Industry Equilibrium With Outside Financing and Moral Hazard: Effects of Market Integration

In this paper we study industry equilibrium and the effects of integration under the assumptions that 1) firms must use outside financing and 2) they face a moral hazard problem due to the possibility of taking excessive risks. These are typical features of banking and insurance, for instance. We examine an industry equilibrium where firms choose not to take excessive risks and compare this with the equilibrium in industries that do not have a moral hazard problem. We show that, as markets integrate, competition intensifies and prices fall in both types of industry. In markets with moral hazard there are relatively more exits, a smaller fall in prices and, contrary to the other case, the market value of the industry increases.

Asiasanat: toimialan tasapaino, ulkoinen rahoitus, riskinotto, markkinoiden yhdentyminen  As markets integrate, due to globalization or the creation of regional common markets, conventional wisdom predicts that competition increases and there is a net transfer of wealth from shareholders to consumers due to lower output prices and smaller pro¿ts. We argue, however, that in industries where moral hazard problems in risk-taking are large, such as ¿nancial intermediation or insurance, for instance, competition can not become very intense, as, if it did, the ¿rms would have an incentive to take excessive risks. Because of this, there must be relatively more exit from industries with a moral hazard problem, in case of market integration, than from industries where the moral hazard problems do not play a role. In fact, we argue that, to prevent ¿rms from taking excessive risks, the exit from such industries must be so large that the remaining ¿rms' pro¿ts increase. In the model below, this effect is so great that, H[ DQWH, the shareholders of ¿rms in such industries prefer integrated markets and higher competition. We analyze a model where all entrepreneurs of an industry must borrow a ¿xed amount from the ¿nancial markets to set up their production facilities. We assume that entrants which have successfully obtained credit have access to two possible production technologies: a safe and a risky technology. Because of the convexity in their payoffs due to their limited liability, the entrepreneurs may have an incentive to choose the risky technology even when it is, in expectation, dominated by the safe technology. As in Stiglitz and Weiss (1983), there is credit rationing in the equilibrium where the ¿rms use the safe technology. In our model, this means that only a limited number of ¿rms obtain credit, competition is imperfect and the entrepreneurs' pro¿ts are positive.
As one would expect, there are more ¿rms in the larger markets, and the competition is therefore more intense. Nevertheless, in contrast to a similar model in the absence of a moral hazard problem, or the free entry model of Cournot competition by Novshek (1980), here the ¿rms' pro¿ts are increasing in the market size, despite the increased number of entrepreneurs. The reason for this is that in larger markets the ¿rms, in equilibrium, produce larger quantities and have greater potential gains from taking risks in relation to their costs of production. Therefore, to prevent these ¿rms from taking risks, the equilibrium pro¿ts must also be increasing in the market size.
We then study the industry equilibrium when 6 markets of equal size are integrated into a single market. We show that there is always relatively more exit from markets with a moral hazard problem than from markets where the moral hazard problems play no role. In addition, the drop in the price cost margin is smaller, and, contrary to the latter case, the total market value of the industry increases. These results are important for understanding the trends in corporate merger activity, competition and equity valuation in Europe today.

The basic model
We assume a single period and two types of agents: lenders and potential entrepreneurs. Both types of agents are risk neutral and derive utility from their end of the period wealth. The entrepreneurs are endowed with a production technology, described shortly, but no initial wealth, and the lenders with 8 units of cash. To set up a ¿rm, and produce, an entrepreneur must borrow 8 units of money from the lenders to buy a machine, or, alternatively, to cover his ¿xed costs. There is limited liability, so the payoff to an entrepreneur can not be negative. The loan markets operate competitively and all agents have access to a storage technology that offers zero returns.
We assume that ¿rms' production, sales and pro¿ts are unobservable to the lenders. We assume, however, the existence of a costly monitoring technology that allows a lender to observe a ¿rm's pro¿ts. The cost of using this monitoring technology is that it destroys a fraction q : f of the ¿rm's revenues if used. We assume also that borrowers and lenders can H[ DQWH commit to the use this costly monitoring technology in case the payment from the entrepreneur falls short of the agreed payment. Under these assumptions, the literature on optimal contracts, see, e.g., Townsend (1979) or Gale and Hellwig (1985), implies that the standard debt contract is optimal.
Once in possession of a machine, an entrepreneur has access to two different production technologies: a safe and a risky technology. With the safe technology, the cost of producing^units of output is: whereas with the risky technology it is: where f S Sc f and : f The idea behind the cost structure is this: If the entrepreneur chooses to use low quality inputs, unskilled labor, for instance, the marginal costs are lower. By doing so, however, he increases the risk that something may go wrong, "the machine breaks down", and additional costs of size must be incurred. For simplicity, we assume that is independent of^ A ¿rm can then sell its production in the output market, where the demand for its output,^c is given by: Here R is ¿rm 's price, ? the total number of ¿rms in the industry and R W the average price of 's competitors, k is a positive constant and C a parameter that reÀects the market size. It is easy to verify that, in this set up, the total demand for the industry output is always equal to Ck Prices being equal, each ¿rm has a demand equal to Ck ? . This demand schedule is similar to monopolistic competition: each ¿rm's demand is decreasing in its own price and increasing in the price of its competitors. As in monopolistic competition, the price elasticity of demand is decreasing in the number of producers.
We have now fully described the the model. It should be clear that depending on the cost parameters and there can exist two types of equilibria in this model. First we can have an equilibrium where all ¿rms, that obtain credit, use the safe technology. Second, we can have equilibria where some or all ¿rms in the industry use the risky technology. Throughout this paper, we con¿ne our analysis to the equilibrium where all ¿rms that obtain credit use the safe technology. This equilibrium is the unique equilibrium when is large. We focus on this equilibrium for two reasons: First, we believe that in many industries moral hazard problems are severe enough to restrict entry, the way they do in the equilibrium with the safe technology that we analyze below. Second, the comparative statics of an equilibrium where ¿rms use the risky technology, which prevails when is small, are similar to those of an equilibrium in the absense of a moral hazard problem, i.e., when the risky technology is not available, which we will analyze later.

Equilibrium with moral hazard
We now characterize a market equilibrium in which the incumbent ¿rms use the safe technology, and no additional ¿rm can obtain suf¿cient capital to enter. In the equilibrium that we consider, the lenders lend 8 units of cash, with zero interest rate, to ?EC randomly selected entrepreneurs. The interest rate is zero because the loan markets are competitive, ¿rms use the safe technology and the return on the alternative storage technology is zero. In equilibrium, the lenders and borrowers commit to the use of the costly monitoring technology, that depletes the ¿rm's revenues, whenever the payment by the entrepreneur is below the scheduled payment. The use of this costly monitoring technology guarantees that the lender is paid as scheduled and allows for the maximum number of ¿rms in the market. As said, we assume that the cost parameters, and c are large enough to deter entry by ¿rms using the risky technology. This condition, which we later characterize, also implies that the number of ¿rms is larger in the equilibrium where the ¿rms use the safe technology than in the equilibrium where the ¿rms use the risky technology.

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In addition to the market clearing conditions in the product markets, the following three conditions must hold for an equilibrium in which the entrepreneurs produce with the safe technology: (1) the incumbent ¿rms must make non-negative pro¿ts and (2) they must have an incentive to use the safe technology and (3) no additional lending to new entrants is pro¿table.
Denote by Z E?c C the equilibrium pro¿t, and by^E?c C the equilibrium output of a single ¿rm, when the market size is C and all ? ¿rms in the industry produce with the safe technology. Each ¿rm's maximization problem is: The ¿rst order conditions imply a unique Nash equilibrium in which all ¿rms set an equal price: This implies that each ¿rm produces^units of output and makes a pro¿t equal to Zc where:^' Ck ? and To characterize the three equilibrium conditions, we must also calculate the pro¿ts of a ¿rm which unilaterally and successfully deviates to the risky technology, Z _ E?c Cc Sc 8 c i.e., when the machine does not break down A deviating ¿rm with marginal cost S maximizes his revenues: The ¿rst order condition gives: In case the machine breaks down, and repair costs must be incurred, the pro¿t is For the moment, it is useful to abstract from any integer problems and treat the number of ¿rms, ?, as a continuous variable. In this case, in any equilibrium, it must be the case that Z _ E?c C | c Sc 8 n f Otherwise, some ¿rms producing with the risky technology can enter the markets. We can now state the ¿rst two of the equilibrium conditions, the non-negative pro¿ts and the incentive compatibility constraints, as: ZE?c C fc ZE?c C E Z _ E?c Cc Sc 8 (4) The third equilibrium condition, of no additional entry, is a requirement that either one of these inequalities holds as an equality.
By looking at equation 4, we note that (because Z _ E?c Cc Sc 8 : Z f), equation 3 is never binding in the equilibrium and therefore, equation 4 determines the number of ¿rms in the market. Let ? W denote the number of ¿rms that satisfy the inequality 4 as an equality. We now want to characterize ? W Assuming that 4 holds as an equality, substituting for ZE?c C and Z _ E?c Cc Sc 8 and rearranging, we obtain: This gives us a second order equation for ? W which has the unique solution: Equation 5 shows that both ? W EC and C ? W EC 2 are increasing in C In fact, it is easy to see from equation 5 or 6, that, for a very large Cc ? W EC approaches a constant, ? " . Thus, We can now determine the actual number of ¿rms, in the equilibrium with the safe technology, by taking into account the fact that the number of ¿rms must be an integer. As both inequalities 4 and 3 are relaxed when we decrease the number of ¿rms in the market, the equilibrium number of ¿rms, ?c is simply the smallest integer below ? W , i.e., ? ' ?|E? W Now, there are two equilibrium conditions that we have omitted so far, and which we can now turn to. The ¿rst one is a condition on and that guarantees that the equilibrium with safe technology is robust to the entry from ¿rms producing with the risky technology. For this, it is suf¿cient that When this condition holds, there is no room for any ¿rm producing with the risky technology to enter, even if the lender could persuade the entrant to distribute its entire pro¿ts as interest to the lender. The second issue is a suf¿cient condition for the number of ¿rms to be larger in the equilibrium with the safe technology than in an equilibrium where all ¿rms use the risky technology. This condition is related to the robustness of the above market equilibrium. For this, it is suf¿cient that the expected pro¿ts be negative, when all ¿rms use the risky technology and the number of ¿rms is ? As the pro¿ts are independent of the marginal costs, when all ¿rms have equal marginal costs, this condition can be stated as: This condition is always satis¿ed when 7 holds. Let us assume, throughout this paper, that and are such that 7 holds.

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From the equilibrium conditions, we have the following results for market conduct.
First, note that ? W EC is uniformly increasing in the market size, C Second, note that the output price is declining in the number of producers, ? These two results show that as the market size increases, typically more ¿rms enter the markets, competition increases and prices decline. Given that C*? W2 is strictly increasing in Cc by 5, we also have the result that typically ¿rms' pro¿ts, ZE?c Cc are increasing in Cc despite the new entry into the markets. In the equilibrium above, the incentive to switch to the risky technology is greater in larger markets (because of larger production). Similarly then, the value of behaving prudently, or, in other words, the equilibrium pro¿ts must also be increasing in the market size. In large markets, as ? $ ? " c the pro¿ts become approximately proportional to the market size, C The result that 3 never binds, i.e., that pro¿ts are always positive, is similar to the result in Stiglitz and Weiss (1983). What we have shown also, however, is that in an industry equilibrium where ¿rms' gains from taking risks are proportional to their production, the pro¿ts are larger in larger markets.
Using 5, and the result that ? ? W ECc we can provide a lower bound on the total industry pro¿ts, ?ZE?c C First note that 5 can be written as: Using this we get: which approaches in¿nity as C $ 4 4 Equilibrium without moral hazard For comparison, let us characterize the market equilibrium in the absence of a moral hazard problem, i.e., in case the risky technology is not available to entrepreneurs. In this case, it is the zero pro¿t condition, 3, that determines the number of ¿rms in the industry. Setting the pro¿ts equal to zero would imply that the number of ¿rms is: This need not be an integer. However, the actual number of ¿rms in the absence of a moral hazard problem must be between ? S and ? S Given this, the ¿rms pro¿ts may be positive, but are always less than Z Z ' Ck 2 E? S 2 8 As we shall see shortly, Z $ f as C $ 4 implying that, in contrast to the previous analysis, ¿rms' pro¿ts, Zc approach zero as the market size increases. A related result, which proves the former result, given that ? S $ 4 as C $ 4c is that the total industry pro¿t, ?Zc is bounded by a function that approaches 28c from above, as C increases. Using the result that ? : ? S c we have: So, although a ¿rm's pro¿ts can be positive, in small markets, as the market size increases, each single ¿rm's pro¿ts approach zero and the bound on the total industry pro¿ts approaches 28 . These results are similar in spirit to those in Novshek (1980), who studies Cournot competition under free entry, and should be contrasted with the results of the previous section.

Market integration
Let us now consider what happens to the number of ¿rms, the price cost margins and the total industry pro¿ts if we, totally unexpectedly, merge 6 markets of equal size C (as in the case of the common market in Europe). For the moment, let us abstract from the integer problems and assume that ? ' ? W under moral hazard and that ? ' ? S in the absence of moral hazard. Our previous results show that the number of ¿rms in the integrated markets is then either ? W E6C or ? S E6Cc depending on whether there is a moral hazard problem or not As in both cases, ?E6C is greater than ?ECc the competition is more intense and prices are lower in integrated markets. Nevertheless, in both cases, some ¿rms must exit as markets integrate.
Let us look at the relative exit ratios from markets in these two scenarios. We have shown that the number of ¿rms in the absence of moral hazard is: In the absence of moral hazard, the exit ratio, due to the integration of 6 markets, is then: .%|I By contrast, in markets with moral hazard, given our previous result that C*? W EC 2 is increasing in Cc we have: .%|I ? S E6C 6? S EC : s 6 Also, given that ? $ ? " , the .%|I in markets with moral hazard approaches 6 as C increases. So there is much more exit from industries with a moral hazard problem, than from industries without, when markets integrate.
Given that the price cost margin is proportional to ?c R S ' k ? c these results also imply a smaller proportional drop in the price cost margin in markets with a moral hazard problem, as compared to markets without. Indeed, in markets without a moral hazard problem, the relative drop in the price cost margin is: By contrast, in case of a moral hazard problem, also using the result that C*? W EC 2 is increasing in Cc we have: s 6 c and, given that ? W $ ? " , the drop in the price cost margin goes to zero as C goes to in¿nity. So, as we merge large economies, in case of a moral hazard problem, the market integration will have no effect on the price cost margins, and the number of ¿rms in the new integrated market is equal to the number of ¿rms in each of the single markets.
Last, but not least, let us look at the effect of market integration on total industry pro¿ts. The proof is given in the Appendix. This result is much stronger than our previous result that, under moral hazard, both individual ¿rms' pro¿ts and total industry pro¿ts are greater in larger markets. The above result says that, in case of moral hazard problems, the industry pro¿ts in integrated markets are more than 6 times the pro¿ts in the smaller, unintegrated markets.
Compare this result to the case of competitive markets with no moral hazard, where the individual ¿rms' pro¿ts, and the industry pro¿ts, are always equal to zero. This result is also different from the conventional wisdom in Industrial Organization, which would predict that the individual ¿rms' pro¿ts and the total industry pro¿ts decline, due to increased competition, when 6 markets of equal size are integrated into a common market. The conventional wisdom, which follows from the analysis in Novshek (1980), can be understood by considering our model in the absence of a moral hazard problem, if we require that the number of ¿rms must be an integer. In this case, we showed that as C increases the bound on total industry pro¿ts approaches 28 from above. If we now merge several markets, where the industry pro¿ts are, say, 8 in each market, the total industry pro¿t decreases from 68 to something less than or equal to 28 So the above result, that the industry pro¿t increases in industries with a moral hazard problem, at least when abstracting from the integer problems, when 6 markets integrate, is intrinsically different from the traditional story in Industrial Organization, and from industries without a moral hazard problem.

Conclusion
We have studied the industry structure and the effects of market integration in industries that rely on outside ¿nancing and have a moral hazard problem in taking excessive risks. Our results suggest that, for such industries, the common markets will result in a large shakeout, only slightly declining prices and an increase in the total value of the industry due to cost savings. Examples of industries with severe moral hazard problem in risk-taking are, for instance, Banking, Insurance, Airlines industries and possibly high tech industry, where it is dif¿cult for the investors to be informed of the size of R&D risks that are being taken. It may not be a coincidence that many of these industries currently undergo major consolidation in Europe either through mergers and acquisitions or the creation of strategic alliances (see Figure  1).
One limitation of our model is that, for expositional reasons, we have assumed a demand structure where the total industry demand is always constant. In reality, for most industries, one would expect the total industry demand to be a decreasing function of the average price of the industry. The likely implication of relaxing this simpli¿cation would be a prediction that the total industry output increases as markets integrate, due to higher competition and lower prices, and does so especially within those industries, where the moral hazard problems do not play a role. Indeed, it is easy to construct more complicated models, along the lines of our analysis, where these predictions always hold.