A note on the coincidence between Stackelberg and Nash equilibria in a differential game between government and firms

In Navas and Mar n-Solano (2008) the coincidence between Nash and Stackelberg equilibria for a modified version of the differential game model first proposed by Lancaster (1973) was proved. However, important restrictions on the value of the parameters of the model were included, in order to obtain an interior solution. In this paper we extend the previous result, in the limit when the discount rate is equal to zero, by eliminating the restrictions and taking into account corner solutions.optimal profit taxation, nash/stackelberg equilibria, time consistency

Discounting Arduousness

There is a growing literature considering deviations from standard constant discounting. In this paper we combine time-inconsistent (non-constant discounting) preferences with recursive utilities. We apply this setting to the demand side properties of what we call arduous goods. The rational for a non-standard discounting is that production and consumption are not separable in these kinds of goods. The necessary effort implies that individuals discount consumption of these goods in a special way: both biased preferences and dynamic recursive adjustment are present. In this way, willingness to make an effort, modeled as a discount factor, becomes endogenous.time-consistent solution, arduous and easy goods, non-constant discounting, continuous-time, recursive utility

User cost of capital with delayed investment grants

The usual assumption when considering investment grants is that grant payments are automatic when investments are undertaken. However, evidence from case studies shows that there can exist some time lag until funds are received by granted firms. In this paper the effects of delays in grant payments on the optimal investment policy of the firm are analyzed. It is shown how these delays lead not only to a higher financing cost but to an effective reduction in the investment grant rate, and in some cases, how benefits from investment grants could be canceled due to interactions with tax effects.user cost of capital, delayed grant payments

A comment on the cost of capital for investments with non-homogeneous components

In this paper, the expression for the cost of capital is derived when net and replacement investments exhibit differences in their effective prices due to a different fiscal treatment. It is shown that, contrary to previous results in the literature, the cost of capital should be constructed under an opportunity cost criterion rather than a historical one. This result has some important economic consequences, since the optimizing firm will take into account not only the effective price for the new investments but also consider the opportunity cost of replacing them.grants on net investments, cost of capital

Non-constant discounting in finite horizon: The free terminal time case

This paper derives the HJB (Hamilton-Jacobi-Bellman) equation for sophisticated agents in a finite horizon dynamic optimization problem with non-constant discounting in a continuous setting, by using a dynamic programming approach. A simple example is used in order to illustrate the applicability of this HJB equation, by suggesting a method for constructing the subgame perfect equilibrium solution to the problem. Conditions for the observational equivalence with an associated problem with constant discounting are analyzed. Special attention is paid to the case of free terminal time. Strotzs model (an eating cake problem of a nonrenewable resource with non-constant discounting) is revisited.naive and sophisticated agents, observational equivalence, non-constant discounting, free terminal time

Time Consistent Pareto Solutions in Common Access Resource Games with Asymmetric Players

In the analysis of equilibrium policies in a dierential game, if agents have different time preference rates, the cooperative (Pareto optimum) solution obtained by applying the Pontryagin's Maximum Principle becomes time inconsistent. In this work we derive a set of dynamic programming equations (in discrete and continuous time) whose solutions are time consistent equilibrium rules for N-player cooperative dierential games in which agents dier in their instantaneous utility functions and also in their discount rates of time preference. The results are applied to the study of a cake-eating problem describing the management of a common property exhaustible natural resource. The extension of the results to a simple common property renewable natural resource model in innite horizon is also discussed.cooperative solutions, dierential games, asymmetric players, resource games, time-inconsistency, heterogeneous discount rates

Heterogeneous discounting in consumption-investment problems. Time consistent solutions

In this paper we analyze a stochastic continuous time model in finite horizon in which agents discount the instantaneous utility function and the final function at constant but different instantaneous discount rates of time preference. Within this context we can model problems in which, when the time t approaches to the final time, the valuation of the final function increases compared with previous valuations in a way that cannot be explained by using a unique constant or a variable discount rate. We derive a dynamic programming equation whose solutions are time-consistent Markov equilibria. For this class of time preferences, we study the classical consumption and portfolio rules model (Merton, 1971) for CRRA and CARA utility functions for time- consistent agents, and we compare the different equilibria with the time-inconsistent solutions. The introduction of stochastic terminal time is also discussed.dynamic programming, consumption and portfolio rules, heterogeneous discounting, time consistency

Parent and Child Language Profiles and their Family and Clinical Predictors

A large number of households in the United States include linguistic minority and immigrant parents. These include parents of Latinx backgrounds and their children who have varying levels of English and Spanish proficiency. Research is needed to examine the nature of parent-child language proficiency patterns and differences and their links to family processes and mental health. To address this gap, a sample of 294 Latinx parent-child dyads of predominantly low-income and immigrant backgrounds were interviewed and reported their English and Spanish language proficiency levels. Latent Profile Analysis (LPA) uncovered four parent-child language profiles including three in which there was a language gap (Large English Gap - LEG, Medium English Gap - MEG, and Medium Spanish Gap - MSG) and one in which parent and children matched in their language proficiency (No Language Gap - NLG). Multinomial logistic regression analyses controlling for key demographic variables revealed that youth who reported higher maternal and paternal alienation, lower paternal communication and higher depressive symptoms were more likely to belong to the NLG profile, compared to the LEG profile. Further, youth who reported higher maternal and paternal alienation, and lower maternal trust were more likely to belong to the MSG profile relative to the LEG profile. Findings point to the vital importance of incorporating multiple reporters of language proficiency and the potential protective value of youth Spanish proficiency, in particular