eco364 - international tradehomes.chass.utoronto.ca/~cdippel/lnmc.pdf · irs natural monopoly model...

$: ECO364 - International Tradehomes.chass.utoronto.ca/~cdippel/LNMC.pdf · IRS Natural Monopoly Model Set-Up I For simplicity: one factor (\Labor"). I Global IRS: \Natural Monopoly"$
ECO364 - International TradeChapter 6 - IRS and Product Variety

Christian Dippel

University of Toronto

Summer 2009

Christian Dippel (University of Toronto) ECO364, Chapter 6 Summer 2009 1 / 51

IRS

I Many features of international trade are difficult to square withRicardian and Heckscher-Ohlin models:

I Two-way trade in very similar goods (“intra-industry trade”).I Intra-industry trade made up 70-80% of world trade in the 80’s 90’s

I We see concentration/clustering of industries in countries/regionsI “Historical Lock-In” (Hollywood, Bollywood, Wall Street, Silicon

Valley, Motorcity Detroit, Bangalore)I Attempts by countries to “capture” industries (e.g. Boeing vs Airbus).

I Two related phenomena seem to be at their root:I Imperfect competitionI Increasing Returns to Scale (IRS)


IRS

Outline

I In this chapter we will use IRS and imperfect competition torationalize intra-industry trade and industry-concentration:

1. We show that the optimal pricing decisions of a domestic and a foreignmonopolist lead to generate intra-industry trade in a homogenousproduct.

2. To generate the empirically much more important intra-industry tradein differentiated products, we combine IRS with a love-for-varietymodel of demand.

3. Lastly, we consider “Marshallian” IRS which give us perfectcompetition with industry-clustering to explain historical lock-in.


IRS

Intra-industry trade

Example: Automobiles between Canada and the United States

I Canada and the United States sell large numbers of cars to each other(“two-way” trade)

I Why? Differences in Factor Endowments? Differences in technology?

I Factor abundance and technology are pretty similar across developedcountries

I So it has to be something else.

I Interestingly, most intra-industry trade is in differentiated products

I But let’s start with a model of intra-industry trade in homogenousgoods.


IRS Natural Monopoly

Model Set-Up

I For simplicity: one factor (“Labor”).

I Global IRS: “Natural Monopoly”

I Firms know they can influence the price of their productsI Simplest form of imperfect competition: the monopoly

I We will do this first and then introduce a taste for product variety andmove to the case of monopolistic competition.



Definitions

I Demand: how many units consumers want to buy at a given price.I Price p is always set on the demand curve which depends on quantity

so we can write p(q)

I Revenue: price times quantity (which is a function of price); p(q)q.

I Marginal Revenue: extra firm revenue generated by selling anadditional unit ( ∂

∂qp(q)q).

I The marginal revenue of a monopolist is below its price (sellingadditional units lowers the price for all units).

I MR = ∂∂q p(q)q = p + ∂p

∂q q, with ∂p∂q < 0

I This is the “Chain Rule” for taking derivatives



I Note: For linear demand, slope(MR) = 2 x slope(Demand)



More Definitions

I Average cost (AC): total cost faced by the firm divided by thequantity produced (TC

q ).

I Marginal cost (MC)is the additional cost for the firm of producing anextra unit (∂TC

∂q ).

I Fixed cost (FC) is a cost that does not depend on the level of outputtotal cost.

I Variable cost (VC) is the sum of marginal costs (summed overintra-marginal units).

I total cost (TC) = fixed cost (FC) + variable cost (VC).



I A Natural Monopoly is one that occurs without governmentinterference.

I Natural Monopolies occur with Increasing Returns to Scale (IRS).I Production Function F (L) exhibits IRS if F (γL) > γF (L)

I With IRS, one large firm is always more efficient than many smallerones, will therefore capture the whole market.

I The simplest form of IRS is to assume constant MC with a (in principlearbitrarily small) FC.



I For constant MC, AC (Q) = MC + FC/Q



I The profit maximizing condition for firms is (always):I MR = MC

I Verify that this is true even in perfect competition.

∂∂qp(q)q = ∂TC

∂q

I To see that this equality has to hold in equilibrium:I If MR > MC additional profit will result from increasing production.I If MR < MC negative profits can be eliminated by cutting production.



Profit maximization by the monopolist:



Monopoly Profits



Main results on the monopoly:

1. Profit is maximized when marginal cost is equal to marginal revenue(but this is actually true in any market).

2. Monopolies can make economic profits.

3. Monopolies involve a welfare loss (the “Harberger Triangle”).


IRS Dumping

Dumping: Introduction

I Price discrimination is the practice of charging different prices todifferent consumers.

I Dumping is the practice of charging less in foreign markets than indomestic markets.

I In discussions of trade policy, dumping is often described as “unfair.”I Accusations of dumping are very common. More than 3000

complaints have been brought before the since 1995. The countriesagainst whom complaints are most common are China (640), Korea(247), the United States (183), and Taiwan/Chinese Taipei (182).

I http : //www .wto.org/english/tratop e/adp e/adp e.htm


IRS Dumping

Two Necessary Conditions for Dumping

I Imperfect competition (allows for any price setting behavior).I which is why we talk about dumping in this chapter.

I Market segmentation (allows for price differences across borders).

I need some trade barriers such as tariffs


IRS Dumping

I A monopolist’s rationale for dumping is exactly the same as forprice-discrimination (you’ve seen this in ECO200)

I With the ability to perfectly price-discriminate, the MR-curve collapsesinto the Demand curve.

I Key Insight:I Dumping can be a simple profit-maximizing rational strategy and does

not have to follow strategic “predatory” objectives

I Imagine a firm that is a monopolist at home but a perfect competitorabroad.

I Motivate this with home bias: people prefer domestic goods. Foreignfirms therefore case a more elastic demand curve in the same market.


IRS Dumping


IRS Dumping

Reciprocal Dumping

I Firms that produce close substitutes in different countries can engagein reciprocal dumping

I Outcome: two-way trade in the same product

I Insight: In the standard monopoly model, monopolies weight fallingmarginal revenue against rising (or flat) marginal cost.

I Insight: Marginal revenue from selling abroad falls less and amonopolist therefore sells at a lower price abroad.


Monopolistic Competition in Variety

I This was a first pass at intra-industry trade but we really want amodel of intra-industry trade in heterogenous products

I homogenous product: oil, salt, agricultural goods, steelI varieties: Coke vs. Pepsi, Mars vs. Snickers, Billabong vs. Burton

I To get intra-industry trade of this form, combine IRS with a demandstructure that exhibits “taste for variety”



Model Setup

I Production is subject to internal IRS.I Firms differentiate their products (an increase in price will lower sales

but not eliminate them).I Consumers possess a “taste for variety.”I Each firm produces a unique variety.

I Firms perceive their price as affecting own sales, but not rivals’ price(unlike oligopoly analysis)

I Firms take other firms’ prices as given but not their own.



I Note that Monopolistic Competition is different from our standardanalysis of smaller oligopolies.

I Oligopolies take their competitors decisions directly into accountthrough

I Cournot competition (over quantity)I or Bertrand competition (over prices)

I Both Monopolistic Competition and standard oligopoly are “inbetween” perfect competition and monopoly.

I Monopolistic Competition is closer to Perfect Competition, Oligopolyis closer to Monopoly.

I Microsoft is an Oligopolist, Coca Cola is in monopolistic competition.


Monopolistic Competition in Variety Demand

A firm sells more:I .. the larger the size (S) of the market.

I S is assumed to be fixed, which is “unusual”

I .. the smaller the number of firms in the market (n)

I .. the lower its price (p)

I .. the higher the average price of its rivals (p̄)

An example of demand with these properties:

q = S

[1

n− b (p − p̄)

]


Monopolistic Competition in Variety Supply

Costs:

I Consider a linear cost function:

C = F + cq

(there is a fixed cost F , and then an extra cost c per unit produced).

I Marginal cost is the extra cost of producing one more unit:

Marginal Cost = MC =∂C

∂q= c


Monopolistic Competition in Variety Supply

I As more units are produced, a smaller part of the fixed cost isallocated to each unit of output:

Average Cost = AC =C

q= c +

F

q

I : Average cost falls so we have IRS


Monopolistic Competition in Variety Market equilibrium

I Assume all firms are symmetric (same cost structure)I While each firm can set a different price, each firm will set the same

price in an equilibrium because there are no differences between firms.

I Determine equilibrium in 3 steps:

1. Derive relationship between number of firms (n) and average cost foreach (AC ).

2. Derive relationship between number of firms (n) and price for each (p).3. Free entry and exit ensures that price (p) equals average cost (AC )

(Firms make zero profits).

I 3 equations and 3 unknowns.



Relationship between the number of firms and average cost

I Assume that all firms are symmetric.

I When all firms charge the same price (p = p̄), they evenly split themarket q = S/n.

Average Cost = AC =TC

q= c +

F

q= c + n

F

S

I For a given market size S , equilibrium AC increase with number offirms.

I if there are more firms, each sells less and cannot exploit economies ofscale as much.



Relationship between the number of firms and the average cost:



Relationship between the number of firms and the price

I Each firm takes p̄ as given, so demand can be written as:

q =

(S

n+ Sbp̄

)− Sbp

p(q) =

(1

nb+ p̄

)− q

Sb

I Marginal revenue:

MR = p + q∂p

∂q= p − q

Sb



I Profit maximization:

MR = p − q

Sb= MC = c

⇒ p = c +q

Sb

I If all firms are symmetric, q = S/n and

p = c +1

bn

I As n increases, the charged price will fall because the market is morecompetitive.

I If n =∞, p = mc as in perfect competition.

I As b ↑, demand is more sensitive and equilibrium markups fall.



Relationship between the number of firms and the price:


Monopolistic Competition in Variety The equilibrium number of firms

I The 3rd condition is free entry. Free entry drives profits to zero(understand this)

I If price is below average cost, firms make losses and some firms willexit which drives down AC (understand why).

I If price is above average cost, firms make profits and some firms willenter which drives up AC.

I That implies p = AC

I We now have 3 equations and 3 unknowns:

AC = c + nFS

p = c + 1bn

p = AC


Monopolistic Competition in Variety The equilibrium number of firms

The equilibrium number of firms can be determined graphically as well:


Monopolistic Competition in Variety Introduce Trade

I This was the autarky equilibrium. Now we consider what trade doesto this equilibrium.

I Trade can be seen as an increase in market size S.

AC = c + nFS

p = c + 1bn



An increase in market size (S ↑):



Welfare Implications

I When two countries open up trade, the integrated market sustainsmore varieties of goods than each of the two markets did alone.

I Consumers gain from more varieties/firms.

I Because under free trade each firm produces at a larger scale, it canexploit economies of scale further, cutting costs and prices.

I Consumer gain from lower prices.

I Firms make zero profits before and after trade-opening



Gains from Trade

I There are no gains from specialization.

I Consumers: face more variety at lower prices (because trade inducestougher competition)

I Firms make zero profits in before and after tradeI Some firms close down - the model does not say which.

I Workers: Factor markets are not modeled (don’t know about factormarket clearing and unemployment)


Monopolistic Competition in Variety Trade Patterns

Context

I The Standard Trade Model (“Old Trade”) illustrates how trade inproducts from different industries (inter-industry trade) can arise, ascountries specialize in goods that they have a comparative advantagein (because of technology or endowments)

I However, a country only exports the good in which it possesses acomparative advantage.

I The Monopolistic Competition Model (one of several “New Trade”models) describes two-way trade in different products within the sameindustry (intra-industry trade).

I A country exports all of its varietiesI Without trade frictions, every firm sells the same share of output in

each country regardless of firm location!.



The Integrated Equilibrium Approach

I Real-world trade is a combination of intra-industry and inter-industrytrade.

I Intra-industry trade is more important between similarly endowedcountries.

I Inter-industry trade is more important between differently endowedcountries (”North-South trade”).

I Consider the Volume of trade in the HO-benchmark, a pure MCmodel and mix:



In HO, given endowment differences, size does not matter



In MC, given size, endowment differences do not matter



A mix of inter- and intra-industry trade:


External IRS

I Up to now, we considered internal IRS which give rise to imperfectcompetition.

I Now imagine that all firms have CRS technology but the aggregateindustry/region has IRS (this is an externality in production).

I Three sources of external IRS (Marshall’s Magic Triangle):I Input-ouput linkages (or specialized suppliers)I Labor market poolingI Knowledge spillovers

I External Economies of Scale can be thought of as “ComparativeAdvantage through Historic Circumstance”.


External IRS Sources of External IRS

Input-ouput linkages

I The production of goods and services and the development of newproducts requires the use of specialized equipment or support services.

I A single firm is not large enough to provide a market for specializedsuppliers.

I But a cluster of firms can make specialized (cheaper) suppliers viable.

I Examples: car parts producers in Michigan/Ontario.



Labor Market Pooling

I Producers are less likely to suffer from costly labor shortages.

I Workers are less likely to become unemployed.

I Examples: movie specialists in Toronto, finance specialists inManahattan, etc.



Knowledge Spillovers

I Informal exchange of information and ideas.

I Movements of workers across firms.

I Reverse engineering.

I Example: Silicon Valley workers.



External Economies and Increasing Returns

I External economies imply increasing returns at the industry level.

I Average costs decline with total industry output.

I With perfect competition, prices have decline with total output.


External IRS Historical Lock-In

Trade implications

I A larger national output will imply lower costs.

I Trade will allow further benefits from economies of scale,

I But production may take place in the ”wrong” country.



Production “should” occur in the foreign country. With externaleconomies, a country can actually be worse off with trade than without.



Dynamic increasing returns and the learning curve

I Learning curve relates unit cost to cumulative output.I How much you have produced over time as opposed to how much in a

given year.

I Hence scale economies are dynamic.

I Example: Automobile in Detroit, Movies in Hollywood (andBollywood), Computers/Software in Silicon Valley.

I Aircrafts are probably natural monopolies but dynamic returns meanvery very few countries produce them: Boeing in US and Airbus inFrance.



Infant Industry Protection

I Note that external Returns to Scale can justify protectionism.I Countries may be locked in the “wrong” industry (agriculture) and

locked out of the “right” one (manufacturing)I Temporary protection of industries enables them to gain experience

I This is the Infant Industry Argument.I But this rarely worked in practice - likely because it gives rise to rent

seeking, lobbying and corruptionI This means “wrong firms” get championed, protection lasts too long

and firms are not allowed to fail.

I More on this in the chapter on trade policy.


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