On relationships between numerical representations of interval orders and semiorders

The extent to which continuous numerical representations of interval orders are unique is considered. Apair of continuous, real-valued functions, <u, v>, represents an interval order, <X, >>, provided that for x, y ϵ X, x > y if and only if u(x) > v(y). Relationships which necessarily hold between any two such numerical representations are presented and a method by which one continuous representation can be derived from another is described. Similar considerations are made for special forms of continuous numerical representations of semiorders.     

Outsourcing via reverse auction with a built-in menu of change orders

Many firms invent and design products while outsourcing their production to independent contractors. We consider a dominant strategy mechanism that selects a contractor using a reverse auction, combined with a menu of permitted change orders from which the contractor can choose after updated cost information has become available. That mechanism maximizes the gain from trade, allows the firm to extract the second highest surplus, and induces the contractor to make efficient adjustments to output after updated cost information has emerged.     

A multi-period portfolio selection optimization model by using interval analysis

Due to few historical data that can be obtained in an emerging securities market, the future returns, risk and liquidity of securities cannot be forecasted precisely. The investment environment is usually fuzzy and uncertain. To handle these imprecise data, this paper discusses a fuzzy multi-period portfolio optimization problem where the returns, risk, and liquidity of securities are represented by interval variables. By taking the return, risk, liquidity and diversification degree of portfolio into consideration, an interval multi-period portfolio selection optimization model is proposed with the objective of maximizing the terminal wealth under the constraints of the return, risk and diversification degree of portfolio at each period. In the proposed model, a proportion entropy is employed to measure the diversification degree of portfolio. Using the fuzzy decision-making theory and multi-objective programming approach, the proposed model is transformed into a crisp nonlinear programming. Then, we design an improved particle swarm optimization algorithm for solution. Finally, a numerical example is given to illustrate the application of our model and demonstrate the effectiveness of the designed algorithm.     

Attitude to child-bearing by single Nigerian women

The author examines attitudes toward childbearing by unmarried Nigerian women using data from interviews with a sample of 212 male and female residents of Ibadan, Nigeria, chosen in order to examine the views of educated Nigerians. The respondents were, for the most part, Yorubas, married, and aged 20-40. "In general, the respondents supported the suggestion that women who are unmarried should try and have children of their own, but they are opposed to the suggestion that such women should have as many children as possible, either from the same man or from different men of their choice." The author suggests that "one significant implication of the survey is that the general fertility rate (that is the annual number of births per 1,000 women of reproductive age) may be very high in developing areas not only because married women produce children, but also because women of childbearing ages who are single [are] also encouraged to have children of their own."     

Limit orders,asymmetric information,and the formation of asset prices with a computerized specialist

We analyze the existence of equilibrium in an asset market under asymmetric information. Price formation is modeled as a bilateral sealed bid auction where uninformed and informed traders submit limit orders to a computerized specialist. The computerized specialist is programmed to sell to the highest bidder and buy from the seller asking the lowest price. We show that this mechanism — which is designed to model the Globex and RAES trading institutions used in Chicago, London, New York, Paris, and Germany — yields an equilibrium in which the bid-ask spread is endogenously random and the passive specialist earns nonnegative profits.     

Welfare-improving financial innovation with a single good

Summary. We show that at any equilibrium of almost every single-good incomplete markets economy, it is possible to find an asset which when introduced makes every agent better-off. Diamond (1967) has shown, however, that such economies are constrained suboptimal, so it is of course impossible to find a new asset which makes all agents worse-off. This contrasts with the case of multiple consumption goods, for which Cass and Citanna (1995) and Elul (1995) demonstrate that equilibrium utilities may be arbitrarily perturbed via financial innovation. Proving our result requires us to exploit not changes in equilibrium prices, but rather the gains to trading the new asset. In particular, we find an asset which when introduced does not change the existing asset prices even though it is traded by every agent – by a revealed preference argument it must therefore make everyone better-off. Received: May 28, 1997; revised version: July 1, 1997     

The production of functionality by the elderly: a household production function approach

This paper extends Becker's model of the household production function of human capital to the production of elderly functionality. In this model, elderly functionality is produced with the direct inputs of assistive devices, personal assistance, and nutritional intake. Education, endowment variables (like genetic endowment and sex) and health conditions (like stroke) determine the production function environment. Data from the Survey of Asset and Health Dynamics Among the Oldest-Old (AHEAD) are used to estimate a production function of bathing functionality, using a two-stage estimation procedure. In the first stage, input demands for the endogenous functionality inputs are estimated, recognizing health heterogeneity. The results suggest that reverses in functionality caused by age and health conditions can be partially compensated for by the use of assistive devices (like grab bars and bathing equipment), secure nutritional intake, and moderate alcohol consumption. However, non-inputs like chronic health conditions, age, sex and genetic endowment exert a strong influence on the level of functionality.     

Efficient egalitarian equivalent allocations over a single good

This paper studies efficient and egalitarian allocations over a single heterogeneous and infinitely divisible good. We prove the existence of such allocations using only measure-theoretic arguments. Under the additional assumption of complete information, we identify a sufficient condition on agents’ preferences that makes it possible to apply the Pazner–Schmeidler rule for uniquely selecting an efficient egalitarian equivalent allocation. Finally, we exhibit a simple procedure that implements the Pazner–Schmeidler selection in a subgame-perfect equilibrium. We thank Gabrielle Demange, William Thomson, two referees and seminar audiences at Boston, Palermo and Rochester University for their comments. Financial support from MIUR is acknowledged.     

Estimating a hedonic earnings function with a nonparametric method

In this paper we apply the nonparametric approach of Bierens and Hartog (1988) to estimating and testing an earnings function which emphasizes the simultaneous impact of supply characteristics (like education) and demand characteristics (like job level). The data support this emphasis and point to significant non-linearities. In particular, job level comes out as an important variable.     

A method for constructing an intertemporal utility function from a Friedmanian consumption function

It is shown that the intertemporal utility function can be reconstructed from data on demands if they are restricted to be linear in wealth, or Friedmanian.     

Markov perfect Nash equilibria in models with a single capital stock

Many economic problems can be formulated as dynamic games in which strategically interacting agents choose actions that determine the current and future levels of a single capital stock. We study necessary as well as sufficient conditions that allow us to characterise Markov perfect Nash equilibria for these games. These conditions can be translated into an auxiliary system of ordinary differential equations that helps us to explore stability, continuity and differentiability of these equilibria. The techniques are used to derive detailed properties of Markov perfect Nash equilibria for several games including voluntary investment in a public capital stock, the inter-temporal consumption of a reproductive asset and the pollution of a shallow lake.     

The duality implications of a concave aggregator function

Suppose a production or utility function F is continuous, increasing and quasiconcave on the non-negative orthant. Let C be the associated cost function, G the associated indirect function, and D the associated distance or deflation function. The implications of the concavity of F on the other three dual representations are exhibited.     

On the existence of a regulated production function

This paper examines the generalization of the regulated production function. It characterizes the set of admissible regulatory constraints that are compatible with the existence of a regulated production function in a sufficiently weak framework to encompass the usual rate-of-return constraints à la Averch and Johnson and value constraints.     

New products with a symmetric AIDS expenditure function

We study a symmetric AIDS expenditure function that allows for variation in the range of goods. Solving for the reservation prices for goods not available, a convenient form for the expenditure function is obtained. This functional form should prove useful in monopolistic competition models were the range of products changes due to entry and exit.     

Corruption in a neoclassical growth model with a non-convex production function

In this article, we analyze the bureaucrats’ corruption problem in a simple neoclassical growth model with a non-convex production function. In this model, we consider direct relations between product (income) taxation and corruption, and between corruption and public goods provision. As the main result, we show that the optimal consumption growth path in this economy is higher in a non-corrupt environment than in a corrupt environment and the higher the proportion of corrupt bureaucrats, the higher the cost of corruption to society.