Concave Demand Research Articles

UPWARD‐SLOPING REACTION FUNCTIONS UNDER QUANTITY COMPETITION IN MIXED OLIGOPOLIES*

ABSTRACTIt is shown that in a mixed duopoly under quantity competition, the public firm's reaction function may be upward‐sloping. This is the case with a concave demand function when the public firm attaches to private profits a smaller weight than to its own profits.

Monopoly Output and Welfare: The Role of Curvature of the Demand Function

A monopolist with increasing marginal cost, facing a concave demand function, is shown to produce at an output level that is at least half as large as the socially efficient level.

The fertility effect of dependent tax exemptions: estimates for the United States.

Many developed countries allow tax subsidies for families to help reduce the costs of bearing and rearing children. Whittington et al. in 1990 developed a theoretical model in which they estimated the effect of tax deductions for dependent children on fertility in the US. This paper develops an empirical model of estimation and reconsiders Whittington's work. Nonlinear specification of the demand curve for children is central to the new model. This change is made based on the hypothesis that nonlinear specification will better capture the shape of demand. Using annual time-series data over the period 1913-84, the study found the marginal effect of dependent exemptions to decrease with exemption level. Given the historically low recent levels of exemptions in real terms, increasing current exemptions will affect fertility to a greater extent than previously estimated. Graphically, results point to the existence of a concave demand for children.

Dynamic demand and optimal OPEC pricing: An empirical investigation

The demand for energy and in particular the demand for oil is very sluggish. Given this dynamic description of demand, a monopoly, or a dominant cartel, may either apply a volatile or a stable price policy in order to maximize profits. In particular, earlier works of Fromholzer and Wirl derive that the shape of the equilibrium demand function determines whether a price is stable or volatile. More precisely, a concave demand relation induces a smooth, and a convex relation leads to a volatile, strategy. This theory is empirically tested for the demand for OPEC oil.

Economies of Scale and Barriers to Entry

Dixit has recently presented a model in which established firms select capacity to discourage entry but cannot employ threats they would not rationally execute after entry. Entry deterrence in a slight modification of this model involves the classical limit-price output. Under linear or concave demand, however, the capital cost of a firm of minimum efficient scale is an upper bound on the present value of the monopoly profit stream that can be shielded from entry. It is argued that this suggests the general unimportance of entry barriers erected by scale economies.