Time Preference Functions Research Articles

Optimal channel decision of retailers in the dual-channel supply chain considering consumer preference for delivery lead time

Facing competition from manufacturers' online direct channels, how retailers make sales channel decisions to increase consumer stickiness has become the core concern of the industry and academia. Empirical research showed that delivery lead time is a key factor that affects consumers' preference for online channels. To analyze the impact of consumer delivery time preference on channel selection and pricing strategy of retailers, consumer delivery lead time preference function was improved from a linear function to an exponential function and consumer demand under the mixed dual-channel supply chain of manufacturer and retailer was derived. Then, the Stackelberg game models under different channel strategies of retailer were established and solved. Results show that consumer preference for delivery lead time has four implications on the channel decision of retailers under manufacturer encroachment in the dual-channel supply chain. First, the dual retail channels strategy is the optimal choice for retailers, and the profit margins that a retailer obtains from dual retail channels supply chain and single online retail channel supply chain will increase as consumers' delivery lead time preference coefficient increases. Second, the optimal pricing of online retail channel and offline retail channel is positively related to consumers' delivery lead time preference coefficient. By contrast, the optimal pricing of online direct channel is negatively related to consumers' delivery lead time preference coefficient. Third, the optimal pricing of online retail channel is higher than that of offline retail and online direct channels. Fourth, a retailer and a manufacturer can adopt a compensation-based whole price contract to address the conflict brought about by the optimal channel choice of the retailer. This study introduces consumer delivery lead time preference into retailer channel decision making and provides a theoretical reference for retailer's mixed channel construction in practice.

A Comparative Study of Equilibrium Equity Premium under Discrete Distributions of Jump Amplitudes

In this paper, we compare equilibrium equity premium under discrete distributions of jump amplitudes. In particular, we consider the binomial and gamma distributions because of their applicability in finance. For the binomial, we assume that the price movement is allowed to either increase or decrease with probability p or 1 &#8722 p respectively. n is the trading period thereby forming a vector x of jump sizes (shifts) whose distribution is a binomial over time. For the gamma, the jumps are taken to be rare events following a Poisson distribution whose waiting times between them follows a gamma. In both distributions, the optimal consumption of the investor is affected by the deterministic time preference function but it has no effect on the diffusive and rare-events premia thereby not affecting the equilibrium equity premium. Also, for , the volatility effect on the equity premium is the same in both the power and square root utility functions although the equity premium is not affected by the wealth process . However, the wealth process affects the equity premium of the quadratic utility fuction. We observe no significant differences in equity premium for the two discrete distributions.

Ratchet consumption over finite and infinite planning horizons

Ratchet consumers want their spending to always increase and never decrease. We find an optimal consumption rule for ratchet consumers by maximizing an expected utility that eschews spending declines, yet permits a range of choices for felicity and time preference functions. This solution can be tailored to fit both retirees with finite planning horizons and endowments with infinite planning horizons. We assume complete markets modeled by a pricing kernel generated by a Lévy process. When the kernel is log-normal, we obtain closed-form solutions for both finite and infinite horizons.

Optimal Continuous Ratchet Consumption

Ratchet consumers want their spending to always increase and never decrease. We find an optimal consumption rule for ratchet consumers by maximizing an expected utility that eschews spending declines, yet permits a range of choices for felicity and time preference functions. This solution can be tailored to fit both retirees with finite planning horizons and endowments with infinite planning horizons. We assume complete markets modeled by a pricing kernel generated by a Levy processes. When the kernel is log-normal, we obtain closed-form solutions for both finite and infinite horizons.

Optimal Discrete Ratchet Consumption

Dybvig [1995] finds optimal spending and investment strategies for a perpetual endowment that has no tolerance for spending declines. His spending rule is a ratchet --- spending never decreases, but has a substantial chance of increasing. We find the ratchet consumption rule for an investor with a finite planning horizon. We maximize an expected utility that eschews pending declines, yet permits a range of choices for felicity and time preference functions. For optimality, a spending rule must be paired with an investment rule. Here, we investigate dynamic investment strategies --- we treat consumption as a derivative security and derive formulas for its delta-hedge.

The economics of interest rates

The paper looks at the behavior of investors in an economy consisting of a production process controlled by a state variable representing the state of technology. The participants in the economy maximize their individual utilities of consumption. Each participant has a constant relative risk aversion. The degrees of risk aversion, as well as the time preference functions, differ across participants. The participants may lend and borrow among themselves, either at a floating short rate, or by issuing or buying term bonds. We derive conditions under which such an economy is in equilibrium, and obtain equations determining interest rates.

On the roles of impatiencein homothetic growth paths

This article reexamines the role of long-run endogenous impatience in homothetic growth paths. Using a class of intertemporal preferences assuming a continuous time generator representation, the existence, uniqueness and determinacy properties of a homothetic growth path with endogenous rates of time preference are checked. The argument is based on extensive use of prospective utility. The associated utilities are shown to exhibit a rate of time preference function that becomes invariant to prospective utility along the homothetic growth solution. They also enter in a normal way in the generating function. Finally and at the opposite of earlier conclusions for steady states, the nil rate of time preference case associated with multiplicatively separable generators cannot anymore be discarded.

On hyperbolic discounting and uncertain hazard rates

The value of a future reward should be discounted where there is a risk that the reward will not be realized. If the risk manifests itself at a known, constant hazard rate, a riskneutral recipient ...

Foresight as a survival characteristic: When (if ever) does the long view pay?

Long-range R&D and capital investment projects are normally evaluated by means of a procedure (cost-benefit analysis) that involves a choice of time preference functions. Cost-benefit analysts and many economists typically assume that time preference is a behavioral fact of life and that the time preference function is essentially equivalent to a compound interest law. In practice, they tend to choose discount rates in the range of 3% to 8% per annum in real terms. Variability in projected cost-benefit ratios resulting from this uncertainty is commonly dealt with ad hoc, e.g., by simply presenting results for several different discount rates and letting the decisionmaker select among them. It is argued in this study that the basic discounting methodology is fundamentally flawed and can lead to significantly inferior social choices, i.e., choices that would be rejected by virtually any rational actor to whom the choice was fairly presented. A more general methodology is needed. Examples from several realms, including energy policy and environmental protection, are discussed to illustrate the thesis.

Time preference and the life cycle: The logic of long-term high risk vs. short-term low risk

This paper argues that time-preference functions (or ‘discount rates’) for R&D should properly be considered to be functions of the economic environment. In particular, during periods of accelerating growth and general increasing prosperity it is appropriate and rational to prefer a marginal dollar in the present to a marginal dollar in the future. Conversely, during periods of saturating growth and deteriorating prospects, the converse holds: it is rational to prefer a marginal dollar in the future to one in the present. Periods of increasing general prosperity — ‘rising tide’ — are likely to be associated with the early phases of an industry ‘life cycle’. Periods of declining prosperity, by contrast, may occur towards the end of the life cycle. The implications for R&D policy are derived in terms of a simple model. The results suggest that at the beginning of the life cycle the optimal R&D policy is to invest in short-term, low risk ventures (i.e. product or process improvements). Late in the cycle, however, the optimal policy reverses to long-term high-risk projects. In simple terms: a firm in a declining industry needs to find a new product or business to replace the old one. Unfortunately, the appropriate behavior is discouraged by most existing B/C methodologies.

A SYSTEM FOR THE PREFERENCE EVALUATION OF CYCLIC MENUS

A quantitative method to evaluate the overall preference of cyclic menus is presented. The model developed consists of two separate factors relating to menu preference rating. The first factor is the time-preference relationship for food items. From survey data, time-preference functions have been constructed which indicate how the hedonic rating of a food item varies with the time since the food was last served. The function assumes a quadratic form with entrees tending to be most time sensitive and salads and vegetables the least. The second factor is the meal component weights for the evaluaton of an entire meal based on the consumer hedonic preference values for the generic components of the meal (entree, starch, vegetable, salad, and dessert). Regression techniques have been applied to survey data to generate the set of importance factors, or meal component weights, for each component. For example, the results indicate that the entree represents about 49% of the total preference value of the meal. This approach has provided a basis for an additive linear model for overall meal preference. A general system for the overall evaluation of cyclic menus has also been developed based on application of an additive linear model. This procedure accounts for the maximum preference values for food items, the time-dependency of the food item preference values, and the meal component weighting factors and is easily adapted to the computer, as shown by a specific example. The overall system appears to offer a logical, realistic, and integrated approach which reflects time factors and the relative importances of the various components of meals in the evaluation of cyclic menus. Further research in this area is recommended to refine this model and test its validity in an operational environment.