Knowledge that Transforms

Journal Article Defensive Foresight Rather than Minimax: A Comment on Eaton and Lipsey's Model of Spatial Competition Get access Rögnvaldur Hannesson Rögnvaldur Hannesson University of Bergen Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 49, Issue 4, October 1982, Pages 653–657, https://doi.org/10.2307/2297294 Published: 01 October 1982 Article history Received: 01 September 1981 Accepted: 01 May 1982 Published: 01 October 1982

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. ||

The paper considers the properties a decision tree needs to guarantee that there are no preferences such that the sophisticated equilibrium is Pareto dominated when all agents act completely myopically. It shows that the only decision trees with this property are the most trivial problems. The analysis is generalized to agents who are not completely myopic and gives an example of union and shareholder conflict to illustrate the results.

This paper generalizes the model developed in Wilde and Schwartz (1979) to allow downward sloping demand curves and u-shaped average cost curves. It shows that the basic qualitative conclusions of Wilde and Schwartz still hold. Moreover, it shows that the critical proportion of comparison shoppers needed to generate a competitive equilibrium falls as demand becomes more elastic or average costs become more inelastic. Finally, it shows that when imperfect information generates non-competitive outcomes, they are bounded below, in welfare terms, by the monopolistically competitive equilibrium.

Nash equilibria of anonymous and efficient mechanisms are studied in economies with a continuum of traders. Conditions are given under which some or all the Nash equilibria of such mechanisms yield competitive allocations. Particular attention is payed to the case of direct mechanisms where the truth constitutes a Nash equilibrium.

This study explores the meaning, some basic implications, and the reasonableness, of adding a modium of topological structure to social choice functions. Only very elementary topological ideas are used, and no previous knowledge of them is required.

A social choice function is said to be implementable if and only if there exists a game form such that for all preference profiles an equilibrium strategy n-tuple exists and any equilibrium strategy n-tuples of the game yield outcomes in the social choice set. A social choice function is defined to be minimally democratic if and only if whenever there exists an alternative which is ranked first by n − 1 voters and is no lower than second for the last voter, then the social choice must be uniquely that alternative. No constraints are placed on the social choice function for other preference profiles. Using the classical definitions of equilibria for n-person games—namely Nash and strong equilibria, it is shown here that over unrestricted preference domains, as long as there are at least as many alternatives as individuals, no minimally democratic social choice function is implementable. A similar result holds in certain restricted domains of the type assumed by economists over public goods spaces. We then show that a different notion of equilibrium—namely that of sophisticated equilibrium—allows for implementation of democratic social choice functions also having further appealing properties.

In this paper, we first present a competitive macroeconomic model of an open economy which is suitable for estimation and contrast this with a non-competitive model. We then derive unemployment equations from the various models and estimate them over annual data from 1948–1979. We draw the following conclusions. (i) The competitive model of the labour market does not fit the facts. (ii) The non-competitive model generates an equation for the constant inflation rate of unemployment which reveals how, at certain times such as the mid 1970s, a combination of factors conspired to raise this level forcing the government into a deflationary stance to prevent inflation rising drastically. (iii) A number of factors have raised the level of unemployment in a secular fashion since the war, in particular the increase in the variation of relative prices, the increase in the benefit to income ratio, the introduction of employment protection legislation and the rise in the intersectoral shifts of the labour force.

The function of monetary policy to alter the informational content of money price signals is examined in a model where traders can observe an economy wide financial signal and a local commodity price. Under a passive policy, money demand disturbances, which are not directly observable, are shown to be confused with real productivity shocks and thereby preclude prices from fully reflecting all information. Even when the policy authority has no informational advantage, prospective money growth feedback rules can “improve” the structure of available information.

The planned level of output is an important variable in modelling Centrally Planned Economies and the present paper discusses several disequilibrium models in which the plan level is an endogenous variable. A key relationship in such a model is the plan-adjustment equation which is the counterpart of the usual price-adjustment equation employed in models of free economies. Seemingly minor differences in assumptions lead to markedly different econometric models. The coherency properties of these are studied and several likelihood functions are derived. The most complex of the models includes both endogenous plan levels and endogenous prices.