Multinationals and the Globalization of Production
Horizontal FDI 1
Penn State // Fall 2016
Administrative things
I
Sit in the first 3 rows!
I Arkaive.com course code: 3D0Y
I Please sign in
I Problem set #1: due Thursday September 8, end of class
I Print out copy, hand in to folder (no e-submission)
I Can discuss with classmates, but turn in your own work
I Read “problem set guidelines”
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Apple and the EU
I European Commission rules Irish tax treatment of Apple illegal
I Issue: Ireland treating MNEs different than other EU countries
I Irish multinationals channel profits to tax havens
I EU wants Ireland to collect $14 bil. in back taxes
I Irish government reluctant to do so
I Discourage future MNE investment
I Ireland is famous for its low corporate tax rate
I Admit that something wrong happened
I Apple: http://www.apple.com/ie/customer-letter/
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Roadmap
I Past: OLI framework
I Identify MNE advantage
I High-level analysis
I Present: Towards a model of horizontal FDI
I Introduce a model of competition
I The closed economy
I Open economy with exporters
I Future: Introduce multinationals to the model
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Horizontal FDI
I Horizontal FDI: Use affiliates to serve foreign market
I Relevant facts
I More multinational activity in bigger markets
I More multinational activity (compared to exports) with distance
I Important model ingredients
I Exporting requires additional costs
I Building a foreign affiliate requires a fixed cost
I Key tradeoff in the model
I Saving on transport costs vs. saving on fixed costs
I Called the “proximity-concentration tradeoff”
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Model overview
I Two countries (“markets”), i = 1, 2
I Total expenditure in each country is Ei
I Two kinds of firms
I Domestic firms: only produce in their home country
I Multinational firms: produce in both countries
I Many firms of each type
I ni = number of domestic firms in i
I mi = number of multinational firms in i
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Model overview
I Two stages to the model
1. Create firms and decide to be national or multinational
2. Firms produce and earn profits
I Stage 1 is about determining n1 , m1 , n2 , m2
I Stage 2 takes n1 , m1 , n2 , m2 as given
I Solve the model by working backwards
I First: given n1 , m1 , n2 , m2 compute profits
I Second: given domestic and MNE profits, choose n1 , m1 , n2 , m2
I Today we work on stage 2
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Firm profits
I Each firm is identical (we will relax this in the future)
I Constant marginal cost of wi
I Inverse demand curve p(xi )
I Sell xi , the price is p(xi )
I This curve slopes down
I Fixed costs [compared to marginal costs]
I f h = fixed headquarters cost
I f p = fixed production cost
I domestic firm pays f = f h + f p
I two-country multinational firm pays f = f h + f p + f p
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Firm profits
I Firm operating in country i has profits
πi = (p(xi ) − wi ) × xi − wi fi
I Q: How much should a firm produce?
I A: Set marginal revenue = marginal cost
pi (1 − 1/i ) = wi
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Elasticity and price
I i = price elasticity of the good
I What is the price elasticity? What does it mean?
pi (1 − 1/i ) = wi
p i = wi ×
1
1 − 1/i
I The markup over marginal cost is 1/(1 − 1/i )
I What is the markup when = 4? = 10?
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Algebra: simplify the profit equation
I Substitute pi (1 − 1/i ) for wi in
πi = (p(xi ) − wi ) × xi − wi fi
I Result
πi =
pi xi
− wi fi
i
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Algebra: simplify the profit equation
I Define the firm’s share of total expenditure as
si =
(pi × xi )
Ei
I So that the firm’s profit is
πi =
si Ei
− wi f i
i
I If I know the firm’s share of the market, I know its profit
I So let’s figure out the firm’s share. . .
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The closed economy
I Only one country: no trade, no MNEs
I We are taking n1 be given (second stage of the model)
I Since each firm is identical, they get identical shares
si =
1
ni
I Example: if there are 10 firms, each gets 1/10 of the market
I Now we know si so we can compute profits
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In class problem: Closed economy
I 5-10 min, work with those around you
I Assume: w1 = 2, E1 = 100, 1 = 2, f h = 0.5, f p = 0.25
1. If n1 = 10, what are a firm’s profits?
2. If n1 = 20, what are a firm’s profits?
3. Why did profit fall by more than one half when we doubled n1 ?
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Two-country model with exporters
I Add a second country to the model
I Today: countries are identical [do not have to be]
I Still no MNEs, m1 = m2 = 0
I Allow domestic firms to export
I How is exporting different than selling locally?
I Exporting is more expensive: tariffs, transport, etc.
I Higher costs mean smaller market share
I si = share of domestic firm in country i
I ρ × si = share of exporter selling in country i
I ρ ≤ 1, so exporter has smaller share than domestic firm
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Two-country model with exporters
I The rest of the model is the same as closed economy
I Profit of a firm in country 1 are
π1 =
s1 E1
ρs2 E2
+
− w1 f 1
1
2
I π1 = profit from selling at home + profit from exporting - fixed costs
I Again, need to solve for shares
I If n1 and n2 firms, what are shares?
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Finding shares
I How many firms sell in country 1?
I n1 domestic firms with share s1
I n2 exporters with share ρs1
I Shares must sum to 1
1 = n1 × s1 + n2 × ρs1
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Computing profits
I Domestic firm share in country 1: s1 =
1
n1 +ρn2
I Export from 2 selling to 1 has share: ρs1
I Since countries are identical
I Domestic firm share in country 2: s2 =
1
n2 +ρn1
I Exporter from 1 selling to 2 has share: ρs2
I Now compute profits
π1 =
s1 E1
ρs2 E2
+
− w1 f 1
1
2
I . . . What are the fixed costs of a domestic firm? Of an exporter?
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In class problem: Two-country economy
I 5-10 min, work with those around you
I w1 = w2 = 2, E1 = E2 = 100, 1 = 2 = 2, f h = 0.5, f p = 0.25, ρ = 0.9
1. If n1 = 10 and n2 = 10, what are country 1 firm’s profits, π1 ?
2. In this model, 20 firms sell to country 1. In the closed economy
example, 20 firms sell to country 1. Why is s1 different in the two
models?
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Takeaways
I Model of identical firms competing in a market
I Two stage model: We worked on stage 2 today
I Closed economy model
I How number of firms affects profits
I Open economy model
I Exporters compete with domestic firms
I Exporters are disadvantage because they pay higher costs
I Key to solving both models is to find market shares
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