Envelope Theorems for Non-Smooth and Non-Concave Optimization

We study general dynamic programming problems with continuous and discrete choices and general constraints. The value functions may have kinks arising (1) at indifference points between discrete choices and (2) at constraint boundaries. Nevertheless, we establish a general envelope theorem: first-order conditions are necessary at interior optimal choices. We only assume differentiability of the utility function with respect to the continuous choices. The continuous choice may be from any Banach space and the discrete choice from any non-empty set

The taxation of discrete investment choices

Traditional analysis of the taxation of income from capital has focused on the impact of tax on marginal investment decisions; the principal impact of tax on investment is through the cost of capital, and is generally measured by an effective marginal tax rate. In this paper, we consider cases in which investors face a choice between two or more mutually exclusive projects, both of which are expected to earn at least the minimum required rate of return. Examples include the location decisions of multinationals, firms' choice of technology, and the choice of investment projects in the presence of binding financial constraints. In these cases the choice depends on the effective average tax rate. We propose a measure of this rate and demonstrate its relationship to the conventional effective marginal tax rate. Estimates of both are presented and compared for domestic and international investment in Germany, Japan, the UK and USA between 1979 and 1997

The taxation of discrete investment choices

Traditional analysis of the taxation of income from capital has focused on the impact of tax on marginal investment decisions; the principal impact of tax on investment is through the cost of capital, and is generally measured by an effective marginal tax rate. In this paper, we consider cases in which investors face a choice between two or more mutually exclusive projects, both of which are expected to earn at least the minimum required rate of return. Examples include the location decisions of multinationals, firms’ choice of technology, and the choice of investment projects in the presence of binding financial constraints. In these cases the choice depends on the effective average tax rate. We propose a measure of this rate and demonstrate its relationship to the conventional effective marginal tax rate. Estimates of both are presented and compared for domestic and international investment in Germany, Japan, the UK and USA between 1979 and 1997.

Discrete Choices under Social Influence: Generic Properties

We consider a model of socially interacting individuals that make a binary choice in a context of positive additive endogenous externalities. It encompasses as particular cases several models from the sociology and economics literature. We extend previous results to the case of a general distribution of idiosyncratic preferences, called here Idiosyncratic Willingnesses to Pay (IWP). Positive additive externalities yield a family of inverse demand curves that include the classical downward sloping ones but also new ones with non constant convexity. When j, the ratio of the social influence strength to the standard deviation of the IWP distribution, is small enough, the inverse demand is a classical monotonic (decreasing) function of the adoption rate. Even if the IWP distribution is mono-modal, there is a critical value of j above which the inverse demand is non monotonic, decreasing for small and high adoption rates, but increasing within some intermediate range. Depending on the price there are thus either one or two equilibria. Beyond this first result, we exhibit the generic properties of the boundaries limiting the regions where the system presents different types of equilibria (unique or multiple). These properties are shown to depend only on qualitative features of the IWP distribution: modality (number of maxima), smoothness and type of support (compact or infinite). The main results are summarized as phase diagrams in the space of the model parameters, on which the regions of multiple equilibria are precisely delimited.Comment: 42 pages, 15 figure

Discrete Choices under Social Influence: Generic Properties

We consider a model of socially interacting individuals that make a binary choice in a context of positive additive endogenous externalities. It encompasses as particular cases several models from the sociology and economics literature. We extend previous results to the case of a general distribution of idiosyncratic preferences, called here Idiosyncratic Willingnesses to Pay (IWP).Positive additive externalities yield a family of inverse demand curves that include the classical downward sloping ones but also new ones with non constant convexity. When $j$, the ratio of the social influene strength to the standard deviation of the IWP distribution, is small enough, the inverse demand is a classical monotonic (decreasing) function of the adoption rate. Even if the IWP distribution is mono-modal, there is a critical value of $j$ above which the inverse demand is non monotonic, decreasing for small and high adoption rates, but increasing within some intermediate range. Depending on the price there are thus either one or two equilibria.Beyond this first result, we exhibit the {\em generic} properties of the boundaries limiting the regions where the system presents different types of equilibria (unique or multiple). These properties are shown to depend {\em only} on qualitative features of the IWP distribution: modality (number of maxima), smoothness and type of support (compact or infinite).The main results are summarized as {\em phase diagrams} in the space of the model parameters, on which the regions of multiple equilibria are precisely delimited.discrete choice; social influence; externalities; heterogeneous agents; socioeconomic behavior