SOME DISCUSSION has arisen recently as to whether the imposition of an entrance fee on arriving customers who wish to be serviced by a station and hence join a waiting line is a rational measure. Not much of this discussion has appeared in print; indeed this author is aware of only three short communications, representing an exchange of arguments between Leeman [1, 2] and Saaty [3]. The ideas advanced there were of qualitative character and no attempt was made to quantify the arguments. The problem under consideration is obviously analogous to one that arises in connection with the control of vehicular traffic congestion on a road network. It has been argued2 by traffic economists that the individual car driver on making an optimal routing choice for himself-does not optimize the system at large. The purpose of this communication is to demonstrate that, indeed, analogous conclusions can be drawn for queueing models if two basic conditions are satisfied:

In this paper, a 14-equation model of the United States potato industry is presented. Four of the equations contain endogenous variables lagged one time period. The solution to this system of first-order difference equations is presented to determine the system's stability. The stochastic stability is then investigated by obtaining estimates of the limiting variance-covariance matrix of endogenous variables. This matrix shows the cumulated effect of historical random shocks. This is followed by a similar study of the effect of erratic variation in exogenous variables. Next is a comparative static analysis, comparing actual values of variables with their stationary state values. The impact of the price support program on the industry is analyzed. Impact and stationary state multipliers are computed and short and long run effects of structural changes are evaluated. RELATIVELY LARGE fluctuations of prices and quantities have characterized the United States potato industry during the last three decades. These fluctuations have had a profound effect on growers' income, regional allocation of production, and the economic efficiency of the industry in general.2 The quantitative analysis of the stability properties of the United States potato industry and its stationary states under changing environmental conditions constitute the main objectives of the present study. In addition, the analysis is so designed as to focus on certain questions pertaining to the particular position maintained by California potato growers in the United States market. The method of analysis consists in formulating an econometric model of the United States potato market. Then, having estimated the parameters of the economic structure, a detailed analysis of the static and dynamic properties of the system is undertaken. The comparative static analysis seeks to evaluate equilibrium values of the endogenous variables both in the short and in the long run and to determine quantitatively the effects of conceivable variation in exogenous variables and certain parameters of the structural relations on these values.

Since network data commonly consists of observations from a single large network, researchers often partition the network into clusters in order to apply cluster‐robust inference methods. Existing such methods require clusters to be asymptotically independent. Under mild conditions, we prove that, for this requirement to hold for network‐dependent data, it is necessary and sufficient that clusters have low conductance, the ratio of edge boundary size to volume. This yields a simple measure of cluster quality. We find in simulations that when clusters have low conductance, cluster‐robust methods control size better than HAC estimators. However, for important classes of networks lacking low‐conductance clusters, the former can exhibit substantial size distortion. To determine the number of low‐conductance clusters and construct them, we draw on results in spectral graph theory that connect conductance to the spectrum of the graph Laplacian. Based on these results, we propose to use the spectrum to determine the number of low‐conductance clusters and spectral clustering to construct them.

Han’s maximum rank correlation (MRC) estimator is shown to be√ n-consistent and asymptotically normal. The proof rests on a general method for determining the asymptotic distribution of a maximization estimator, a simple U-statistic decomposition, and a uniform bound for degenerate U-processes. A consistent estimator of the asymptotic covari-ance matrix is provided, along with a result giving the explicit form of this matrix for any model within the scope of the MRC estimator. The latter result is applied to the binary choice model, and it is found that the MRC estimator does not achieve the semiparametric efficiency bound.

A structural consumption model incorporating endogenous liquidity constraints is fit to a cross section of 798 U.S. families. Liquidity constrained families are estimated to constitute 19.4 percent of the population sampled, a group that accounts for 16.7 percent of consumption in the population sampled. In-sample simulations of the model suggest that a temporary tax has three to four times more impact on aggregate consumption than it would if liquidity constraints were not in effect.

[This paper considers a repeated principal agent relationship where the principal is risk neutral, the agent is risk averse, the principal can borrow or save at a fixed interest rate, and the agent discounts future consumption. It is shown that memory plays a very strong role in every Pareto-optimal contract. Sufficient conditions for Pareto-optimal contracts to exhibit rising or falling wages are identified. Finally, it is shown that the restriction of the agent's access to credit is necessary to achieve a Pareto-optimal outcome. In particular, under every Pareto-optimal contract for every outcome of every period the agent would choose to save some of his wage if he could.]

The first-order approach to principal-agent problems involves relaxing the constraint that the agent choose an action which is utility maximizing to require instead only that the agent choose an action at which his utility is at a stationary point. Although more mathematically tractable, this approach is generally invalid. This paper identifies sufficient conditions-the monotone likelihood ratio condition and convexity of the distribution function condition-for the first-order approach to be valid. The Pareto-optimal wage contract is shown to be nondecreasing in output under these same conditions. MIRRLEES [5] WAS THE FIRST to point out that the standard method for analyzing the principal-agent problem is not generally correct. This method, the so-called first-order approach, involves weakening the constraint that the agent choose a utility-maximizing action to require instead only that the agent choose an action at which his utility is at a stationary point. The resulting problem is more mathematically tractable. However, as Mirrlees [5] has shown, necessary conditions for a contract to solve the first-order program are not generally even necessary conditions for the valid program. Therefore qualitative propositions about the nature of the Pareto-optimal contract derived from the first-order approach are not in general valid. This has motivated researchers to try to identify classes of cases where the first-order approach is valid.

[This paper analyzes nonlinear growth models in which agents' expectations have a role in determining present behavior. Assuming agents have perfect foresight, we develop sufficiency conditions for the local stability of a given steady state. We then briefly discuss several examples in which stability prevails.]