The quality of economic institutions, such as contract enforcement, property rights, and rule of law is increasingly viewed as a key determinant of economic performance. While it has been established that institutions are important in explaining income differences across countries, what in turn explains those institutional differences is still an open question, both theoretically and empirically.
In this paper we ask, how does opening to international trade affect a country’s institutions? This is an important question because it is widely hoped that greater openness will improve institutional quality through a variety of channels, such as reducing rents, creating constituencies for reform, and inducing specialization in sectors that demand good institutions (Johnson, Ostry, and Subramanian, 2005; IMF, 2005). Although trade openness does seem to be associated with better institutions in a cross-section of countries,2 the relationship between institutions and trade is likely to be nuanced. In the 1700’s, for example, the economies of the Caribbean were highly involved in international trade, but trade expansion in that period coincided with the emergence of slave societies and oligarchic regimes (Engerman and Sokoloff, 2002; Rogozinski, 1999). During the period 1880–1930, Central American economies and politics were dominated by large fruit-exporting companies, which destabilized the political systems of the countries in the region as they jockeyed to install regimes most favorable to their business interests (Woodward, 1999). In the context of oil exporting countries, Sala-i-Martin and Subramanian (2003) argue that trade in natural resources has a negative impact on growth through worsening institutional quality rather than Dutch disease. The common feature of these examples is that international trade contributed to concentration of political power in the hands of groups that were interested in setting up, or perpetuating, bad institutions. Thus, it is important to understand under what conditions greater trade openness results in a deterioration of institutions, rather than their improvement.
The main goal of this paper is to provide a framework rich enough to incorporate both positive and negative effects of trade on institutions. We build a model in which institutional quality is determined in a political economy equilibrium, and then compare outcomes in autarky and trade. In particular, to address our main question, we bring together two strands of the literature. The first is the theory of trade in the presence of heterogeneous firms (Melitz, 2003; Bernard et al., 2003). This literature argues that trade opening creates a separation between large firms that export, and smaller ones that do not. When countries open to trade, the distribution of firm size becomes more unequal: the largest firms grow larger through exporting, while smaller non-exporting firms shrink or disappear. Thus, trade opening potentially leads to an economy dominated by a few large producers.
The second strand of the literature addresses firms’ preferences for institutional quality. Increasingly, the view emerges that large firms are less affected by bad institutions than small and medium size firms.3 Furthermore, larger firms may actually prefer to make institutions worse, ceteris paribus, in order to forestall entry and decrease competition in both goods and factor markets.4 In our model, we formalize this effect in a particularly simple form. Finally, to connect the production structure of our model to the political economy, we adopt the assumption that political power is positively related to economic size: the larger the firm, the more political weight it has.
We identify two effects through which trade affects institutional quality. The first is the foreign competition effect. The presence of foreign competition generally implies that each firm would prefer better institutions under trade than in autarky. This is the disciplining effect of trade similar to Levchenko (2004). The second is the political power effect. As the largest firms become exporters and grow larger while the smaller firms shrink, political power shifts in favor of big exporting firms. Because larger firms want institutions to be worse, this effect acts to lower institutional quality. The political power effect drives the key result of our paper. Trade opening can worsen institutions when it increases the political power of a small elite of large exporters, who prefer to maintain bad institutions.
When is the political power effect stronger than the foreign competition effect? Our comparative statics show that the foreign competition effect of trade predominates when a country captures only a small share of world production in the rent-bearing industry, or the country is relatively large. In this case, while the power does shift to larger firms, these firms still prefer to improve institutions after trade opening. On the opposite end, institutions are most likely to deteriorate when the country is small relative to the rest of the world, but captures a relatively large share of world trade in the rent-bearing industry. Intuitively, if a country produces most of the world’s supply of the rent-bearing good, the foreign competition effect will be weakest. On the other hand, having a large trading partner allows the biggest exporting firms to grow unchecked relative to domestic GDP, giving them a great deal of political power. We believe our framework can help explain why, contrary to expectations, more trade sometimes fails to have a disciplining effect and improve institutional quality. Indeed, our comparative statics are suggestive of the experience of the Caribbean in the 18th century, or Central America in the late 19th through early 20th: these were indeed small economies that had much larger trading partners, and captured large shares of world trade in their respective exports. At the end of the paper, we describe in detail three cases that we believe our model captures well: the Caribbean sugar boom in the 18th century; the coffee boom in Latin America in the 19th; and the cotton and cattle boom in Central America in the mid-20th century.
Our environment is a simplified version of the Melitz (2003) model of monopolistic competition with heterogeneous producers. Firms differ in their productivity, face fixed costs to production and foreign trade, and have some market power. If the domestic variable profits cover the fixed costs of production, the firm enters. If the variable profits from serving the export market are greater than the export-related fixed cost, the firm exports. Variable profits depend on firm productivity, and thus in this economy only the most productive firms export. Melitz (2003) shows that when a country opens, access to foreign markets allows the most productive firms to grow to a size that would not have been possible in autarky. At the same time, increased competition in the domestic markets reduces the size of domestic firms and their profits. The distribution of profits thus becomes more unequal than it was in autarky: larger firms grow larger, while smaller firms become smaller or disappear under trade.
The institutional quality parameter in our model is the fixed cost of production. When this cost is high, institutions are bad, and fewer firms can operate. Narrowly, this fixed cost can be interpreted as a bureaucratic or corruption-related cost of starting and operating a business.5 More broadly, it can be a reduced-form way of modeling any impediment to doing business that would prevent some firms from entering or producing efficiently. For example, it could be a cost of establishing formal property rights over land or other assets. Or, in the Rajan and Zingales (2003a) view of financial development, our institutional quality parameter can be thought of as a prohibitive cost of external finance.
In our model, every producer has to pay the same fixed cost. We first illustrate how preferences over institutional quality depend on firm size. We show that each producer has an optimal level of the fixed cost, which increases with firm productivity: the larger the firm, the worse it wants institutions to be. Why wouldn’t everyone prefer the lowest possible fixed cost? On the one hand, a higher fixed cost that a firm must pay decreases profits one for one, and same for everyone. On the other hand, setting a higher fixed cost prevents entry by the lowest-productivity firms, which reduces competition and increases profits. This second effect is more pronounced the higher is a firm’s productivity. More productive firms would thus prefer to set fixed costs higher.
As a last step in characterizing our model environment, we require a political economy mechanism through which institutional quality is determined. The key assumption we make here is that the larger is the size of a firm, the greater its political influence. There is a body of evidence that individuals with higher incomes participate more in the political process (Benabou, 2000). There is also evidence that larger firms engage more in lobbying activity (see, for example, Bombardini, 2004). We adopt the political economy framework of Benabou (2000), which modifies the median voter model to give wealthier agents a higher voting weight. These ingredients are enough to characterize the autarky and trade equilibria. Firms decide on the fixed costs of production common to all, a decision process in which larger firms receive a larger weight. Then, production takes place and goods markets clear. We use this framework to compare equilibrium institutions under autarky and trade, in order to illustrate the effects of opening that we discussed above.
Our paper is closely related to several contributions to the literature on trade and institutions. In a seminal article, Krueger (1974) argues that when openness to international trade is combined with a particular form of trade policy—quantitative restrictions—agents in the economy will compete over rents that arise from possessing an import license. In this setting, one of the manifestations of rent seeking will be greater use of bribery and thus corruption. Other papers have explored the effects of trade on institutions unrelated to distortionary trade policy. For instance, Acemoglu, Johnson, and Robinson (2005) argue that in some Western European countries during the period 1500–1850, Atlantic trade engendered good institutions by creating a merchant class interested in establishing a system of enforceable contracts. Thus, trade expansion affected institutions by creating a powerful lobby for institutional improvement. Levchenko (2004) argues that trade opening changes agents’ preferences in favor of better institutions. When bad institutions exist because they enable some agents to extract rents, trade opening can reduce those rents. In this case, trade leads to institutional improvement by lowering the incentive to lobby for bad institutions. Our model exhibits both the foreign competition effect related to Levchenko (2004), and the political power effect of Acemoglu et al. (2005). However, in our framework, the more powerful groups need not favor better institutions under trade.
In focusing on the interaction of trade and domestic political economy, our paper is related to Bardhan (2003) and Verdier (2005). These authors suggest that trade may shift domestic political power in such a way as to prevent efficient or equitable redistribution. Finally, our work is also related to the literature on the political economy dimension of the natural resource curse. It has been argued that the presence of natural resources lowers growth through worsening institutions. This is because competition between groups for access to natural resource-related rents leads to voracity effects along the lines of Tornell and Lane (1999) (see also the discussion in Isham et al., 2005).
The rest of the paper is organized as follows. Section II describes preferences, production structure, and the autarky and trade equilibria. Section III lays out the political economy setup and characterizes the political economy equilibria under autarky and trade. Section IV presents the main result of the paper, which is a comparison between the autarky and trade equilibria. We start with an analytic discussion of the conditions under which institutions may deteriorate with trade opening. Then, we present the results of a numerical simulation of the model, and use it to discuss the comparative statics. Section V presents three case studies, in which we believe that the mechanisms described by our model were at work. Section VI concludes. Proofs of Propositions are collected in the Appendix.
II. Goods and Factor Market Equilibrium
A. The Environment6
Consider an economy with two sectors. One of the sectors produces a homogeneous good z, while the other sector produces a continuum of differentiated goods x(v). Consumer preferences over the two products are defined by the utility function
Utility maximization leads to the following demand functions, for a given level of total expenditure E :
∀v ∈ V, where ε = 1/(1−α) > 1, and we define A ≡ βE/∫v∊Vp(v)1−εdv to be the demand shift parameter that each producer takes as given.
There is one factor of production, labor (L). The homogeneous good z is produced with a linear technology that requires one unit of L to produce one unit of z. We normalize the price of z, and therefore the wage, to 1.
There is a fixed mass n of the differentiated goods firms, each of whom is able to produce a unique variety of good x. Firms in this sector have heterogeneous productivity. In particular, each firm is characterized by a marginal cost parameter a, which is the number of units of L that the firm needs to employ in order to produce one unit of good x. Each firm with marginal cost a is free not to produce. If it does decide to produce, it must pay a fixed cost f common across firms, and a marginal cost equal to a. The firm then faces a downward-sloping demand curve for its unique variety, given by (2). As is well-known, isoelastic demand gives rise to a constant markup over marginal cost. The firm with marginal cost a sets the price p(v) = a/α, total production at
The distribution of a across agents is characterized by the cumulative distribution function G(a). In order to adapt our model to a political economy framework in the later sections, we need to obtain closed-form solutions in the goods and factor market equilibrium. We follow Helpman, Melitz, and Yeaple (2004) and use the Pareto distribution for productivity. The Pareto distribution seems to approximate well the distribution of firm size in the U.S. economy, and delivers a closed-form solution of the model. In the Appendix, we describe it in detail, and present solutions to the autarky and trade equilibria when G(a) is Pareto.
To pin down the equilibrium production structure, we need to find the cutoff level of marginal cost, aA, such that all firms above this marginal cost decide not to produce. In this model, firm productivity takes values on the interval
When the equilibrium cutoff is aA, the demand shift parameter A can be written as:
where we define
The equilibrium value of E can be pinned down by imposing the goods market clearing condition that expenditure must equal income:
We do not have free entry in the model, that is, we have a fixed mass of producers. This means that total income, given by the equation above, is the sum of total labor income and the profits accruing to all firms in the economy.8 We can use (3) and (5) to write this condition as:9
The two equations (5) and (6) in two unknowns E and aA characterize the autarky equilibrium in this economy, which we illustrate in Figure 1. On the horizontal axis is a, which is the firm’s marginal cost parameter (thus, the most productive firms are closest to zero). On the vertical axis is firm profit. The zero profit cutoff, aA, is defined by the intersection of the profit curve with the horizontal axis. All firms with marginal cost higher than aA don’t produce. For the producing firms, profit increases in productivity. Higher f means that in equilibrium fewer firms operate:
Figure 1.Profits as a Function of Marginal Cost
Suppose that there are two countries, the North (N) and the South (S), each characterized by a production structure described above. The countries are endowed with quantities LN and LS of labor, respectively, and populated by mass nN and nS entrepreneurs. Let fS be the fixed cost of production in the South, and fN in the North.
Good x can be traded, but trade is subject to both fixed and per unit costs.10 In particular, in order to export, a producer of good x must pay a fixed cost fX, and a per-unit iceberg cost τ. We assume that these trade costs are the same for the two countries. A firm in country i that produces a variety v faces domestic demand given by
for i = N, S.
If the firm with marginal cost a decides to pay the fixed cost of exporting, its effective marginal cost of serving the foreign market is τa, and thus it sets the foreign price equal to τa/α, and its profit from exporting is
where j ≠ i designates the partner country, and i = N, S.
What determines whether or not a firm decides to export? A firm cannot export without first paying the fixed cost of production fi. We also assume that τ and fX are large enough that not all firms which find it profitable to produce domestically find it worthwhile to export. Thus, only the higher-productivity firms end up exporting, which seems to be the case empirically. We illustrate the partition of firms into domestic and exporting in Figure 2. The two lines plot the domestic and export profits as a function of a. As drawn, firms with marginal cost higher than aD do not produce at all. Firms with marginal cost between aX and aD produce only for the domestic market, while the rest of the firms serve both the domestic and export markets.
Figure 2.Profits and Firms’ Segmentation into Domestic and Exporting
To pin down the equilibrium, we must find the production cutoffs
where i = N, S, and j ≠ i. Comparing these to the autarky demand (4), we see that the denominators in these expressions reflect the fact that some varieties of good x consumed in each country are imported from abroad. The cutoff values for production and export are characterized by:
where i = N, S, and j ≠ i. The model can be closed by imposing the condition that expenditure equals income in both countries. In particular, total income is the sum of labor income and all profits accruing to firms from selling in the domestic and export markets:
Equations (11)–(14) determine the equilibrium values of
III. Political Economy
In this paper, we think of the fixed cost of production, f, as the parameter that captures institutional quality. It can be interpreted narrowly as a corruption cost of starting or operating a business, or more broadly as any effect of poor institutions that acts to restrict entry. The quality of institutions, f, is determined endogenously through a political economy mechanism in which entrepreneurs participate; for simplicity we abstract from the participation of L in the political process. In order to characterize the equilibrium outcome, we need to specify the agents’ preferences, and the political economy mechanism through which institutional quality is determined. In our framework, preferences are equated with agents’ wealth, and wealthier agents prefer to have worse institutions. For this, the connection to the production side of the model is essential. As we show below, when a firm’s wealth is a positively related to its profits, it is indeed the case that larger firms prefer worse institutions.
When it comes to the political economy mechanism, the effect we would like to capture is that agents with higher incomes have a higher weight in the policy decision. For instance, Bombardini (2004) documents that larger firms are more involved in lobbying activity, and thus we would expect them to have a higher weight in the determination of policies. Rather than assuming a specific bargaining game, we adopt a reduced-form approach of Benabou (2000). This approach modifies the basic median voter setup to allow for a connection between income and the effective number of votes.
This section provides a general characterization of the political economy environment. We state the regularity conditions that must apply in our setting, define an equilibrium, and then prove a set of propositions showing its existence and stability. We then apply the general results to the case in which agents’ preferences and voting weights come from the firms’ profits in the autarky and trade equilibria. Finally, we present the main result of the paper, which is the comparison between the autarky and trade equilibrium institutions.
A. The Setup
Firms participate in a political game as an outcome of which the level of barriers f ∈[fL, fH] is determined.13 An agent is characterized by a political weight, λ(w), which is a function of the agent’s wealth w. We assume that the political weight function λ(w) is identical for every agent, and takes the following form:
For a given distribution of wealth F(.), the pivotal voter is characterized by a level of wealth wp defined by
We therefore assume that λ1, λ0, and F (.) are such that
The parameter λ1 can thus be seen as the wealth bias of the political system. Higher values of λ1 give more political power to richer individuals, while λ1 = 0 yields the median voter outcome, which we denote by wm. It is then straightforward to see that for every possible political weight profile, the associated pivotal voter is always wealthier than the median voter as long as λ1 > 0. The following Lemma characterizes pivotal voters at different levels of λ0 and λ1.
Defining by wp (λ0, λ1) the pivotal voter that prevails when the political weight schedule is
- wp (λ0, λ1) is increasing in λ1 and decreasing in λ0;
- wp (λ0, λ1) ≥ wm for any λ0 > 0, λ1 ≥ 0;
For the rest of the paper, we assume that wealth is derived from profits, so that for any agent with marginal cost
We now discuss the two ingredients necessary to find a political economy equilibrium: we need to know the identity of the pivotal voter, given by the marginal cost a = p, and we need to know what institutions that pivotal voter prefers. We start with the latter.
B. The Preference Curve
The Preference Curve is the locus of all the points
Furthermore, the Preference Curve fr(p) is nonincreasing, and strictly decreasing for some values of p.
The first part of the Proposition shows that when the wealth-maximizing level of f is interior, it can be obtained simply by taking the first-order condition of wealth with respect to f. When the profit-maximizing level of f is not interior, the entrepreneur prefers either fH or fL, and all entrepreneurs that are more (less) productive also prefer fH (fL). The second part states that wealthier agents prefer worse institutions. The non-standard assumption driving the latter result is that ∂wr (a, f)/∂f is decreasing in a: the marginal benefits of raising entry barriers must be higher for higher productivity agents. Then, higher marginal cost entrepreneurs prefer lower levels of entry barriers, all else equal.
Let us now make the connection between the goods market equilibrium outcomes and the Preference Curve. In particular, suppose that the wealth functions take the following form:
in autarky, and
under trade, where P(f) and PS (f) are consumption-based price indices in autarky and under trade in the South, respectively. That is, agents’ wealth is simply real profits.
Why would any producer prefer to set f at any level higher than fL? The fixed cost f affects real wealth through three channels. The first two have to do with nominal profits. The key tradeoff is that while a higher level of fixed cost has a direct effect on every firm’s nominal profits, a higher f also leads to less entry. With fewer producers operating in the economy, the active firms’ variable profits are higher. Most importantly, this second effect is more pronounced for higher productivity firms, which implies that the more productive firms prefer to live with worse institutions. The third effect has to do with the price level. A higher value of f leads to fewer producers, and thus fewer varieties and a higher consumption price level. We can rewrite the expression for autarky real profits, (3), using (4):
keeping in mind that P, E, and aA are equilibrium values that are themselves functions of f. The first term in the numerator is the variable profits. It is true that raising f lowers the total profits one for one, because the firm must pay higher fixed costs. However, raising f also raises the nominal variable profits, because it pushes more firms out of production. Furthermore, variable profits are multiplicative in a1−ε, a term that rises and falls with the firm’s productivity. Thus, a firm with a higher productivity will reach maximum nominal profits at higher levels of f. In the Appendix (section A. 4), we use the closed-form solutions of the model to show under what conditions this effect dominates the other two, and more productive firms indeed prefer worse institutions. It turns out that without the price level effect it is always the case that more productive firms prefer worse institutions. The price level effect, in turn, can be made weak enough not to overturn this pattern by lowering β, the share of the differentiated good CES composite, in the total consumption basket.
Figures 3 and 4 illustrate this Proposition. Figure 3 reproduces Figure 1 for two different levels of f. We can see that raising f forces the least productive firms to drop out. Furthermore, the slope of the profit line is higher in absolute value for higher f: variable profits are higher at each productivity. Thus, firms above a certain productivity cutoff actually prefer a higher f, as the variable profit effect is stronger than the fixed cost effect. To illustrate this point further, Figure 4 plots the profits of two firms as a function of f. The profits of each firm are non-monotonic in f, first increasing, then decreasing in it. A firm with a higher productivity attains maximum profits at a higher level of f. This heterogeneity in firm preferences over institutions is the key feature of our analysis.
Figure 3.Profits As a Function of Marginal Cost for Two Different Values of f Figure 4.Profits As a Function of f
In the trade equilibrium, firms’ preferences over institutional quality differ from those in autarky. This is because the level of f in the domestic economy affects both the domestic production and the pattern of its imports. Nonetheless, the essential trade-off remains unchanged. On the one hand, a higher f implies higher variable profits, an effect that is stronger for more productive firms. On the other, the higher fixed cost decreases profits one for one, and pushes the consumption price level up. Comparing to autarky, we must keep in mind that f may also affect the firms’ decision whether or not to export, and its profits from exporting.
Having completed our description of firms’ preferences, we now move to a discussion of the political economy mechanism.
C. The Political Curve
The Political Curve is defined by the set of points
when the pivotal voter thus defined is unique for every f. Here we express the identity of the pivotal voter in terms of marginal cost a rather than wealth w. Furthermore, we would like to equate wealth with profits in our analysis. In this formulation, for a unique mapping between wealth and productivity of the pivotal voter to exist, we must ensure that the pivotal voter always produces under autarky and under trade. In what follows, we assume that parameter values are such that this condition is always met. This can be achieved by either a low enough fH or a high enough λ1.
When regularity conditions (A.6) and (A.7) are satisfied, and
The first part of this Proposition formally establishes the equivalence between defining a pivotal voter by her wealth and by her marginal cost of production. This result comes from the assumption that there exists a one-to-one correspondence between wealth and marginal cost in the neighborhood of any potential pivotal voter. We can hence restate previous results in terms of marginal cost of production a rather than wealth, keeping in mind that the mapping between the two is decreasing.
The second part of the Proposition takes one extra step in characterizing the Political Curve. In particular, we would like to show that under certain conditions, the Political Curve is downward sloping. That is, we would like to restrict attention to cases in which a higher level of fixed cost results in a pivotal voter that is more productive. This is a sensible requirement: a higher level of f decreases the wealth of the least productive firms, and increases the wealth of the most productive firms, thus shifting the voting weight towards the higher productivity firms. We illustrate this in Figure 5, which plots the densities of profits for two values of fixed cost, fH > fL. Nonetheless, for this Proposition to hold, certain restrictions on the function λ(w) must be satisfied: it must give enough weight to wealthier agents relative to less wealthy ones.
Figure 5.Densities of Distributions of Profits and the Pivotal Firms
D. Equilibrium: Definition, Existence, Characterization
We now define the equilibrium that results from the agents’ preferences and the voting. As the discussion above makes clear, there is a two-way dependence in our setup: the identity of the pivotal firm, p, depends on the level of f, while the level of f depends on the identity of the pivotal firm. Our equilibrium must thus be a fixed point.
An equilibrium of the economy is a pair (fr, pr) such that fr = fr(pr), and pr = pr(fr), where fr ∈[fL, fH] and
There exists at least one equilibrium.
Given our characterization of the Preference Curve and the Political Curve above, the definition of equilibrium and its existence can be illustrated with the help of Figure 6. The proof of this Proposition shows that one of three cases are possible: fL, fH, or an interior value of f. The first two occur when the two curves intersect on the flat portion of the Preference Curve.
Figure 6.The Preference Curve, the Political Curve, and Possible Equilibria
Having established existence, we now would like to characterize potential equilibria. We will not consider an explicitly dynamic setting to address issues of stability. We instead define the following functions: ∀f ∈[fL, fH],
and by induction, for n ≥ 1,
Similarly, we define for
and for any n ≥ 1,
An equilibrium (fr, pr) is stable if there exists ρ > 0, such that for any η > 0, there exists an integer ν ≥ 1 such that for any n ≥ν,
In other words, an equilibrium will be considered stable if, after a small perturbation (of size ρ) around the equilibrium point, the system converges back to the equilibrium, with (20) and (21) characterizing the dynamic process. The definition of stability above corresponds to the concept of asymptotic stability in dynamic processes. Two generic cases of equilibria that violate the stability requirement that might arise are: (i) a “cycling” case, whereby the process is bounded but does not converge; (ii) the process diverges after a perturbation and reaches a corner solution. We prove the following proposition by considering these two cases. We first argue that cycling cannot occur as Preference and Political curves are downward sloping, and then establish that if there does not exist any stable interior equilibrium, then one of the two corners is an equilibrium, and corner equilibria are stable.
There exists a stable equilibrium.
We can now apply the results proved in this section to the autarky and trade regimes. When wealth equals profits, and is thus defined by (16) and (17) in autarky and trade respectively, we have the following result:
Under regularity conditions, both autarky and trade regimes are characterized by downward sloping Preference and Political Curves. Furthermore there exists a stable equilibrium in both autarky and trade regimes.
IV. Institutions in Autarky and Trade
We now compare the equilibrium institutions in the South that occur under autarky and trade. We assume all throughout that the North’s institutions are exogenously given, and all adjustment in the North takes place on the production side. When an economy opens to trade, both the Preference Curve and the Political Curve shift. We investigate the behavior of Political and Preference Curves in turn.
A. The Political Power Effect
The reorganization of production due to trade opening leads the Political Curve to shift “inwards.” In particular, at any f, the most productive firms begin exporting, and the distribution of profits becomes more unequal: relative wealth shifts towards the more productive firms. This means that the pivotal voter moves to the left, pT(f) ≤ pA(f) ∀f ∈ [fL, fH]. We label this the political power effect: the power shifts towards larger firms under trade compared to autarky. Once again, while the notion that increased profit inequality leads the pivotal voter to shift in this direction is intuitive, the proof depends crucially on regularity conditions governing λ(w): the political weight function must be sufficiently increasing in wealth.
Under regularity conditions on λ(w), the Pivotal Voter curve moves inward as the economy opens to trade.
B. The Foreign Competition Effect
We now need to make a statement about how the Preference Curve shifts. It turns out that for most parameter values, and for values of a high enough, a firm at a given level of a prefers to have better institutions under trade than in autarky. This very much related to the Melitz effect, and comes from the fact that domestic profits are lower under trade due to the increased foreign competition.14 We label this inward shift of the Preference Curve the foreign competition effect. We must keep in mind that the most productive of the exporting firms may actually prefer worse institutions under trade, because as we saw above, export profits increase in f. It is also true that in principle, parameter values may exist under which the inward shift of the Preference Curve does not occur. This would happen, for example, is
C. Comparing Institutions in Autarky and under Trade
In comparing the equilibria resulting under trade and autarky, we face the potential difficulty that the trade equilibrium may not be unique. Thus we must define an equilibrium selection process. We assume that the equilibrium resulting from trade opening is the one to whose basin of attraction the autarky equilibrium fA belongs. To do so, we must define a basin of attraction with respect to f.
The basin of attraction of a stable equilibrium (fT, pT) is denoted B(fT) and is defined as
We now show that there exist parameter values under which the transition from autarky to trade implies a worsening of institutions.
Consider an interior and stable autarky equilibrium (fA, pA). If
The above Proposition shows that if the political power effect is large enough compared to the foreign competition effect, the economy will converge towards an equilibrium with worsening institutions. In order to compare the foreign competition and political power effects, let’s compare the pivotal voter under trade starting from autarky institutions, pT(fA), and the entrepreneur who prefers fA under the trade regime,
It is positive if and only if
The first part of this expression represents the magnitude of the Political Power curve shift. It is positive, because pT(fA) < pA(fA). The second term proxies for the strength of the foreign competition effect. It will be large in absolute value when there is a large difference between pA(fA) and
We present the two cases graphically in Figure 7, starting from the same interior autarky equilibrium. The first panel illustrates a transition to a trade equilibrium in which institutions improve as a result of trade. For this to occur, the shift in the Political Curve must be sufficiently small, and the shift in the Preference Curve sufficiently large. The former would occur, for example, if the function λ(w) was flat enough. The latter would occur if the foreign competition effect is sufficiently pronounced, that is, when nN is large enough relative to nS. The second panel illustrates a case in which institutions deteriorate as a result of trade. If the political power effect is strong enough, or the foreign competition effect is weak enough, institutions will worsen.
Figure 7.Comparing Institutions in Autarky and Trade
What are the conditions under which the two different scenarios are more likely to prevail? The model does not offer an analytical solution with which we could perform comparative statics with pencil and paper, due to both the algebraic complexity of the trade side of the model, and the fact that we cannot find closed-form expressions for the pivotal firm. Nonetheless, we can implement the solution numerically in a fairly straightforward manner. In order to focus especially on the South’s market power and the resulting magnitude of the foreign competition effect, we compare changes in institutions for a grid of parameter values. Starting from an interior autarky equilibrium, we check how it changes in response to trade opening for a grid of LN ‘s and nN ‘s.17
The results are illustrated in Figure 8. It depicts ranges of LS/LN and nS/nN for which institutions improve and deteriorate as a result of opening. The shaded area represents parameter values under which institutions deteriorate. Trade is most likely to lead to a deterioration when the economy is both small in size (LN is large compared to LS), and captures a large share of world trade in the differentiated good (that is, nS is large relative to nN). Under these conditions, there is a large movement in the pivotal voter, while the movement in the Preference Curve is small, or can even be positive—that is, some range of firms may want worse institutions under trade than in autarky in some cases. Intuitively, when there are relatively few producers of the competing good in the North (nN is low), the disciplining effect of opening up to foreign competition will be weak. On the other hand, when the size of the foreign demand is large relative to the home labor force, the incentive to push smaller firms out of the market in order to earn higher profits will be higher. In addition, for those firms that do export, larger size of the foreign export market means higher profits, ceteris paribus, and thus more political power at home. We can also highlight the conditions under which the opposite outcome obtains: the disciplining effect of trade predominates. When the number of domestic firms is small vis-a-vis its trading partner, foreign competition in the domestic market forces even the biggest firms to want to improve institutions in order to increase their profits. Thus, when domestic firms capture a very small share of the world market under trade, the shift in the Preference Curve is large. When this is the case, the economy is likely to retain good institutions or even improve them. This effect is more pronounced when the South is also relatively large—the mirror image of the previous case we analyzed. Figure 9 reports equilibrium trade institutions for the same grid of parameter values. The darkly shaded area represents all cases under which institutions deteriorate as a result of trade, while in the lightly shaded area institutions improve. We can see that the nS/nN dimension matters more than the LS/LN dimension: institutions always worsen more sharply when raising the latter than the former. We can also see that when the South’s market power is sufficiently high, institutions deteriorate quite sharply.
Figure 8.Ranges of Parameter Values Such that Institutions Deteriorate Under Trade Figure 9.Institutions Under Trade As a Function of Parameter Values
What evidence can we provide in support of the claims made in the model? As we saw, trade opening has an ambiguous effect on institutional quality, but can result in a deterioration under some circumstances. Since episodes of institutional change are relatively rare, and systematic data on economic institutions are available for only the last 20-30 years at best, regression analysis is not a promising way to illustrate our model. Nonetheless, trade opening episodes that took place farther back in time shaped institutions for decades if not centuries to follow, and thus remain relevant. Thus, we will proceed by illustrating our model with a number of case studies, fully acknowledging the usual caveats that come with that approach.
We show that the effects illustrated in our model were at work during the sugar boom in the Caribbean starting in the mid-18th century, coffee boom in Central and South America in the 19th, and the cotton and cattle booms in Central America in mid-20th century. These are cases of abrupt trade opening—as evidenced by sharp increases in volumes—that were due to conditions largely outside of the exporters’ control. In all three, export markets were quite large relative to country size, and the affected countries enjoyed large market shares in their exports—conditions for institutional deterioration identified by the model. We then illustrate the Melitz effect: sharp changes in the production structure in favor of a smaller number of larger producers. We argue that these changes in production structure led to the political power effect described in our model. Finally we show that the large producers used their power to bring about a deterioration in institutions.
In connection to the last point, it may be worth highlighting an important caveat. While we would argue that our model describes the Melitz and the political power effects in these cases quite precisely, the parameter that captures institutional quality is reduced-form in our model. Though we formalize institutions as a fixed cost of production that acts to deter entry, clearly economic institutions are much more sophisticated objects than that. Thus, we would like to caution against interpreting our institutional quality parameter too literally when going to the case studies. That is, when we describe deteriorations in institutional quality, we necessarily interpret institutions more broadly than fixed entry costs. What we observe in our case studies are land expropriations, general deteriorations in property rights, and legal systems partial to those in power. We do find clear evidence, however, that deteriorations in institutions we describe were intended by their designers to increase the effective entry barriers that small producers face, in order to lower competition and raise profits for the largest producers.
A. Sugar in the Caribbean, 1650–1850
Beginning with Barbados in the 1650’s, a sugar boom swept most of the Caribbean islands over a period of 200 years. Pre-sugar Caribbean islands were typically smallholder peasant societies, farming foodstuffs and perhaps tobacco for export. Some were sparsely populated, though others were quite successful. For instance, European settlement in Barbados started in 1641, and by 1655 it had 10,000 British settlers, resulting in a population density higher than most regions in England (Rogozinski, 1999, p. 71). By then, all of the island’s arable land had been distributed to farmers.
When sugar was introduced to the islands, the transformation was typically quite rapid. In the most extreme cases, land use was given over almost entirely to sugar, so much so that many islands had to import food. Land ownership consolidation was swift as well, with islands going from smallholder patterns of land use to giant plantations. For instance, in 1750’s Barbados, 74 families owned 305 out of 536 estates. On Nevis, the number of plantations went from over 100 to around 30 a century later. The dominance of sugar in the Caribbean economies was mirrored in the region’s position as the primary exporter of sugar in the world. The Caribbean produced between 80 and 90 percent of sugar consumed by Western Europeans in the 18th century (Rogozinski, 1999, p. 107). It was also clear that power was derived from being a planter, and that economic power—the size of plantation and the resulting profits—was key to political power. For instance, Stinchcombe (1995) notes that “[plantation] size measures the main causal complex that produced and maintained slave societies, societies in which the main public good was reliable repression of all rights of slaves, and constraints on the rest of the society deemed necessary to the security of the slave regime.” (p. 89).
The final piece of the argument concerns the way in which planters, once in power, changed institutions. Clearly, the most significant consequence of planter power was the slavery that was prevalent in the sugar-boom Caribbean. At the height of the sugar era, almost 9 out of 10 inhabinants of the Caribbean were slaves, a proportion of slave-to-free never before recorded in human history. The Caribbean slavery system was by all accounts the most extreme form practiced at the time. However, and more relevant to our model, planters also went to great lengths to curtail the property rights of the free members of society, such as farmers. In plantation economies, all of the land suitable for sugar cultivation was used for sugar. But even for unsuitable lands, the government policy was to explicitly discourage cultivation. Stinchcombe (1995) notes that “[t]hroughout most of the colonial period on most of the sugar islands, the formal government policy was to prevent peasant cultivation in the highlands, since that provided a peasant alternative to plantation labor for freedmen” (p. 104). This was apparently done at least in part through deliberately insecure property rights: “[m]any of the tenures on which small holdings have been held in the Caribbean have been legally precarious” (p. 93). The more planters were in control, the more precarious were peasant tenures, since secure tenures raised the “reservation wage” of free peasants in the free labor market, and provided a comparison point for slaves before emancipation. After emancipation, the governments of the islands attempted to keep the wages low and reduce earnings opportunities outside the plantations by restricting access to crown lands by either prospective planters or by peasants. (Stinchcombe, 1995, ch. 10). Thus, in the Caribbean we can see the essential outlines of our story. The export boom brought power to large exporters; those exporters used that power to reduce competition, in this case in the factor markets.
B. Coffee in Latin America 1850–1920
Coffee production started in the New World during the eighteenth century, and trade in coffee soared from 320 metric tons in 1770 to 90,000 in 1870 and 1.6 million in 1920. This increase is often attributed to rising demand, which was partly a result of aggressive marketing campaigns. Coffee consumption in the U.S. grew from 3 pounds per person in 1830 to 16 pounds per person in 1960. This explosion of coffee consumption in the U.S. and Europe was associated with a transformation of the economic, social and political landscape in coffee producing countries, especially in Latin America. As noted by Roseberry et al. (1995), “coffee is both a product of ‘free trade’ ideology and practice and the first ‘drug food’ not controlled by colonial or imperial trading blocs. For those newly independent countries from southern Mexico to southern Brazil with exploitable subtropical soils, coffee served as a principal point of linkage to an expanding world economy, the means by which they could turn toward an ‘outwardly focused’ model of development” (p. 10). Thus, we have reasons to believe that the environment described in our model fits well the conditions of coffee economies: trade as the driving factor behind economic, social, and political change, and a multitude of independent actors that nonetheless does not result in perfect competition. While there are important differences between the Latin American countries that turned to coffee production during the second half of the nineteenth century, they share some significant common patterns to which we now turn.
Increased profitability from coffee production induced prices of inputs to rise, leading to a sharp increase in land prices. Pico (1995) reports that in Roncador, one of Puerto Rico’s highland regions, the average price of land rose from 3.41 pesos per cuerda in 1863 to 28.14 in 187718 (Table 4.3, p. 106). Consistent with the implications of our theory, increased land prices came with land ownership concentration: “coffee expansion in the Cordillera Central of Puerto Rico, while it was still a Spanish colony, entailed the progressive concentration of land ownership to the detriment of small farms in a process that was dominated by and consolidated the hold of immigrant merchants. (…) Whereas in the 1850’s about half of the population had access to land, by the 1870’s, this proportion had declined to 17 percent. Thus, although smallholders predominated numerically, most coffee was produced on large estates” (Stolcke, 1995, p. 73). As expected, concentration of economic power came hand in hand with concentration of political power, itself used to perpetuate economic dominance. Analyzing the experience of other coffee economies, Roseberry et al. (1995) note in the introduction to their book: “[g]iven the importance of the coffee sector within Costa Rica, the processors were able to establish themselves as an economic and political elite (…)” (p. 23). The political power effect was also observed in Brazil: “Here we could with reason point to the ‘oligarch pacts’ that emerged in the late nineteenth century, the way in which state policies and practices responded to or ‘expressed’ the needs of the planters and merchants, and the coffee planters who held positions of state power in the various republics. (…) as Holloway notes, ‘the economic dominance of coffee was unquestionable. Among the property-owning sectors of society the right of the planters to control the political system was unquestioned, and the mass of working people, slaves, freedmen, native Brazilian peasants, and immigrants, had no political voice. The government of Sao Paulo was itself the instrument of the coffee planters’” (Roseberry et al., 1995, p. 25).
Analyses of social transformation in Latin America and its economic and political origins have largely focused on labor-related conflicts. As the explosion of coffee exports pushed up wages, attempts to secure a source of cheap labor has always been a concern for coffee producers. Direct conflicts between landowners and workers in coffee economies have received a great deal of attention from historians and economists alike (see, e.g., De Janvry, 1981).19 Nonetheless, other means were also used to secure the supply of cheap labor. In particular, another strategy for keeping labor costs down was to reduce competition from other potential sources of employment, which corresponds to the mechanism we describe in our model. This was done, for example, by raising “barriers to entry in the form of a tax in 1903 on new planting” (Greenhill, 1995, p. 192), or through restricting access to land, as emphasized by Rosewell et al. (1995): “[t]his is not to say that landholders were powerless and a free market prevailed: the monopolization of land in some regions was the most effective means for securing a labor force” (p. 8). Examples of land expropriation abound. “In Guatemala and El Salvador, (…) the state played a decisive role in creating the conditions for the development of a coffee economy based on large estates. Under the liberal reforms in Guatemala in the 1870’s extensive church lands were confiscated and sold or distributed. In addition, a form of land rent in perpetuity was abolished, with renters being forced to purchase the land” (Stolcke, 1995, p. 74). The implication is then immediate: “In El Salvador, the massive and radical expropriation of the indigenous population and their displacement created a dispossessed population available for seasonal work on the coffee estates” (Stolcke, 1995, p. 75). This case thus provides a good illustration of the central point of the paper: property rights (of the indigenous population in this precise example) were revoked, thus freeing labor for large coffee growers.
C. Cotton and Beef in Central America, 1950-1980
Cotton production in Central America was minimal until 1950, and exports outside the region were virtually nil. The combination of a rise in foreign demand following the end of World War II and improvements in technology produced growth in the cotton sector that was nothing short of spectacular. The most important technological advance was the invention of insecticide DDT. Large scale attempts to grow cotton in Central America had failed in the past because there had been no effective means to combat insects in the area. That changed dramatically once DDT was invented in 1939.
During the 1940’s, all of Central America produced only about 25,000 bales a year, most of it for textile mills within the region. Central American production exceeded 100,000 bales in 1952, 300,000 in 1955, and 600,000 in 1962. At that time, the region ranked 10th in the world in cotton production. By mid-1960’s, production rose to more than 1 million bales, and by the late 1970’s, Central America as a whole ranked third in the world in cotton production, below only the United States and Egypt. A key feature of this growth is that while at the beginning of the period virtually all of the cotton production was consumed within the region, from 1955 onwards 90% of it was exported outside Central America.
The cotton industry was characterized by significant dispersion in firm size, a prominent feature of our theory. The average size of a cotton plot over this period was 100 acres. Across the different Central American countries, between 25 and 60% of all growers planted an average of 5 acres of cotton. The overwhelming majority of land under cotton cultivation belonged to large producers. For example, in Guatemala, farms with fewer than 122 acres made up less than 2% of cotton-growing lands, while farms larger than 1100 acres produced 62% of the cotton. The picture is quite similar in other countries. These figures, however, do not reveal the full extent of concentration, because often the same family controlled multiple estates. Available evidence indicates that the large cotton growers were none other than the established landholding aristocracies in these countries. All in all, these were a few dozen families.
The cotton boom of such proportions naturally involved significant growth of the land area under cotton cultivation. While some of it came from deforestation, another major source of new cotton lands was through eviction of small farmers. This process came in two varieties. First, peasants were expelled from lands which were clearly titled to the landlord. This kind of eviction was usually regarded as benign, and did not produce much overt social conflict.
Second, landlords and other prospective cotton growers used their political power to get titles to the lands previously owned by the national government and municipalities. According to Williams (1986), “[u]ntitled lands lying near proposed roadways were quickly titled and brought under the control of cotton growers or others with privileged access to the land-titling institutions in the capital city.” (p. 56). Once the land was titled in this manner, peasants cultivating this land were promptly evicted. Some lands were owned by a municipality and cultivated by the peasants for a nominal fee. This was called the “ejidal” system, and represented something akin to communal ownership of land by peasants. Since in this case, the legal status of the lands was more clear than when the lands were untitled, more effort was required to expropriate them. Nevertheless, “[w]here ejidal forms came in the path of the cottonfields, the rights were transferred from municipalities to private landlords through all sorts of trickery and manipulation.” (Williams, 1986, p. 56).
The takeoff in the beef production and exports followed a path similar to cotton, albeit a few years later. As of the 1950’s, the Central American beef industry was still in a primitive state, with virtually no export activity. A combination of factors, once again largely outside Central American control, were behind the beef boom. First, the growth of the fast food industry in the United States increased demand for the cheaper, grass-fed beef normally produced in Central America. Second, the United States put in place the so called aftosa quarantine, in order to prevent hoof and mouth disease from entering North America. As it happens, the entire South American continent between the Panama Canal and Tierra del Fuego is subject to the quarantine, but Central America is not. Third, Central America was given preferential access to the highly protected U.S. market for geopolitical reasons. There were substantial rents to be had from access to the U.S. market, as the price of beef in the U.S. was more than double of world prices.
As a result of these developments, exports of beef soared. The first cow was exported in 1957. In 1960, exports totaled 30 million pounds of boneless beef, in 1973, 180 million pounds, and in 1978, 250 million pounds. In this period, the size of the Central American herd grew 250%. More than 90% of Central American beef exports went to the highly protected U.S. market.
As is the case with cotton, some the biggest beneficiaries of the cattle boom were the established landholding families, who expanded their cattle operations. On the other hand, smaller ranchers lost livestock in this period. Before the boom, smaller owners held 25% of the cattle. After the boom, the number of cattle held by small owners decreased by 20% in absolute terms, and accounted for less than 13% of the total. Thus, the Melitz effect, according to which the smallest producers don’t survive after trade opening, seems to have taken place here.
The path of cattle ranching expansion was similar to that of cotton. Forests were cleared, and peasants were evicted from lands that legally belonged to the would-be cattle ranching operations. Then, the boom extended into areas that were owned by the national government or the municipality (ejidal lands). Expulsion of peasants was often done through violent means, and led to unrest. The large numbers of dispossessed peasants were one of the factors behind the wave of guerrilla wars and instability that swept through the region in the 1980’s.
In summary, the remarkable growth in export opportunities in the cotton and beef industries both increased the political power of the largest producers, and provided them with a strong incentive to push smaller producers out. The result was a deterioration of institutional quality, evidenced by a wave of land expropriations, consistent with the effect we are illustrating in our model.
What can we say about how trade opening changes a country’s institutional quality? Country experiences with trade opening are quite diverse. In some cases, opening led to a diversified economy in which no firm had the power to subvert institutions, whereas in others trade led to the emergence of a small elite of producers captured all of the political influence and installed the kinds of institutions that maximized their profits. In this paper, we model the determination of equilibrium institutions in an environment of heterogeneous producers whose preferences over institutional quality differ. When it comes to the consequences of trade opening, we can separate two effects. First, trade will change each agent’s preferences over what is the optimal level of institutions. In most cases, though not always, each firm will prefer better institutions under trade than in autarky. This is the well-known disciplining effect of trade.
The second effect, which is central to this paper, is that trade opening shifts political power toward larger firms. This is because profits are now more unequally distributed across firms, and thus economic and political power is more concentrated in the hands of a few large firms. This can have an adverse effect on institutional quality, because in our model large firms want institutions to be worse.
Which effect prevails depends on the parameter values. A large country that has a small share of world trade in the rent-bearing good will most likely see its institutions improve as a result of trade. On the other hand, a small country that captures a large part of the world market will likely experience a deterioration in institutional quality. Thus, our model is flexible enough to reflect a wide range of country experiences with liberalization, while revealing the kinds of conditions under which different outcomes are most likely to prevail.
Proofs of Propositions
1. The Pareto Distribution and the Closed-Form Solutions to the autarky and Trade Equilibria
The cumulative distribution function of a Pareto(b, k) random variable is given by
The parameter b > 0 is the minimum value that this random variable can take, while k regulates dispersion. (Casella and Berger, 1990, p 628). In this paper we assume that 1/a, which is labor productivity, has the Pareto distribution. It is straightforward to show that marginal cost, a, has the following cumulative distribution function:
for 0 < a < 1/b. It is also useful to define the following integral:
Using the functional form for G(a), we can calculate V(a) to be:
where we impose the regularity condition that k > ε −1. When this condition is not satisfied, the total profits in this economy are infinite. Armed with this functional form assumption, we can characterize the goods market equilibria in autarky and trade.
A. Autarky Closed-Form Solution
and the aggregate price is proportional to:
B. Trade Closed-Form Solution
Equations (11)-(14) determine the equilibrium values of
while the aggregate price is proportional to:
where A, B, C, D, and F are positive constants. It is clear from these expressions that
2. Regularity Conditions on the Admissible Functions
For some marginal entrepreneur
That is, wealth is everywhere weakly increasing in firm productivity, and strictly increasing below a certain well-defined marginal cost cutoff ar.21 We further assume that: wr(a, f) is twice piecewise continuously differentiable with respect to f; uniformly continuous with respect to a; and
Conditions (A.8) and (A.9) guarantee that the second-order conditions hold, and more productive entrepreneurs are less affected by higher levels of entry barriers. Inequalities (A.10) guarantee existence of an equilibrium.
We also impose some technical regularity assumptions regarding the asymptotic behavior of the wealth function: there exists a constant γ > 0, and two continuously differentiable functions γ1(f), γ2(f) > 0 and
This regularity condition implies that the wealth function can be approximated by a parabolic branch in the neighborhood of 0.22
3. From Autarky to Trade
The mechanisms at work in our paper rely on the impact of trade on the distribution of wealth. Two effects are driving our results: (1) The most productive entrepreneur (a → 0) is wealthier under the trade regime than he is in autarky, and (2) domestic producers experience a drop in profits as a consequence of trade (this is the effect analyzed at length by Melitz, 2003).23
Condition (1) corresponds to:
Condition (2) is satisfied when for any f ∈[fL, fH]:
Let’s also recall two assumptions that have been made to make the model interesting. The first one is the condition that the lowest-productivity entrepreneur does not produce in autarky, which requires that:
Condition (A.14) is also sufficient for the trade case when (A.13) holds: as producers experience a drop in profits after trade opening, the lowest-productivity entrepreneur will be even less willing to produce under trade than in autarky.
Finally, the second condition ensures that the pivotal voter is uniquely defined by its marginal cost a. A necessary and sufficient condition for this to be the case is that the pivotal voter produces, or
which is sufficient in autarky as (A.13) holds.
4. Real Profit Functions
We adopt throughout the paper the convention that wealth is defined by (16) and (17) in autarky and under trade respectively. In this subsection, we determine sufficient conditions for real profits to verify conditions (A.6) to (A.11).
A. Autarky: The Preference curve is downward sloping as long as:
To see this, we can simply write out the expression for real profits for each entrepreneur, and check the conditions directly. Equations (3), (5), and (A.3), and the expression for the price level (A.4) imply that each firm’s profits can be written as:
B. Trade: Under trade, we can write the expressions for profits,
for a non-exporting firm, and
for an exporting firm.
(ii) condition (A.8): We first note that nominal profits from domestic production and exports are concave in f. Second, we note that in order to ensure concavity of the real profits, we must compare relative concavity of nominal profits and aggregate price with respect to f. Examining the expression for the price level, (A.5), we can see that because it ihas exponent
(iii) For the condition (A.9), the argument is very similar. First, we verify that (A.9) holds unambiguously for the nominal profits only. Then, we make the argument that the responsiveness of PS (f) to f can be made arbitrarily small as one decreases
A detailed treatment of the compatibility of the requirements (concavity of real profit functions, conditions (A.12) to (A.15)) is computationally involved, and does not present much interest here. We can intuitively see that we have enough degrees of freedom concerning parameter values for all the restrictions to hold simultaneously. A comprehensive derivation of sufficient conditions for propositions and corollaries to hold is available upon request.
Consider the pivotal voter wp (0, λ1) defined by
And w < wp (λ0, λ1) if and only if
This implies that
As wp (λ0, λ1) ≥ wm, we thus have
and given the definition of the median voter:
The right-hand side of (A.17) converges to zero as λ0 grows large, so that
The first-order conditions imply that such value f is characterized by
The Preference Curve is constant over
See discussion and derivation of conditions on parameter values in section A. 4 above.
To prove the first part, note that as wr(a, f) is nondecreasing, the left-hand side of (19) is increasing and continuous in p, thus there exists a unique pr(f) that satisfies (19). We now need to verify that pr(f) corresponds to the pivotal voter with wealth wp as defined in (15):
First, by definition of F(.) we have
is well-defined as wr(a, f) is piecewise continuously differentiable, which implies that pr(f) is continuously differentiable with respect to f.
To prove the second part, we first state the following Lemma:
If pr(f|λ0, λ) is the marginal cost of production of the pivotal voter that prevails when entry barriers are equal to f and political weights are given by
- pr(f|λ0, λ1) is decreasing in λ1 and increasing in λ0.
- pr(f |λ0, λ1) ≥pm for any λ0 > 0, λ1 ≥ 0 and f ∈[ fL, fH]
for any λ0 > 0, λ1 ≥ 0 and f ∈ [ fL, fH]
Furthermore, if w (a, f) satisfies (A.11), then in order to ensure that the integral for the total number of votes does not diverge,
The first three points are immediate consequences of Lemma 1, and given that there is a one-to-one decreasing correspondence between wealth levels and marginal costs of production. Finally, the Pareto distribution with parameter k assumption implies that the integral
Returning to the proof, differentiating equation (19) implicitly with respect to f, we obtain the following expression:
The sign of
There are two cases:
, we can rewriteand a sufficient condition for ∆ to be negative is that
, we can rewriteand a sufficient condition for ∆ to be negative:
Let’s now consider
Condition (A.11) implies that
Putting the two inequalities together, a sufficient condition for (A.18) to hold is that
If the political weight function is “convex enough,” then (A.19) eventually holds as more political weight is moved towards lower marginal cost entrepreneurs. To see this, let’s consider
Then, as (A.11) holds, there exists a threshold
There exists an equilibrium. We prove stability by first stating two Lemmas, one that rules out cycling equilibria, and another that shows corner solution equilibria to be stable.
Lemma (no cycling): The functions Φr(.) and Πr(.) are increasing so that for any f ∈[fL, fH] and any
Proof:fr(.) and pr(.) are both decreasing functions, so that Φr(.) and Πr(.) are increasing. The previous lemma shows that there is no cycling possible. The sequences
Lemma (corner solutions): If the political curve intersects the preference curve in either fL or fH, then the resulting equilibrium is stable.
Proof: Let’s consider (fH, pr (fr)) such intersection point. A corner solution is thus characterized by
Coming back to the proof of the main theorem, if there exists a corner-solution equilibrium, the previous lemma showed that such candidate is stable. Otherwise, suppose that such equilibrium is an interior equilibrium. The Lemma above shows that it is not a cycling one. The absence of corner solutions implies that
See discusion on the real profit functions in the section above.
Define the following difference:
- We can rewrite ∆ as:The last term is unambiguously positive. Therefore, the sufficient condition for ∆ > 0 is:
- We can rewrite ∆ as: The last term is unambiguously positive. Therefore, the sufficient condition for ∆ > 0 is:
Let’s now consider
which we can rewrite
The integral on the right hand side is bounded from above. Suppose that
as assumed in (A.12). For each f, consider
The integral on the right hand side is bounded from above. Then, as (A.11) holds, there exists a threshold
Note that for any entry barrier level f, fr[ΠN(pr(f))] = ΦN+1(f), and pr[ΦN (fr(p))] = ΠN+1(p), so that by continuity of fr(.) and pr(.), the two requirements (22) and (23) are redundant. We will thus restrict ourselves to condition (22).
Taking the limit, and defining
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