Mohamed El-Hodiri

An Economic Model of a Professional Sports League

This paper investigates the economic structure of professional sports to determine the extent to which the current operating rules justify exemption of professional sports leagues from some aspects of antitrust statutes. We construct a formal decision-making model incorporating certain fundamental features of the industry. Within the context of the model we find that, under current rules of operation, equalization of playing strengths is generally not consistent with profit maximization by teams. However, we suggest a rule that guarantees convergence to a path of equal playing strengths under decentralized control of teams. As an example we study baseball leagues. Some refinements of the model are introduced, for example, incorporating time lags and training costs that result when teams train their own players.

An Optimal Growth Model with Time Lags

The paper discusses the allocation of output among consumption and two types of capital with different gestation periods. Along an optimal path, we show that the imputed prices of capital goods, from the time they start production, do not exceed the prices of output, which are not less than the marginal instantaneous utility of consumption. A simple numerical example helps to illustrate some further implications of the model. RECENT PAPERS on optimal growth consider models of allocation of resources between consumption and investment. It is invariably assumed that investment results in an instantaneous increase in the stock of capital. Such assumptions obscure differences in the gestation periods among various capital goods. In [1] we discuss how a growth problem with time lags can be formulated and interpreted and explain the derivation of the necessary conditions for optimization. In this note we study the effects of differences in gestation periods on optimal investment plans for a growth problem including depreciation and population growth. Consider an economy where two capital goods and labor are used in the production of a single commodity. The per capita output at time t is given by the production function: f (kl, k2), where k, is the per capita stock of capital of type one, and k2 is the per capita stock of capital of type two. From now on, all variables will be per capita and we drop the designation. We assume the following:

Dynamic behavior of the firm with adjustment costs, under regulatory constraint

Abstract This paper investigates the optimal investment behavior of the regulated (profit-maximizing) firm in a dynamic context. The modern adjustment cost approach to investment is incorporated into the theory of a regulated firm, which has typically been discussed in a static framework. This paper thus generalizes the well-known Averch-Johnson thesis which is proved in the static context. The paper investigates both the finite and infinite horizon cases.

Comparative Statics When the Objective Function Is Concave: Old Wine in Old Bottles?

This is the publishers version, also available electronically from http://www.jstor.org/stable/1830228?seq=1#page_scan_tab_contents

Price Taking Firms

In this chapter we study the behavior of a price taking profit maximizing firm. Section 1 will be devoted to investigating the consequences of the short run profit maximization. We will obtain the basic properties of the short run profit functions, short run output supply functions and short run derived demand functions for variable inputs. Finally we ill note the duality between production functions and profit functions.

Sensitivity analysis for an optimal control problem

This note considers an optimal control problem where the maximand, right-hand side of the systems equations and the constraints are concave and differentiable. The question asked is: What happens when there is a shift or a change in the parameters of the problem? Inequalities indicating the relation of the direction of change in the optimal choices as well as in the maximand to the direction of change in the parameters are derived under alternative hypothesis about the dependence of the problem on the parameters.

Optimality Criteria of Economic Growth as Examples of Optimal Resource Allocation Over Time

This is my PhD dissertation defended in 1966 at the University of Minnesota and it was never published. It has been cited and used in other researchers work so I now make it available. The problem of optimal resource allocation over time is formulated as an optimal control problem. This is where the existence of optimal programs is investigated (and sufficient conditions are provided) for the first time in economics. When earlier authors spoke of existence, they spoke of convergence of the integral defining the optimality criterion. Optimal programs were characterized in terms of market equilibria at each point in time as well as imputed prices for stocks of capital.One of the propositions in the paper establishes the principle of centralization of planning and decentralization of implementation (this closely relates to polycenterism advocated by European socialist parties in the late 1950s. If one uses a measure space of traders instead of the basic time interval and assume pure exchange then the existence theorem of this paper can greatly simplify the proof of existence of equilibrium in a or a much more flexible model of exchange with continuum of traders.

No Major Constraints

The mathematical content of this chapter is well known, and can be found in any reasonable book on multivariable calculus, e.g. Fleming (1977). Nevertheless, the chapter serves two purposes. First, it presents a wish list, an ideal for which we address the smooth optimization problem comprehensively. We pose certain questions more easily asked now than later. Second, the chapter samples some of the applications of smooth optimization theory to economic analysis.

Optimal Control with Multiple Criteria and Time Lags: Some Economic Applications

Consider a system where the motion is given by