本文介紹了市場的開放性和公司的標記分布之間的關系。理論預測的企業異質性與國際貿易Melitz和Ottaviano最近文獻的描述和建立工作的基礎。Melitz和作品提供了一個框架，可以容納多個異構的國家內和產業間貿易。此外，它允許變量的加價率，較低的溢價更激烈的競爭同時高溢價的公司更富有成效的指控。在企業層面，Melitz和Ottaviano預測：1）標記是負相關的市場規模；2）標記和企業生產率呈正相關。

 

This paper presents the relationship between market openness and markup distribution of firms. Theoretical predictions by the recent literature on firm heterogeneity and international trade by Melitz and Ottaviano (2007) are described and build up the infrastructure of the work. Melitz and Ottaviano offer a framework that can accommodate multiple, heterogeneous countries in intra and inter industry trade. Moreover, it allows variable markups, lower markups with tougher competition meanwhile higher markups are charged by firms that are more productive. At the firm-level, the Melitz and Ottaviano predict that: 1) markups are negatively linked to market size; 2) markups and firm productivity are positively related.

 

INTRODUCTION 簡介

This seminar paper on the topic of "Firm-level Heterogeneity and markups", aims to analyze heterogeneous firms' behavior in the international trade. "Heterogeneity of firms in productivity creates gains from trade so that the more productive firms gain market share at the expense of the less productive ones raising the average productivity in the economy". (Bekkers 2008, p.16).

 

Two factors can contribute to the reallocation effect of trade in the new trade theory: enhanced labor market competition or enhanced product market competition. Since 2003 that Melitz significant paper on firms' decision to export was published, there have been several other literatures on the topic with heterogeneous firms' behavior.

 

The paper presented here is based on the paper introduced by Melitz and Ottaviano (2007) that particularly links productivity, prices and markups to the number of competing firms. It predicts the effects of openness to trade on the market structure and explains on the firm-level performance levels. Ottaviano, Tabuchi and Thisse (2002) model the monopolistically competitive markets differently, they develop a linear demand system with horizontal product differentiation where the price elasticity of residual demand is not fixed anymore but it is increasing in the number of competitors. The preferences are not CES. The MO model takes this demand system and builds the model on it. Relaxing the CES assumption in MO model is a distinction to Melitz work before. The performance measures are: price, productivity, market size and mark-ups. Pricing behavior depends on the number of competitors and the average price level in contrast to standard CES-preferences where prices are .fixed mark-ups over marginal cost. (Bekkers 2008, p25) A monopolistic competition model is to set where firms maximize profits based on their linear residual demand curve, taking N and p as given, and there is free entry into the industry. The closed-economy version and then the open-economy with a two-country case are presented followed by predictions for the effects of trade liberalizations on trade considering a bilateral and unilateral liberalization. An overview of similar models is given with a try to explain and motivate why this model is important#p#分頁標題#e#

 

Motivation 動機

An assumption that Melitz uses, is that it models the demand side using constant elasticity of substitution preferences. This generates markups. on marginal costs which is constant. The problem with constant markups in Melitz is that "the Melitz model with its constant markups,- depending neither on cost nor on demand- predicts identical revenue-based productivity across all firms. This is clearly rejected by the data" (Ottaviano&Corcos&Del Gatto&Mion 2009, p16). Nevertheless, "the empirical evidence on regional markets in the United States suggests that higher demand, as measured by market density, reduces markups and price dispersion "(Helpman p. 601)

 

The model introduced by Melitz and Ottaviano (2007) is another model of trade with heterogonous firms. The model is also inspired from Melitz (2003) in which the firms are heterogeneous in productivity and only those more productive firms can enter the market and export in the open economy and the less productive ones must exit the market. It is built on the demand system by OTT (2002).

 

Bernard, Eaton, Jensen and Kortum (2003), have proposed an alternative framework that introduces firm heterogeneity on a model of comparative advantage. Their model differs from MO model, the structure; they apply to their model is the Bertrand price competition between several potential producers of each variety. This is a difference to the other two models explained above. They also use CES preferences. However, though in that context more productive firms make higher markups, some surprising predictions for mark-ups are also obtained. In particular, the distribution of mark-ups is the same in any destination and does not depend on the level of technology or geographic barriers.( Moreno& Rodríguez p.2) MO model is the only model that uses the linear demand system and therefore allows markup differences. They show that market size has an influence on the productivity and number of varieties, and that the firms in larger markets set lower markups therefore it is more sensible in terms of explaining trade liberalization effects.

 

The table on the next page shows an overview of all three models, Melitz (2003), BEJK: Bernard, Eaton, Jensen and Kortum (2003) and MO.: Melitz and Ottaviano (2007):

 

Entry and Exit 進入與退出

Steady state of entry and exit, firms enter without knowing their productivity, exit after a change in cut-off level

 

Entry and exit are not modeled as a steady state. Firms enter when competitors for the same variety become more productive

 

Steady state of entry and exit, firms enter without knowing their productivity, exit after a change in cut-off level

 

Labor market structure

Inelastic supply,#p#分頁標題#e#

 

Labor can move freely between firms

 

Fully elastic supply of labor.

 

Inelastic supply,

 

Labor can move freely between firms

 

Product market structure

Monopolistic competition;

 

Number of firms doesn't affect pricing policy

 

Bertrand price competition.

 

Price competition between several potential producers of each variety

 

Monopolistic competition:

 

Composition effect: The possibility to export ….

Increase the market for high productive firms and entry more attractive

 

This raises the demand for labor, and increase the real wage. The less competitive firms have to exit.

 

Increase price competition for a certain variety.

 

High productive exporting firms replace domestic suppliers by undercutting their price.

 

Increase the number of competitors in the market. The general price level declines and high cost producers disappear.

 

Source: Adapted and modified from Bekkers 2008, p.38.

 

CLOSED ECONOMY 閉關自守經濟

In order to explain the closed-economy version of the model, the demand side and the production side are explained. Then the technology is parameterized and the free entry equilibrium is built which induces the short-run equilibrium.

 

Assumptions in the closed economy

An economy with L consumers

 

Each of the L consumer can supply one unit of labor

 

One numeraire good, differentiated goods, produced by the firms in the economy

 

Consumers have positive demands for the numeraire good (>0).

 

Consumers may have zero demand for the varieties ()

 

The Demand side

All consumers in the economy share the same utility function as below, Preferences are defined over a continuum of differentiated varieties indexed by iïƒ?ï?-, and a homogenous good as a numeraire:

 

This utility function shows the quadratic preferences which is an alternative specification of the preference for variety (OTT.,p.410 ). As already mentioned in the introduction there is a horizontal differentiation among products which indicate love of variety. represents the individual consumption level of the numeraire good and the consumption of each variety i. i is an index for the varieties that are available in the set ï?-. Furthermore, α, and are defined as demand parameters and are all positive.#p#分頁標題#e#

 

Higher means more product differentiation between varieties, when = 0, the varieties become perfect substitutes and consumers will then take care about their consumption over all varieties and index the substitution pattern between the differentiated varieties and the numeraire. Higher or lower lead to higher demand for differentiated varieties relative to the homogenous good.

 

Therefore, Qc can be written as below:

 

Qc signifies the individual consumption in each sector, inserting (3) in aggregate demand function we come to (4), which is a linear demand function in which the demand for each variety is increasing in the average prices of that product including the price that competitors set, and it is decreasing in the variety's price , meaning higher price leads to less demand for that variety:

 

In the equation above, N is the measure of consumed varieties in ï?-*, where ï?-* is the largest subset of ï?- which satisfies:

 

For positive demand for the variety i the inequality (5) must hold.. pmax is then the "choke price" or the price under which the consumer is willing to pay for a variety, at this point the demand for this variety is driven to zero. This Price goes down if N goes up or the average price goes down, in both cases, i.e. rise of N or fall of the competition gets tougher. The price elasticity is (See Appendix A.2):

 

As it can be seen and is shown in the appendix A.2. the price elasticity is not constant and not only dependent on the level of product differentiation,ï?§, but also depends on average prices and N number of varieties and pi This is a distinction to the case with constant elasticity of substation where the elasticity is exogenously fixed.

 

The indirect utility function can be taken to evaluate the welfare.

 

is the variance of the prices. It is assumed that. The individual income is larger than the total amount of expenditure on different varieties to assure positive demand for the numeraire good. Welfare, then changes by the change in of course income, Ic and average prices, it rises when average price falls, and if is held constant it then rises by increase of the variance of prices, because then the consumers shift their purchases towards less expensive products. If both of the latter are held constant the welfare increases as N, number of varieties increases, meaning if there are more varieties available, then the economy is better off; this is the meaning of "Love of varieties".

 

The Supply Side

The homogenous good is produced one-to-one with labor, with constant return to scale and at unit cost. For the production of differentiated varieties, as in Melitz (2003) the firms face an irreversible investment cost prior to the production. But then after entry, they will have constant return to scale, at marginal cost c. Again as it was in Melitz model, there is an uncertainty for firms which can be covered only after they have made the irreversible investment. This investment is sunk and is equal to fE. Productivity is then revealed. The uncertainty is modeled by draw from a common and known distribution G(c) over [0, cM ];#p#分頁標題#e#

 

The differences here to Melitz model is that there are no overhead costs in production. Only the firms that are able to cover their marginal cost can survive and produce, otherwise they have to exit the market. Firms that remain in the economy will maximize their profit. (See Appendix A.3).

 

cD (cD < cM) is the cut-off cost for the firm which is indifferent between production or leaving the industry, (Zero Profit Condition) the firms with c>cD exit the market because they make negative profits and those with c<cD will survive and continue production. Given the inverse demand function, the maximum price can be written as . From first order conditions we have:

 

Then the price:

 

Similarly other performance measures can be written:

 

Prices

 

Mark-ups Revenue

 

Profit

 

As it can be seen above and is expected, lower cost firms set lower prices, earn higher revenues and profits than firms with higher costs. They also set higher mark-ups. Melitz(2003) introduces markups as exogenous and says that "Regardless of its productivity, each firm faces a residual demand curve with constant elasticity σ and thus chooses the same profit maximizing markup equal to σ/(σ − 1) = 1/Ï?".(Melitz 2003,p.1699)

 

Like in Melitz model to have a general equilibrium in the economy there two conditions must be fulfilled. Free entry equilibrium (FE) and zero profit condition (ZPC).

 

Free Entry Equilibrium 自由進入均衡

In order to enter the industry, the ex-ante expected profit for a firm and prior to entry must be non-negative. The free entry condition can be written

 

where G(c) is the Pareto distribution. Since cD=p(cD) must also be equal to the zero demand price threshold in , therefore it can be concluded that Surviving firms are those firms which have their marginal cost lower than cD. Solve for N and get the zero cut-off profit condition. is the average cost of surviving firms ; average prices can be written as a function of average cost and cost cut-off [1] :

 

,

This is the zero cut-off profit condition, expressing the number of firms' dependence on the varieties and productivity level of the firms. The number of entrants can then be determined by

 

Referencing production technology by G(c) average productivity is higher or is lower, if sunk costs are lower, if varieties are closer substitutes (lower ï?§) and in bigger markets with more number of consumers, larger L, averaged productivity will be higher. Thus, the firm exit rates are also higher, in other words the probability of survival is lower (before entry). α and affect only the number of firms but have no effect on the selection of firms. There is a tougher competition in the larger market because more firms are competing and average prices are lower. To sum up, a firm with cost c responds to the tougher competition by setting a lower mark up relative to the mark up it would set in a smaller market (MO, p.300).#p#分頁標題#e#

 

Parameterization of Technology 參數化技術

 

For simplicity Melitz and Ottaviano assume that the distribution of cost draws G(c) is such that 1/c has a Pareto distribution with lower productivity bound 1/cM and shape parameter k1 indexing the dispersion of cost draws. When k=1 then the cost distribution is uniform on . Using this parameterization the free entry condition can then be written as follows:

 

CD (see Appendix A.4) is dependent on L the market size, ï?§ the degree of substitution between varieties, fE , entry sunk costs and cM, distribution of cost draws.. The lower the cD is, the more productive the firm. CD is lower when L is higher, i.e. the market is bigger, the varieties are closer substitutes, the CM is lower which means a better distribution of cost draws and naturally if the sunk cost of entry is lower. All these changes means an increase in toughness of competition. As previously mentioned cD<cM holds.

 

Using the parameterization:

 

Welfare can be rewritten by use of this parameterization.

 

which is decreasing in cD, (higher firm productivity), lower cD, increases the welfare.

 

The performance measures can also be rewritten(see appendix A.5):

 

Under the Pareto distribution, , and are higher and is lower in larger markets because of lower cD .

 

Number of surviving firms can be achieved by inserting the cD into the equation (14) and will be written

 

Short Run Equilibrium 短期均衡

In the short run, the number and the distribution of incumbents are fixed. The operating firms decide to stay and produce or shut down and leave the economy; yet the restart of the production would not be costly. No entry is possible in the short run. The determination of the cut-off level will be the same as in the long-run. Those firms with costs below cD produce and the others exit. Number of producing firms is then N=(cD)=(cD/M)k If cD= all firms produce in the short run. The unique short run cut-off cD can be derived from the non-negative profit condition. Previously number of firms N was determined in (14), as shown in the previous section, knowing that it can be written:

 

Setting this equal to N=(cD)=(cD/M)k we get the zero cut-off profit condition in the short run:

 

In the short run equilibrium, changes in the market size do not induce any changes in the distribution of producing firms as L does not appear in the equation above. The reason is that when market size changes the firms adjust their output to the market size. Since cD .remains constant the price distribution ( ) and markups ( ) are not affected either.

 

OPEN ECONOMY 開放的經濟#p#分頁標題#e#

As usual the model set up in the open economy, considers the case that the countries move from autarky to free trade. This immediately means an increase in the market size. As it was in the case of closed economy and the effect of market size on the performance measures were derived, however, in the open economy where the countries are interacting with trade, and trade is costly the results of the closed economy cannot be directly extended to the open economy.

 

Assumptions and set up

In the open economy, we assume:

 

Two countries, H and F

 

Each country is endowed with consumers, LH and LF.

 

Both countries share the same technology

 

Both countries have identical preferences and the same inverse demand function

 

In both countries markets are segmented and firms produce under constant return to scale

 

Firms can export in both countries but must bear a per unit trade cost (iceberg transportation cost) >1 ,

 

Entry is unrestricted in both countries

 

Countries are different in market size and barriers to trade

 

As we had in the closed economy: The choke price (price threshold) for each country can then be written as:

 

At this price the demand will be driven to zero

 

Nl is the number of firms selling in country l (total number of domestic and exporters)

 

l is the average price for both local and exporting firms in country l

 

The firms in both countries maximize their profits from their total sales that means from what they sell in the domestic market and what they export and sell in the export market. For the firms located in l we have:

 

Domestic sales

 

Export sales

 

Profit

 

Profit maximizing price

 

Profit maximizing output

 

Now there will be two different cut off levels for the domestic market and the export market exporting from l to h.ClD and ClX. These must satisfy

 

Dividing the above equations by each other we receive ClX=ClD/Ï„l. The upper bound cost for exporters from l to h is the upper bound cost for firms selling in the domestic market divided by the per unit transportation cost to l. This means that the trade barriers in the form of transportation costs make it harder for exporters to break even relative to the domestic producers. As in the case of closed economy we write the optimal prices and output levels as functions of the cut-offs: Again setting and equal we get the as a function of CD., inserting it into gives the optimal output as a function of ClD . Similarly, the maximized profit levels can also be written as function of cut-off levels:#p#分頁標題#e#

 

Domestic sales

Export sales

Maximized profit

Profit maximizing price

Profit maximizing output

Free Entry Condition

In the open economy version firms choose their production location prior to the entry and investment of the sunk cost entry. Hence, for the domestic firms in order to enter the domestic market and the export market holds the zero expected profit condition:

 

this can be written as below (see Appendix A6)

 

is an index for technology. It combines the effects of both distribution of cost draws and entry costs. If any of these are lower, then is lower, and the cost cut off level will be also lower. In order to simplify it is assumed that there is always a positive number of entrants, other wise and NE=0. In such a situation the country will specialize in the production of numeraire good. Having ClX=ClD/Ï„h. from the last part, we can rewrite :

 

Ï? is an inverse measure for the freeness of trade. The cut off levels in both countries:

 

Comparing the outcome of closed economy and open economy

The results of close economy and open economy are compared to explain the effects of trade. Comparing cut off level in the open economy with the case of autarky induces that:

 

This shows that opening to trade lowers the cut-off level for the firms relative to the autarky.

 

The number of selling firms in each country and number of entrants is then to be determined.

 

In each country there are domestic prices and export prices to be considered, the product prices produced by domestic firms but also the imported products which are produced in the other country but sold in the domestic market.

 

Under Pareto distribution , the distribution of clD and Ï„l c are identical over [0; clD]. Hence, plD (c) and ph X (c) have identical distribution too. Therefore the average price in both countries as we had in section 2.4.1 will be:

 

Nl, the number of varieties can be calculated using the latter average prices and the price threshold in as below:

 

Comparing this to the autarky we see that the number of varieties is larger than in the autarky situation after opening up to trade.

 

The number of sellers in each country is comprised of domestic sellers and exports from the other country and holds to the condition: combining this with the equation given for Nl above gives us the number of entrants:

 

It is assumed that there is always a positive number of entrants in each country (>0) rearranging the equation (23) leads to , only a subset of more productive firms export and the ones with cost between these two will only produce domestically.#p#分頁標題#e#

 

Welfare comparing this to the welfare we had in before we see that.

 

The Impact of Trade 貿易影響

In the open economy model, the distribution of the exporters' cost to deliver product to the country l, is equivalent to the distribution of the domestic firms' cost c in country l. This leads to identical price distributions for both domestic firms and exporters to that country. It can be concluded that the distribution of all the other firm-level performance measures are identical. Hence, when analyzing the effect of trade in open economy the concentration can be focused on the cut-off level derived for closed and open economy.

 

is the cut off level as calculated in , which is lower than the cut-off level in the closed economy.

 

Trade increases the aggregate productivity, forcing the less productive firms to exit.

 

Unlike Melitz model (2003), increased labor market plays no role here, because in the current model there is elastic supply of labor.

 

Increased product market competition is the only operating channel.

 

Opening up to free trade is similar to increasing size in the closed economy. Due to trade there is a tougher competition causing a downward shift in the distribution of mark-ups, this is despite the fact that those firms that can survive are more productive relative to the ones which have to exit and have higher mark-ups. The point here is that the average mark-up is lower. The foreign competition affects the selection of best firms. The reason for this is that in the domestic market, the presence of import competition leads to the shift of demand price elasticities for all the firms and at any demand level. Domestic firms face imported products which compete with their products in terms of price. Lower mark-up and the selection of best firms lead to prices shift down.

 

Market size effects 市場規模的影響

Costly trade is when trade costs such as transportation costs (Ï„>1) are present between countries that are interacting by trade. As defined above 1/Ï? is a measure for freeness of trade where.When ï?²l=ï?²h then there are symmetric trade costs, meaning that both countries face the same trade cost in order to trade with the other country. Now we imagine a case where one country is larger than the other one. The larger country will then have a relatively lower cut-off inducing higher productivity, more varieties and lower mark-ups and prices. Correspondingly, the welfare levels are relatively higher in the larger country attracting more entrants. Looking at the cut-off we see that the size of the partner country does not appear in the term and thus has no influence on the domestic cut-off level. This is while the larger country offers larger export opportunities and attracting more entrants, at the same time larger market means tougher competition-a greater number of more productive firms are competing in the market, driving down the mark-ups. There are effects offsetting each other. From export point of view, larger country offers higher export opportunities which is offset by its increased competitiveness. From import side of view, a lager partner country characterizes an increased level of import competition. The number of entrants in each country is:#p#分頁標題#e#

 

As country size differences become larger the number of entrants in the smaller country drives to zero, hence less competition in the smaller market in the long run.

 

Short Run Equilibrium in Open Economy

In the short run there is no entry and no exit possible. Firms decide to produce or shut down. Therefore in each country

 

The number of incumbents is fixed.(Dl)

 

The cost distribution is

 

If a firm can make non negative profits from its sale either in domestic or export market then it produces.

 

Again we have the conditions

 

to sell in the domestic market:

 

and to sell in the export market.

 

If then the firms with cost cut-off level between will be producing and not selling in the domestic market but selling in the export market. If the cut offs reach the upper then all the incumbents will be producing in that market.

 

As long as the cut offs satisfy and similarly as long as the cut offs satisfy. Like in the long run we have the total number of selling firms in a country as the sum of the domestic firms and exporters from the other country selling in the domestic market:. Hence, the cut off levels in both countries can be calculated and holds whenever and :

 

The size of the trading partner in the short run is significant. In a situation where the trading partner is bigger in size which means there is greater number of sellers on the market. If increases the right side of the equation is then greater that implies that on the right side there should be a decrease in , reduction of cut off level in the country l. This forces some of the less productive firms to shut down. However, the overall number of sellers in country l increases because there are more exporters on the market and this effect dominates the shutdown of the domestic firms. Nevertheless; this is happening particularly in the short and will be offset with entry in the long run.

 

BILATERAL AND UNILTERAL TRADE LIBERALIZATION 雙邊貿易自由化

In this section of the paper the authors consider a case of a fall in transportation costs and analyze how this affects the performance measures and the long-run consequence of this trade liberalization. Trade liberalization is introduced in two major forms in the paper, Bilateral liberalization and Unilateral liberalization, the authors then analyze the effect of a fall in transport cost in both cases and explain it by its effects on the cut-off condition:

 

The drop in the trade costs is assumed to be so that the number of entrants in the smaller economy would not drive to zero; otherwise the smaller country would not produce the differentiated good anymore.#p#分頁標題#e#

 

Looking at the equation above it is straightforward that the rise of Ï? must be limited that the NE does not drive to zero. Bilateral liberalization is a change in trade costs in the case of symmetric liberalization. In symmetric liberalization the assumption is that the same trade costs are imposed by both countries Ï„H=Ï„F=Ï„, which leads to equal trade openness Ï?H=Ï?F=Ï?.) and there is a simultaneous reduction in both countries' trade costs.

 

In the unilateral liberalization only one country is reducing its imposed transportation costs (τl , ï‚­Ï?l ) whereas Ï„h and thus Ï?h remain constant.

 

Table 2 Effect of bilateral and unilateral liberalizations

 

Bilateral liberalization

Ï„H=Ï„F=Ï„, Ï?H=Ï?F=Ï?

Ï„'< Ï„, Ï?'>Ï?

Unilateral liberalization

Ï„H=Ï„F=Ï„, Ï?H=Ï?F=Ï?

Ï„H= Ï„ , Ï?H= Ï? Ï„F> Ï„, Ï?F>Ï?

(for both countries)

 

Increase in Ï? leads to :

 

Decrease in , increase in productivity

 

Higher competition

 

Product variety increases

 

Average Prices decrease

 

Average Mark-ups decrease

 

Welfare rises (higher productivity, lower mark-ups and increased product variety

 

Results are identical to the case of opening up to free trade.

 

Increase in Ï?l leads to :

 

Increase in , decrease in

 

Less competition in the liberalizing country , instead tougher competition in the trading partner (higher productivity)

 

Liberalizing country experiences a welfare loss. The trading partner is better off.

 

Number of entrants in the liberalizing country decreases. While the number of entrants in the trading partner increases.

 

There is a pro-competitive effect in unilateral liberalization.

 

Distinction between short run and long run 短期和長期之間的區別

In the long run the size differences between countries induce important changes in the entry pattern. If Ll>Lh the NlE - NhE becomes bigger because entry in the larger market is more attracting. The authors prove that the number of domestic producers (in the bigger country) in the long run becomes greater.#p#分頁標題#e#

 

The unilateral liberalization induces different effects in the short run as in the long run, in order to explain this, we take a look at the short run cut-off that was derived in (25):

 

The rise of Ï?l leads to a fall in while remains unchanged; the increase in in the liberalizing country is to the benefit of the trading country (Pro-competitive effect). The fall of implies an increase in the import competition in the country l. making the country more attractive for the producers on the other side, exit of some of the least productive firms in l. Therefore there will be more exporters from h to l. This automatically means an increase in the product variety in country l. (), which dominates the reduction of the domestic varieties. Consequently, in the short run (prior to entry of new firms) welfare in the liberalizing country rises, as a result of increased product varieties, higher productivity and lower mark-ups. The trading country's welfare remains the same as before.

 

In the long run, however, the cut-offs depend on the freeness of trade present in each country, therefore,, and rise and fall respectively, leading to the welfare rise of the non-liberalizing country and welfare loss of the liberalizing country as was shown in table 2.

 

Preferential Liberalization

Preferential liberalization considers a world with more than two countries as was studied until now. In order to simplify in the paper the preferential liberalization is illustrated in a three-country case. Particularly whenever there are bilateral trade-liberalizations and these are allowed to differ among countries. Hence, the situation is set up as follows:

 

Three countries and LH=LF=LT. We let these three countries only differ in trade barriers. They would be then pair-wise symmetric. which is a measure for freeness of trade between two countries and each of these two countries h and l have ï?²lt and ï?²ht as freeness of trade measure with the third country t.

 

Long run and short run Equilibrium

The free entry condition from can be written for country l: the three country case: The domestic cut offs can be written for each country and then solving the system of three linear equations we receive the long-run cut-offs as follows:

 

�

When a preferential agreement is signed between two countries, then we have Ï?HF= Ï? ´>Ï? = Ï?FT= Ï?HT. Trade costs between H and F decrease, but remain unchanged between H or F and the third country. Thus we can write the cut-offs before any liberalization, the cut-off level for H and F after the liberalization as well as the cut-off for T:

 

, and

 

Comparing these: . This is an important result that indicates that the preferential liberalization lowers the cut-off in the liberalizing countries, increasing their accessibility and causing a higher cut-off in the "excluded" country.#p#分頁標題#e#

 

In the short run the entry is fixed and in the equilibrium we have:

 

the number of incumbents in all countries is constant, then the country with best accessibility (highest ï?²hl +ï?²lt) will have the lowest cut-off. The cut-off in the third country remains unchanged in the short run. Only in the long -run the fall in the competition and welfare loss is to be considered. Liberalizing countries gain in both short-run and long-run.

 

CONCLUSION 結論

Melitz and Ottaviano present a model of trade with heterogeneous firms with focus on the differences in the market size and trade costs across trading countries and analyze how these affect the distribution of the firm-level performance measures. A specific feature of MO model is the different shape of the demand functions, compared to similar previous studies, like Melitz (2003). Melitz and Ottaviano use the linear demand function allowing the elasticities to be non-constant and consequently allow endogenous markups. This set up allows the authors to analyze the effect of trade and trade liberalization on markups too. They build up the model in closed economy, expand it to open economy and finally analyze the effects of a fall in transportation cost on the performance measurements. In the closed-economy generally in the larger markets the average productivity is higher; when the sunk costs of f E are lower and goods are more substitutable, the cost cut-off level will be lower meaning higher average productivity. Since a lower cost cut off correspond to lower price and larger product variety the welfare in such economies will be higher. Finally, in larger markets, there is tougher competition (higher average productivity, lower prices) and firms have larger sales and profits and lower markups. Larger market increases the competition which lowers the markup but it drives selection toward the more productive firm with higher markups. However the first effect dominates and the markup are lower. Opening to trade implies that the price elasticity of demand increases and the choke price fall. In the open economy trade increases the aggregate productivity because the least productive firms that cannot afford lower prices exit. Moreover, trade reduces the markups. The effect of opening to trade is like an increase in size in the closed economy. There will be tougher competition the firms' respond to the tougher competition is to lower markups. The welfare gains by trade as a combined result of higher productivity, increased product variety and lower mark-up. In the trade liberalization analysis the authors consider that liberalization induces welfare changes. Market size remains important; bigger markets become more attractive location for firms as trade costs fall.