Lambert Schoonbeek

The specification of the probability functions in Tullock's rent-seeking contest

In his model of a rent-seeking contest, [Tullock, G., 1980. Efficient rent seeking. In: Buchanan, J.M., Tollison, R.D., Tullock, G. (Eds.), Toward a theory of the rent-seeking society. Texas A and M University Press, College Station, pp. 97-112] uses a simple concrete specification for the probability functions which determine the probability that a player wins the contest, given the bids made by the players. We discuss in general terms a set of conditions that can be imposed on probability functions in this game. Next, we show that the specification chosen by Tullock is the unique one that satisfies these conditions

A delegated agent in a winner-takes-all contest

A standard winner-takes-all rent-seeking contest with a principal-agent relationship is extended. One of the two players offers a contract to an agent to act as a delegate on his behalf. The wage offered to the agent is deliberately chosen. The equilibrium of the extended contest is characterized.

The impact of advertising in a duopoly game

We investigate the impact of advertising in a static differentiated duopoly. First, we consider the Nash equilibrium if firms compete with both prices and advertising. Second, we examine the Nash equilibrium if firms only compete in prices and do not advertise. We characterize the circumstances in which the profit, output, and/or price of each firm is greater (or smaller) with advertising than without advertising.

Stability and the structure of continuous-time economic models

Abstract In this paper we investigate the relationship between the stability of macroeconomic, or macroeconometric, continuous-time models and the structure of the matrices appearing in these models. In particular, we concentrate on dominant-diagonal structures. We derive general stability results for models with first-order as well as second-order adjustment lags. Recalling that many existing macroeconometric models are ‘marginally’ unstable, we apply our results to a well-known prototype model, i.e. the model of the United Kingdom of Bergstrom and Wymer. Our analysis explains, in terms of the structure of the matrices involved, why this model is marginally unstable.

Tullock's Rent-Seeking Contest with a Minimum Expenditure Requirement

We consider a rent-seeking contest of the kind introduced by Tullock (1980) in which two players compete for a monopoly rent. We extend the contest by requiring that if a player puts forward an effort, his expenditures must be larger than or equal to some minimum level. We show that, depending on the model parameters, the number of Nash equilibria of the extended model can be zero, one, two or four. Furthermore, it turns out that the extent of rent dissipation in a Nash equilibrium of the extended model can be larger than, equal to, or smaller than the extent of rent dissipation in the unique Nash equilibrium of the original model.

Coefficient values and the dynamic properties of econometric models

Abstract As a tool to simplify an econometric model dynamically, this paper proposes to interpret sums of elasticities of eigenvalues. It is demonstrated that this approach unifies and generalizes some known related procedures.

A dynamic Stackelberg model with production-adjustment costs

We investigate the (dynamic) stability of a stackelberg oligopoly model of a market of a homogeneous good, with output competition, one Stackelberg leader and a number of identical followers. We assume that each firm incurs quadratic production-adjustment costs if it changes its output. We present a simple necessary and sufficient condition for stability of the model. Using the condition, we compare the stability of this model with the stability of two related Cournot models in which all firms present are followers. It turns out that the Stackelberg model is “more stable” than these two Cournot models.

The size of the balanced growth rate in the dynamic Leontief model

The size of the growth rate of a balanced growth solution of the closed dynamic Leontief model is characterized in terms of the properties of the current input coefficient matrix and the capital coefficient matrix associated with the model. Next, the values of balanced growth rates are analysed for which the open dynamic Leontief model is compatible with balanced growth in output as well as final demand.

On the number of non-zero eigenvalues of a dynamic linear econometric model

According toWolters [1976], there are 7 non-zero eigenvalues for each of four alternatively estimated versions of an Econometric Model of the Federal Republic of Germany.In a comment,Uebe [1977] asserts that the number of non-zero eigenvalues of each of these four versions is 11. However, we shall argue on theoretical grounds that there cannot be more than 10 non-zero eigenvalues. Stating the exact number is a delicate matter.

Stackelberg price leadership in the linear heterogeneous duopoly

We consider for the linear heterogeneous duopoly with substitutive goods and with price strategies the situations in which one firm, firm 1 say, prefers to be price leader, whereas firm 2 prefers to be price follower. Conditions that necessarily hold in that case are derived and interpreted in economic terms. These conditions characterize the powerful position of firm 1 relative to firm 2 on the market.