Volker Nocke

Firm Turnover in Imperfectly Competitive Markets

This paper is motivated by the empirical regularity that industries differ greatly in the level of firm turnover and that entry and exit rates are positively correlated across industries. Our objective is to investigate the effect of fixed costs and, in particular, market size on entry and exit rates and hence on the age distribution of firms.We analyse a stochastic dynamic model of a monopolistically competitive industry. Each firms efficiency is assumed to follow a Markov process. We show existence and uniqueness of a stationary equilibrium with simultaneous entry and exit: efficient firms survive, while inefficient ones leave the market and are replaced by new entrants. We perform comparative dynamics with respect to the level of fixed costs: entry costs are negatively related and fixed production costs positively related to entry and exit rates. A central empirical prediction of the model is that the level of firm turnover is increasing in market size. In larger markets, competition is endogenously more intense than in smaller markets, and so price-cost margins are smaller. This price competition effect implies that the marginal surviving firm has to be more efficient than in smaller markets. Hence, in larger markets, the expected lifespan of firms is shorter, and the age distribution of firms is first-order stochastically dominated by that in smaller markets.In the empirical part, the prediction on market size and firm turnover is tested on an industry where firms compete in well-defined geographical markets of different sizes. Using data on hair salons in Sweden, we show that an increase in market size or fixed costs shifts the age distribution of firms towards younger firms, as predicted by the model. Copyright 2006, Wiley-Blackwell.

Globalization and Endogenous Firm Scope

We develop a theory of multiproduct firms to analyze the effects of globalization on the distributions of firm size, scope, and productivity. Our model explains two puzzles. First, it explains the well-known size-discount puzzle: large firms have lower values of Tobin’s Q than small firms. Second, it explains the globalization-skewness puzzle documented in the empirical part of our paper: a multilateral reduction in trade costs leads to a flattening of the size distribution of firms. In our model, globalization not only affects the distribution of observed productivities but also productivity at the firm level.

Dynamic Merger Review

We analyze the optimal dynamic policy of an antitrust authority toward horizontal mergers when merger proposals are endogenous and occur over time. Approving a currently proposed merger may affect the profitability and welfare effects of potential future mergers, whose characteristics may not yet be known. We identify conditions under which discounted expected consumer surplus is maximized by using a completely myopic merger review policy that approves a merger if and only if it does not lower consumer surplus given the current market structure. We also discuss a number of extensions as well as factors that undermine the optimality of myopic merger review policies.

A Gap for Me: Entrepreneurs and Entry

We present a theory of entrepreneurial entry and exit decisions. Knowing their own managerial talent, entrepreneurs decide which market to enter, where markets differ in size. We obtain a striking sorting result: each entrant in a large market is more efficient than any entrepreneur in a smaller market. The result obtains since competition is endogenously more intense in larger markets. The sorting and price competition effects imply that the number of entrants (and hence product variety) may actually be smaller in larger markets. In the stochastic dynamic extension of the model, we show that the churning rate of entrepreneurs is higher in larger markets.

Advance-Purchase Discounts as a Price Discrimination Device

In an intertemporal setting in which individual uncertainty is resolved over time, advance-purchase discounts can serve to price discriminate between consumers with different expected valuations for the same product. Consumers with a high expected valuation purchase the product before learning their actual valuation at the offered advance-purchase discount; consumers with a low expected valuation will wait and purchase the good at the regular price only in the event where their realized valuation is high. We provide a necessary and sufficient condition under which the monopolists optimal intertemporal selling policy features such advance-purchase discounts.

A Theory of Clearance Sales

Clearance sales are widely used by firms as an intertemporal selling policy, in particular in markets where firms face demand uncertainty and need to choose capacity in advance. Clearance sales consist in charging a high price initially but then lowering the price in the sales period. High-valuation consumers purchase the good at the high initial price so as to avoid rationing at the low price, while low-valuation consumers wait for the price to drop. We develop a simple model of intertemporal monopoly pricing under demand uncertainty, and show that clearance sales may be the optimal intertemporal selling policy.

When the Punishment Must Fit the Crime: Remarks on the Failure of Simple Penal Codes in Extensive-Form Games

In repeated normal-form games, simple penal codes (Abreu 1986, 1988) permit an elegant characterization of the set of subgame-perfect outcomes. We show that the logic of simple penal codes fails in repeated extensive-form games. We provide two examples illustrating that a subgame-perfect outcome may be supported only by a profile with the property that the continuation play after a deviation is tailored not only to the identity of the deviator, but also to the nature of the deviation.

Exclusive Dealing and Vertical Integration in Interlocking Relationships

We develop a model of interlocking bilateral relationships between upstream firms (manufacturers) that produce differentiated goods and downstream firms (retailers) that compete imperfectly for consumers. Contract offers and acceptance decisions are private information to the contracting parties. We show that both exclusive dealing and vertical integration between a manufacturer and a retailer lead to vertical foreclosure, to the detriment of consumers and society. Finally, we show that firms have indeed an incentive to sign such contracts or to integrate vertically.

Quasi-Linear Integrability

Applied researchers often work with demand systems that do not depend on income, with the implicit assumption that preferences are quasi-linear and income sufficiently large. The classic approach to the integrability of demand does not readily apply in this case. Adopting a much simpler approach that is based on integrating the vector field defined by the demand system and on duality, we provide necessary and sufficient conditions for the quasi-linear integrability of such (continuous) demand systems. We also derive results on the associated utility function and its domain, and provide an application to the analysis of demand systems in the presence of measurement errors.

Monopoly Pricing Under Demand Uncertainty: Final Sales Versus Introductory Offers

We study rationing as a tool of the monopolist’s selling policy when demand is uncertain. Three selling policies are potentially optimal in our environment: uniform pricing, final sales, and introductory offers. Final sales consist in charging a high price initially, but then lowering the price while committing to a total capacity. Consumers with a high valuation may decide to buy at the high price since the endogenous probability of rationing is higher at the lower price. Introductory offers consist in selling a limited quantity at a low price initially, and then raising price. Those consumers with high valuations who were rationed initially at the lower price may find it optimal to buy the good at the higher price. We show that the optimal selling policy involves either uniform pricing or final sales. Introductory offers may dominate uniform pricing, but can never be optimal if the monopolist can also use final sales.