Master EPP, Eco-572 International Economics PC 3 Imperfect Competition

Exercice 1: The gravity model We seek to build a micro-founded model which could explain the following empirical pattern:

We proceed as follows. The nominal revenue of a given country j is Yj . Country j consumes Ni varieties of goods imported from each of its partner countries i, with i ∈ {1..C}. The price of variety k ∈ {1..Ni } imported by country j from country i is called pkij . The utility function of the representative consumer of country j writes: " Uj =

Ni C X X

ckij

σ−1 σ

σ # σ−1

with σ > 1

i=1 k=1

Assume for simplicity that all varieties k shipped by country i to country j are sold the same price: pkij = pij ∀k. Quantities sold are therefore identical as well: ckij = cij ∀k. The utility function can be simplified as: σ " C # σ−1 X σ−1 Uj = Ni cijσ with σ > 1 i=1

1

Finally, we define the price index of country j as: " Pj =

C X

1 # 1−σ

1−σ Ni pij

i=1

1) Write the budget constraint of country j and derive the utility-maximizing consumption of each variety cij . Hint: form the Lagrangian and derive the first-order condition. From these expressions, calculate cij and add up over i. 2) We suppose that proportional transport costs τij apply to the importing country: pij = (1 + τij )pi where pi is the price in the exporting country i (the so-called “free-on-board” or “FOB” price) and pij is the price in the destination country j (“cost, insurance and freight” or “CIF” price). How do transport costs impact the volume of exports from i to j? 3) Infer from the last question the equation explaining the value of aggregate trade between i and j. 4) Based on the following pooled regression, assess the effect on trade in goods and services of sharing a common currency.

Source: Head, Mayer and Ries (JIE 2010) Notes:

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The first three columns portray results where exporter and importer population and per-capita GDP proxy for exporterspecific and importer-specific effects. In the ensuing three columns, these effects are eliminated by creating tetradic trade flows. This requires choosing reference countries. To investigate the robustness of the method, we employ three country pairs-Great Britain-France, the United States-Germany, and Switzerland-Canada- as the reference countries and report estimates for all three. All specifications include year dummies that are not reported in the table;

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’RTA’ signals the existence of a regional trade agreement;

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Standard errors in parentheses with a, b and c respectively denoting significance at the 1%, 5% and 10% levels. Standard errors are corrected to take into account correlation of errors within dyads in columns (1) to (3). Columns (4) to (6) use three-way clustering by dyad, i-year, and j-year using Cameron et al. (2006) method.

Exercise 2: Love-of-variety, linear demand and heterogeneous firms 1) Consider the utility function 

U

q0 , [qi ]N i=1



Z

N

1 qi di − γ = q0 + α 2 i=1

Z

N

1 (qi ) di − η 2 i=1 2

Z

N

2 qi di

(1)

i=1

Here, q0 is an “outside good”. It has price 1, and can be thought of as “the rest of the economy”. Our main interest is in the continuum of varieties [qi ]N i=1 . How does the utility function express “love-of-variety”? Which parameter(s) (α, γ or η) govern how much consumers value variety?   2) Consumers maximise U q0 , [qi ]N i=1 subject to the budget constraint Z

N

q0 +

pi qi di = 1

(income has been normalized to 1, and q0 has price 1).

i=1

Construct the Lagrangian and show that the optimal consumption satisfies the inverse demand curve, Z N pi = α − γqi − ηQ, where Q = qi di (2) i=1

Define 1 p¯ = N

Z

N

pi di, i=1

the mean price. Find an expression for Q and show that demand can equivalently be expressed as qi =

α 1 ηN 1 − pi + p¯ ηN + γ γ ηN + γ γ

(3)

Interpret 3) Find an expression for the price that gives zero demand (pi such that qi = 0, expressed in p¯ and N , not in Q). 4) Firms have cost function CD (q) = cq (irrespective of what variety i they are producing). What is the highest level of c that a firm can have and still make positive sales on the market? Call this value cD . Assuming that the mean price is left unchanged, explain what is the impact of opening up on cD . 3

5) There are two identical countries with the characteristics described so far. If a firm wishes to export to the other country, it must pay an iceberg cost τ > 1. The marginal cost of delivering a product to the foreign market is therefore τ c. (Cost function of exporting: CX (q) = τ cq.) Firms face a demand abroad identical to their domestic demand. What is the highest value of c a firm may have and still export? Call this value cX . Compare with cD and interpret. 6) Firms are monopolies in their variety. They maximize profits taking other firms’ behavior (summarized by the average price p¯ and the total quantity Q) as given. Show that by rewriting (3) in terms of cD and inserting (3) in π (p, q) = pq − cq, profits can be expressed as πD (pD ) = (pD − c)

1 (cD − pD ) γ

and πX (pX ) = (pX − τ c)

on the domestic market, pD is domestic price

1 (τ cX − pX ) γ

on the export market, pX is export price

7) Solve the firms’ profit maximization problems for pD and pX , respectively. Your solutions should enable you to express domestic and export profits as πD =

τ2 1 (cD − c)2 and πX = (cX − c)2 . 4γ 4γ

Discuss the “pro-competitive” effect of international trade that this model features.

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