Internal scale economies, product differentiation and trade patterns

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Internal scale economies, product differentiation
and trade patterns

• Applied International Trade Analysis
• Lecture 9

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Contents

• further readings
• introduction
• assumptions
• preference structure
• basic model of production
• effects of trade
• empirics.

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Further readings

• Krugman Paul Increasing returns, monopolistic
  competition, and international trade. JIE, 1979.
• Krugman Paul Scale Economies, Product
  Differentiation and the Pattern of Trade. AER,
  1980.
• Bowen, et.al. Applied International Trade
  Analysis, 1998, 364-380.
• Borkakoti J. International trade Causes and
  consequences, 1998, 377-401.
• Rivera-Batiz, Oliva International trade. Theory,
  Strategies and Evidence. 2003, 39-75.

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• Intra-industry trade and FDI, 1992-4 average

Trade FDI
US-Germany 0.67 0.64
US-UK 0.66 0.58
US-France 0.50 0.44
US-Canada 0.37 0.45
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Introduction

• empirical evidence 1960s trade
• Grubel-Lloyd (1975)- Intra-Industry trade
• Scale economies, product differentiation,
  imperfect competition
• No factor differences between countries
• Both countries export differentiated products
  (direction of trade is not determined)
• Trade between two countries is intra-industry
  trade (trade volume depends on country sizes).

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Assumptions

• 1 factor of production (labor), 1 product, 2
  countries
• monopolistic competition, internal economies of
  scale
• product differentiation (number of firms equals
  the number of varieties)
• a large number of identical consumers (symmetric
  demand of all available varieties of all
  products)-preference for variety (more varieties
  lead to greater utility)
• both technology and preferences are identical
  across countries. Countries differ only in their
  size
• only IIT is possible between the two countries.

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Preferences

• Spence- Dixit- Stiglitzeva utility function
  identical consumers consume all varieties
  symmetricaly (in equal quantities). The common
  utility function for all consumers is
• v' gt0, v''lt0
• consuming more varieties is prefered to
  consuming less
• 0 lt ? lt 1
• parameter of substitution
• elasticity of substitution

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Basic model of production

• Labor is the only factor of production. All goods
  are produced with the same cost function
• Fixed costs are assumed and constant marginal
  costs (ßw). Average costs decline at all levels
  of output (at a diminishing rate) wli i/xi .
• Output of each good must equal the sum of
  individual consumptions. If we can indentify
  individuals with workers, output must equal
  consumption of a represenative individual times
  the labor force

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• If we assume full employment, so that the total
  labor force must just be exhausted by labor used
  in production
• Firms maximize profits, but free entry and exit
  ensure that profits will be zero.
• Large number of firms means that firms can ignore
  their effects on other firms behaviour,
  eliminating the indeterminacies of oligopoly.
• An individual maximizing his utility subject to
  the budget constraint. FOCs have the form
• Since all individuals are alike, the above
  equation can be
• rearanged to
• form the demand curve facing the single firms
  proiducing that good.

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• Provided a large number of goods are produced,
  the pricing decision of any one firm will have a
  negligible effect on the marginal utility of
  income. In this case each firm faces a demand
  curve with an elasticity 1/(1-?) and the
  profit-maximizing price therefore is
• Since ß, ? and w are the same for all firms,
  prices are the same for all goods (ppi)
• Profits of the firm producing good i are
• Since profits are zero the representative firms
  output (which is equal for all firms) equals

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• The zero-profit condition can be rewritten as
• combined with a reworked pricing equation
• where e is price elasticity of demand facing the
  firm. Krugman (1979) assumes that the elasticity
  of demand facing an individual producer becomes
  smaller as the firms output increases (by
  proposing restrictions on the utility function).
• These two equations allow for the determination
  of equilibrium p/w and c as shown in Figure 1.

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Z
P
p/w
E
(p/w)0
P
Z
ß
c
c0
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• Finally, the number of goods produced can be
  determined using the full employment condition.
• however, which n varieties are produced remains
  indeterminate. This, though, is considered
  unimportant since varieties enter into utility
  and cost function symmetrically.

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Effects of trade

• Supposing the two countries can trade with each
  other at zero transportation costs. If the
  countries have the same tastes and technologies,
  given that there is only one factor of production
  (there is no difference in endowments).
• Trade occurs solely because the world economy
  produces a greater diversity of goods than each
  country alone could, therefore offering each
  individual a wider range of choice.
• World economy equilibrium
• Individuals maximizing utility will now
  distribute their expenditure over both the n
  goods produced in the home country and the n
  goods in the foreign country.
• Despite the fact that the real wage remains
  unchanged the welfare will increase.

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• Individuals in the home country spend n/nn of
  their income on foreign varieties and the rest on
  their home varieties.
• The value of home country imports measured in
  wage units is
• The volume of trade is determinate, the direction
  of trade (which country produces which good) is
  not. Trade is balanced when the value of goods
  imported from the home country (M) equals the
  value of goods imported from the foreign country
  (M)
• Trade has no effect on the scale of production
  and the gains from trade come from increased
  product diversity.

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The Lancaster model

• Lancaster (1980) proposes two sectors
  differentiated goods sector and another sector
  producing outside goods. All differentiated
  goods are of the same quality.
• Individuals are assumed to have preferences over
  characteristics of goods, characteristics of
  goods are variable in a continuous manner over a
  convex set. If all goods had equal prices,
  consumers would always buy their ideal variety.
• A consumer chooses a product based on two
  criteria
• the relative price of the product
• the relationship of the products characteristics
  to those of the ideal variety
• The price the consumer is willing to pay given
  her income and other prices, is inversely
  proportional to a convex function of spectral
  distance between that good and the ideal
  variety. The distance function is assumed to
  be the same for all consumers and the consumers
  are distributed uniformly over the variety
  spectrum

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• the outside goods sector has constant relative
  prices, can therefore be called outside good.
  It is homogeneous. It impacts only the consumers
  decison of the quantity of differentiated goods
  consumed and not which goods are consumed.
• all consumers have the same relationship between
  differentiated and outside goods and it depends
  on
• the elasticity of substitution between
  differentiated and homogeneous goods
• the share of total income spent on differentiated
  goods.
• demand for differentiated goods therefore depends
  on its price, its specification, the prices and
  specifications of the adjacent differentiated
  goods, the price of the outside goods, and
  income.

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• Production
• economies of scale in production (in production
  of every new good new fixed costs have to be
  applied)
• costs functions for all gods are identical
• an individual firm producing differentiated goods
  has two decision variables
• price
• product specification
• each firm faces competition from the two adjacent
  firms (one in each direction along the
  two-characteristic product spectrum line
• The profit maximizing solution will be a joint
  price-specification pair that (1) marginal
  revenue is equalised between two half markets and
  (2) marginal revenue equals marginal costs

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• Suppose there are N firms in the market, one of
  the possible and simplest Nash equilibrium is the
  symmetric equilibrium characterized by (proof in
  Lancaster, 1980)
• no two firms produce the same specifications
• the specifications of goods produced are at equal
  distances from each other
• all goods have equal market areas
• all goods will be sold at the same price.
• This equilibrium is stable only if the elasticity
  of substitution between varieties is greater than
  unity and less than some maximum value (then
  equilibrium n is finite).
• In order to see the development of intra-industry
  trade two identical economies are assumed (in
  equilibrium both of those will produce n
  differentiated products in Q quantities and sold
  at p which equals average costs
• C(Q )/Q where is C(Q) is the cost function

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• Since the two countries are identical n1 n2
• By construction all trade is intra-industry
  trade, since each firm exports half its output to
  the foreign country (symmetry). Similarly as
  before (Krugman) only the level of trade can be
  predicted and not pattern.
• The two countries have equal incomes and
  consumption patterns, each consumes Q amount of
  each differentiated product and X amount of a
  homogeneous good. If Yi is income, Xi
  agricultural product and ni the number of
  differentiated products in the country i, we
  have
• Assuming V is the resource endowment, and C the
  cost function in the differentiated good sector,
  the following resource constraint must be
  satisfied

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• The two countries engage in free trade. The
  combined large market lowers average costs and
  will generally result in more variables produced
  than under autarky (n1n2gtn)
• the total consumption is given by
• The trade balance Ti , i1,2 is given by the
  difference between production and consumption
• Substituting out X yields

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• Trade is in equilibrium when T1 T2 yielding the
  balance condition
• Equilibrium is obtained when price equals average
  costs so that
• For any combination of n, the above equation
  holds with zero-profit pricing.
• Lancaster (as Krugman before) demonstrates how
  IIT in differentiated products opens up between
  two countries as a consequence of preference
  diversity and increasing returns to scale.

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Trade with differentiated products empirical
analysis

• Theory on trade with diff. products spurred by
  empirical findings from the early 1960s
• Early econometric studies found correlations
  between the extent of intra-industry trade among
  country pairs and per capita income as well as
  measures of cross-country differences in per
  capita income
• Grubel and Lloyd (1971, 1975) and Linder (1961)
• Linder hypothesis states that much trade arises
  from similarities in tastes among consumers
  across different countries. Manufactured goods
  are produced in countries where there is strong
  demand for them and exported from those countries
  to countries with similar tastes.

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Trade with differentiated products empirical
analysis (continued)

• Helpman (1987) study
• Using data on 14 OECD countries over the period
  1956-1981
• Looking at whether the share of IIT in GDP is
  negatively related to the disparity in country
  size
• Implicit assumption that each variety is produced
  in only one country
• Examines two hypotheses
• Share of IIT in total trade between OECD
  countries was larger when the dispersion of per
  capita income was smaller
• Share of IIT in bilateral trade was larger for
  country-pairs with more similar per capita
  incomes.

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Trade with differentiated products empirical
analysis (continued)

• Only the second hypothesis was formally tested
  while the first was only graphed
• A graph of IIT indices against Herfindahl measure
  of dispersion of per capita incomes indicates a
  negative relationship.
• The second hypothesis was tested annually. For
  1976 the results are
• IITih a-0.04log(GDPi/POPi-GDPh/POPh)
• 0.035minlog(GDPi),log(GDPh)-
• - 0.021maxlog(GDPi),log(GDPh)

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Trade with differentiated products empirical
analysis (continued)

• Hummels and Levinsohn (1995) study
• hypothesized positive correlation between trade
  to income ratio and size similarity holds for
  country groups of any size
• Essentially repeat the Helpman study but treat
  individual country pairs in the OECD group as
  individual observations (Helpma used the entire
  OECD as an observation) when fitting
  trade-to-income ratios to the Herfindahl measure
  of size similarity.
• Their estimation supports Helpmans findings

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Trade with differentiated products empirical
analysis (continued)

• Hummels and Levinsohn also find that if the model
  is estimated for lower-income OECD members the
  variation in trade volumes is equally well
  explained.
• This leads them to conclude that there should be
  a different explanation for the observed findings
  
• Testing IIT they employ panel data estimation
  techniques to account for cross-sectional and
  time series variations in IIT indices.
• They find dramatically different results

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Trade with differentiated products empirical
analysis (continued)

• The proxy for endowment differences namely
  becomes either positive or insignificant.
• Country par-specific effects explain most of the
  variance in IIT, while the remaining residuals
  are largely related to distance
• These results severely weaken the earlier
  conclusion that the monopolistic competition
  model is empirically supported.