In Hart (1979), a model of monopolistic competition in a large economy with differentiated commodities was developed. In this model, firms had a choice whether to set up or not. One feature of the model was that free entry of firms was not assumed. Barriers to entry were captured by assuming that there was a large (generally, infinite) set of potential firms F. Corresponding to each f ∊ F, there was a firm (called “firm f”) with a production set Y(f). Each firm had a set-up cost associated with it. Only very weak conditions were placed on the set F and the production set mapping Y(·), so that in particular the case where different firms could produce a commodity on different terms was allowed for. The economy was made large by replicating the consumer sector, keeping the production sector, i.e. the set of potential firms F, fixed. The number of operating firms in equilibrium generally increased, however, since in view of the set-up costs there was “room” for more firms in a large economy. Unfortunately, it turns out that this procedure, while correct, does not capture quite what was intended. In particular, while in the resulting monopolistically competitive equlibrium, some firms will earn supernormal profits, it can be shown that, for any η > 0, the per capita number of firms earning profits in excess of η tends to zero as the size of the consumer sector tends to infinity (see Corollary 6 in the Appendix to Hart (1979)). In other words, in per capita terms, almost all firms earn approximately zero profits in a large economy. Thus while barriers to entry may be significant in absolute terms, in per capita terms they are negligible. The way round this difficulty is to drop the assumption that the set of potential firms is fixed. Instead substitute the assumption that the set of potential firms in the economy rE, where the consumer sector is replicated r times, is given by where F is as before. That is, one replicates the set of potential firms at the same time as the consumer sector. Then the theorems of Hart (1979) continue to hold. Corollary 6 in the Appendix must be modified as follows. Corollary 6′. There exists h > 0 such thatfor all f ∊ F. Corollary 6′ is proved below. Otherwise the proofs of Theorem 1 and Proposition 2 are unchanged (one no longer sets h = 1 after Corollary 6). As an example, F might consist of one firm with an efficient technology for producing some commodity and one firm with an inefficient technology. Then in the economy rE, there will be r potential firms with the efficient technology and r potential firms with the inefficient technology. It is easy to construct cases where both types of firms operate in the monopolistically competitive equilibrium in rE and the efficient firms earn supernormal profits which are bounded away from zero as r → ∞. Thus barriers to entry which are significant in per capita terms are now allowed for. A justification for replicating F along with the consumer sector can be given. In the above example, the efficient firms may owe their superior technology to the fact that they are situated on good land, say, of which there is a scarcity (thus the supernormal profits are just rents on the land). When one replicates the economy, it is natural to replicate the scarce land and hence the number of firms which are situated on it, so as to keep everything constant except for scale. Note finally that it may be possible to generalize the analysis to the case where the set of potential firms in the economy rE is given by rF, where 1F, 2F are exogenously specified sets and rF is not necessarily the r-fold union of some set F. We have not investigated this, however. Proof of Corollary 6′. Suppose not. Then for each h > 0, we can find f ∊ F with . By Lemma 5 (2), rπf > h for all r ≧ some r*. But in rE there are r firms identical to firm f and so each of these firms makes profit in excess of h in the monopolistically competitive equilibrium when r ≧ r*. Hence total per capita profits of all firms exceed h in equilibrium when r ≧ r*. It follows that, letting h → ∞, we can find a subsequence of the economies rE such that total per capita profits tend to infinity along the subsequence. However, applying Corollary 4 and an argument similar to that in (A.30)–(A.32), we see that ʃArp(a)drY1(a) is bounded. Hence so are per capita profits, ʃArp(a)drY1(a) + rY0. Contradiction. ||

Journal Article Monopolistic Competition in a Large Economy with Differentiated Commodities Get access Oliver D. Hart Oliver D. Hart Churchill College, Cambridge Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 46, Issue 1, January 1979, Pages 1–30, https://doi.org/10.2307/2297169 Published: 01 January 1979 Article history Received: 01 February 1977 Accepted: 01 December 1977 Published: 01 January 1979

Consider an investor who has a certain amount of wealth to invest in a riskless security and several risky securities. The investor's optimal portfolio will depend on his attitudes towards risk, his wealth and the probability distribution of the security returns. An interesting question to ask is how the investor's optimal portfolio is affected by changes in his wealth, given that all other things remain constant. For example, does the total amount invested in risky securities increase as wealth increases? Does the proportion of wealth invested in risky securities decrease as wealth increases? Questions such as these have been investigated by Arrow [1, Chapter 3] in the case of one riskless security and one risky security. Arrow showed that if the investor's von Neumann-Morgenstern utility function exhibits decreasing absolute risk aversion and increasing relative risk aversion, the amount invested in the risky security is an increasing function of wealth and the proportion of wealth invested in the risky security is a decreasing function of wealth. More recently, Cass and Stiglitz [3] have shown that Arrow's results do not generalize to the case of many risky securities. They give an example where an investor who can purchase one riskless security and two risky securities invests a greater proportion of his wealth in the two risky securities when his wealth increases, even though his utility function exhibits increasing relative risk aversion. Cass and Stiglitz note, however, that Arrow's results do generalize for an important, if highly restrictive, class of utility functions-those for which the mix of risky securities in the investor's optimal portfolio is independent of the investor's wealth for all probability distributions of security returns. Such utility functions are said to possess the separation property. The purpose of this paper is to prove that the separation property is a necessary condition as well as a sufficient condition for the generalization of Arrow's results to the case of many risky securities. We will show that given more than one risky security and a utility function which does not possess the separation property, it is always possible to pick probability distributions for the returns of the risky securities so that the directions of change which Arrow established for the single risky security case are reversed; that is, for some probability distributions of security returns, the total amount invested in risky securities decreases as wealth increases, and for other probability distributions of security returns, the proportion of wealth invested in risky securities increases as wealth increases. In fact, we will show that there always exist probability distributions of security returns such that the amount (proportion of wealth) invested in every risky security decreases (increases) as wealth increases. It should be emphasized, moreover, that this is the case

Oliver Hart delivered his Prize Lecture on 8 December 2016 at the Aula Magna, Stockholm University.

I. Introduction, 579—II. The model, 581.—III. The linear case, 586.—IV. Proofs, 593—V. Conclusion, 596.

In an economy with complete markets, the owners of a firm will unanimously desire the firm to maximize profits if it is a perfect competitor. We generalize this result to an economy with incomplete markets. We show that if competitive conditions prevail-that is, if each firm is negligible relative to the aggregate economy-a firm's shareholders will want the firm to maximize the (net) market value of its shares. This result holds whether or not the so-called spanning condition is satisfied. However, while there may be agreement about what goal the firm should pursue, there may be disagreement among shareholders about how best to pursue this goal.

Our theory of costly contracts emphasizes the contractual rights can by of two types: specific rights and residual rights. When it is costly to list all specific rights over assets in the contract, it may be optimal to let one party purchase all residual rights. Ownership is the purchase of these residual rights. When residual rights are purchased by one party, they are lost by a second party, and this inevitably creates distortions. Firm 1 purchases firm 2 when firm 1's control increases the productivity of its management more than the loss of control decreases the productivity of firm 2's management.

It is sometimes asserted that rational speculative activity must result in more stable prices because speculators buy when prices are low and sell when they are high. This is incorrect. Speculators buy when the chances of price appreciation are high, selling when the chances are low. Speculative activity in an economy in which all agents are rational, have identical priors, and have access to identical information may destabilize prices, under any reasonable definition of destabilization. It takes extremely strong conditions to ensure that speculative activity (of the commodity storage variety) "stabilizes" price, even in a very weak sense.

In the last few years, a new area has emerged in economic theory, which goes under the heading of 'incomplete contracting'. However, almost since its inception, the theory has been under attack for its lack of rigorous foundations. In this paper we evaluate some of the criticisms that have been made of the theory, in particular, those in Maskin and Tirole (1998a). In doing so, we develop a model that provides a rigorous foundation for the idea that contracts are incomplete.