market – Oligopoly

– Monopolist with Competitive Fringe

2 Dixit-Stiglitz model: demand side

Demand side: Introduction BGM Chapter 3.4

• The economy has two good sectors: agriculture (F) (producing food) and manufacturing industry (M) (producing manufacturing varieties)

• Firms produce plenty of varieties (N) in the manufacturing industry

• Consumers have Cobb-Douglas utility function

U=F^1−δM^δ, 0<δ<1 (1)

• Let the price of food be equal to one, that is all other products are expressed relative to this (numèraire).

• Let the price index of manufactures beI(it will be defined later)

• The income of the consumers:Y; the budget constraint:

F+I M=Y (2)

Demand side: Budget constraint

• Optimal spending on food and manufactures? U=F^1−δM^δ,F+I M=Y

• L=F^1−δM^δ+κ(Y−(F+I M))

• First-order Conditions (FOC):∂L/∂F,∂L/∂M (1−δ)F^−δM^δ=κandδF^1−δM^δ−1=κI

• Taking the ratio of the two first-order conditions: I M= _1−δ^δ F

• Substituting this in budget constraint:Y=F+I M=F+₁₋^δ

δF thusF= (1−δ)YandI M=δY

• Consumers spend a fraction, δ, of income on manufactures and a fraction, 1−δ, of income on food

Demand side: Utility

Dixit, A - J. Stiglitz 1977 “Monopolistic competition, and the optimum product diversity,” AER (top 20),

• CES preferences

• i = 1...Nnumber of available varieties, where Nis a very big number (or in continuous setting the set of varieties has measureN)

• Consumption of all varieties are symmetrical:ci

• The only arguments of the utility function are the consumption of theNvarieties:

M=

∑

c^ρ_i

!¹_ρ

0<ρ<1 (3)

• Love-of-variety:ρ

• Ifρ'1, the varieties are perfect substitutes and only the total amount of consumption matters.

Demand side: CES CES preferences

• If the level of consumption of each variety is the same:

M=

∑

c^ρ

!¹_ρ

= (Nc^ρ)^1ρ = (N)^1ρ c= (N)^1ρ−1(Nc)

• Nc - total amount of product produced

• (N)^1ρ−1- externality, which arises because of more varieties

Demand side: derivation (1)

Manufacturing market, budget constraint,p_i= the price of varietyi

∑

p_ic_i =δY (4)

• Optimally allocate spendingamongthe different varieties of manufactures

•

L=

∑

c^ρ_i

!¹_ρ

+κ δY−

∑

p_ic_i

!

(5)

• FOC:∂L/∂cj ⇒

∑

c^ρ_i

!¹_p−1

c^ρ_j⁻¹=κpjfor eachj=1...N

• Let us choose two varietiesi=1 andi=j, then:c^ρ−1_j /c^ρ−1₁ =pj/p1

• e:=1/(1−ρ)

• c_j =p⁻_j ^ep^e₁c₁

Demand side: derivation (2)

• Back to the budget constraint:

• δY=

∑

p_ic_i=

∑

p_i(p^−e_i p^e₁c1) =p^e₁c1

∑

p^1−e_i

• Let the price index be

• I=

∑

p¹⁻_i ^e

!1/(1−e)

• then

• p^e₁c1

∑

p¹⁻_i ^e= p^e₁c1I^1−e=δY⇒c1=p⁻₁^eI^e−1δY

• The demand for varietyiis derived analogously:

• ci= p⁻_i ^eI^e−1δY

Demand side: I

• Why the definition of price indexIis good for us? Substitute it in the CES utility function:

• M=

∑

c^ρ_i

!¹_ρ

=

∑

(p^−e_i I^e−1δY)^ρ

!¹_ρ

=δYI^e−1

∑

p^−eρ_i

!¹_ρ

• e=1/(1−ρ)

• M=δY/I

Demand effects:

• The demand for varietyiis given by:ci =p⁻_i ^eI^e−1δY, which appears to be influenced by:

• (1) the incomeδYspent on manufactures (proportional), (2) the price p_i of goodi, (3) some pa- rametere, (4) the price indexI

• What is the connection between the quantity demanded and the price?

• We know, thatI^e−1δY=const

– There appearspiinI, however, ifNis big enough, the effect of it is negligible

• As a result of optimization: constant elasticity of substitution (CES) -(−∂ci/∂pi)(p1/c1) =e

Demand function ande– Figure 1

The higher thee, the more rapidly falls the demand for a variety as a result of a small price increase

Demand function ande– Figure 2

The limitation of the Dixit-Stiglitz model: there is a relationship between the price elasticity (e) and the ‘substitution parameter’ (ρ)

Price index

• c_i= p⁻_i ^eI^e−1δY= ^p_I^{i−e δY}_I

– The demand for a given variety depends on the average price level, that is on the average of the prices of the other varieties = substitutes

– In other words, the quantity demanded hinges on the relative price and the relative income.

– Price indexI- utility derived from the consumption of manufactures (one unit of consump- tion bundle) = consumption-based price index

• I, i.e. the utility depends positively on the number of varieties:

• Proof: Suppose that every variety has the same price,p₀

• I=

∑

p¹⁻_i ^e

!1/(1−e)

= p0N^1/(1−e)

Price index

• Indirect utility can be derived from the budget constraint and the utility function

• What is the minimum amount of expenditure required to buy one unit of utility?

• The price of food = 1

• The utility rises ifY/I^δincreases

• therefore the real income:y=YI^−δ

Key terms

• Monopolistic competition

• Marginal rate of substitution between products

• CES utility

• Love-of-variety

3 Monopolistic competition II - Supply

3.1 Production structure

Basics

• BGM Chapter 3.5

• Supply side: two sectors

• Total labor force: L

• Manufacturing industry:γL, Food sector:(1−γ)Ls.t. 0<γ<1

• Agriculture: CRS, competitive market

• numèraire

• Production function:F= (1−γ)L

• aspF =1 andMPL=1⇒wF=1

Industry

• Industry: increasing return to scale, imperfect competition

• Manufacturesaresymmetrical:

– Each variety has the same technology

– Different varieties are produced by different firms (the firm with the largest sales can always outbid a potential competitor)

• Economies of scale (l_iis the amount of labor necessary to producex_iof varietyi)

•

l_i =α+βx_i (6)

• FC:αand MC:β

• = Increasing internal economies of scale

Industry: products

• Each variety is produced by a single firm - monopolist behavior

• But: each firm takes the price-setting behavior of other firms as given

• Thus there is no strategic behavior: if firmiincreases its price, it does not assume that the other firms react.

• The firm also ignores the effect of changing its own price on the price indexIof manufactures

3.2 Price setting and profit

Profit

• Symmetrical firms that producex unit of output, usinglunit of labor and paying wage rateW will earn profitsπ:

•

π= px−Wl= px−W(α+βx) (7)

• Recall that the demand forx:x=p^−econwherecon=I^−eδY

• Thenπ=p^1−econ−W(α+βp^−econ)

• ∂π/∂pandFOC=0

•

p=βW/(1−1/e) =βW/ρ (8)

Price setting (2)

•

p=βW/(₁−1/e) =βW/ρ (9)

• constant margin (price – marginal cost = mark-up), asβWdenotes the marginal cost

• Ife=5 the mark-up is 20%

• Why the mark-up is ‘necessary’?

• In order to recuperate the fixed costs of labor

Price setting (2a)

• Recall that in case of DS: constant mark-up -p(1−¹

e) =βW

• In opposition to this, oligopoly, e.g. Cournot is somewhat different

• p(1−_e(Y)^s ) =MC, wheree(Y)is the demand elasticity and MC is equal toβW

• The mark-up depends on the market share. Ifs→0 it is the same.

• IfNis large (sis small), equilibrium price does not depend on the type of competition.

Profit and the equilibrium output

• Suppose, that the profits are positive (economic profit). Then it is worth setting up a firm and beginning to produce a new variety.

• Consumers: ifN↑thenx_i↓andπ_i ↓- lim_N=∞(π_i) =0, i.e. ifNis large enough,π_i=0

• π=0⇒px=W(α+βx)andp=βW/(1−1/e)

• ( ^e

e−1)βWx=Wα+Wβx⇒( ^e

e−1−1)βWx=Wα

•

x= ^α(e−1)

β (10)

• The output per firm is fixed in equilibrium - it depends only on exogenous parameters

Profit and the equilibrium output

• How much labor is required?

• l=α+βx=α+β^α(e−1)_β =αe

• How much is N? – total labor force/the amount of labor required to produce one unit of output

• N=γL/l =γL/αe

• Size of the economy = number of varieties (asx_iis fixed)

• Cheating: Nis finite and can be determined. However, we have repeatedly supposed thatNis almost infinite.

Economies of scale

• Does the economies of scale matter?

• AC/MC(l):

• AC=l/x=_αe/^α(e−1)

β =_βe/(e−1)_,

• MC=β

• Economies of scale = _e−1^e

• For a high value ofe(similar products, substitutes) this measure of scale economies is low.