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We study a method for calculating the utility function from a candidate of a demand function that is not differentiable, but is locally Lipschitz. Using this method, we obtain two new necessary and sufficient conditions for a candidate of a demand function to be a demand function. The first concerns the Slutsky matrix, and the second is the existence of a concave solution to a partial differential equation. Moreover, we show that the upper semi-continuous weak order that corresponds to the demand function is unique, and that this weak order is represented by our calculated utility function. We provide applications of these results to econometric theory. First, we show that, under several requirements, if a sequence of demand functions converges to some function with respect to the metric of compact convergence, then the limit is also a demand function. Second, the space of demand functions that have uniform Lipschitz constants on any compact set is compact under the above metric. Third, the mapping from a demand function to the calculated utility function becomes continuous. We also show a similar result on the topology of pointwise convergence.

This article investigates household consumption in 2011 and 2021, to see if there is evidence of changes in household demands of food. The European policy from Farm to Fork aims at providing sustainable, healthy food for all consumers, through an increase in vegetable consumption at the expense of meat consumption. We estimated demand functions for 8 groups of commodities, estimating expenditure and cross-price elasticities. Our finding suggests that Romanian households still view meat as an important dietary requirement, and since its demand is one of the most elastic, the intake will further increase. The quantity and expenditure share of vegetables decreased in the interval. The expenditure elasticity shows that urban households value vegetable consumption more than rural ones. The demand for fruits is elastic, in some cases more so than the one for meat, so it is likely that the fruits demand will continue to grow. From the analysis we can conclude that Romanian households diet preferences are not fulfilling the European aim of achieving “food consumption and healthy diets”, since the demand for meat continues to grow, while the demand for vegetables is at best stationary.

Utilizing the urban water demand function and the Cobb-Douglas (C-D) production function, an economic control model for the multi-input-multi-output (MIMO) nonlinear system was designed and implemented to describe urban comprehensive water consumption, where the urban water demand function was expressed as the product of the number of water users and per capita comprehensive water consumption, and the urban water supply function was expressed as a C-D production function. The control variables included capital investment and labor input for the urban water supply. In contrast to the Solow model, Shell model and aggregate model with renewable labor resources, the proposed model eliminated value constraints on investment and labor input in the state equations and hence avoided the difficulty in applying these models to urban water supply institutions. Furthermore, the feedback linearization control design (FLCD) method was employed to accomplish stability of the system. In contrast to the optimal control method, the FLCD method possesses an explicit solution of the control law and does not require the solution of a two-point boundary value problem of an ordinary differential equation, making the method more convenient for application. Moreover, two different scenarios of urban water consumption, one for the growth period and the other for the decline period, were simulated to demonstrate the effectiveness of the proposed control scheme.

Extant literature on anchoring demonstrates that priming affects willingness-to-pay (WTP), but it mainly focuses on average WTP values, neglecting the aggregate effects of priming on WTP distributions. In this research, we argue that when priming is in effect, WTP distribution rather than the average should be analyzed because important pricing decisions, such as optimal price determination or price customization, require an assessment of distributions. Therefore, the objective of this research is to uncover how priming affects WTP distributions and, consequently, the demand curve. The results of these two studies suggest that priming affects not only the average but also the whole distribution and that this effect is in the form of a shift/stretch to the right for high-priming manipulations and to the left for low-priming manipulations.

Although the marketing literature is abundant with studies dealing with the responsiveness of consumption to price changes, not much has been said about the elasticity of household expenditures from a macroeconomic perspective. Focusing on several categories of non-durable and semi-durable goods, we provide a pan-European comparative analysis of both price and income elasticities of demand. Income elasticities consistently dominate the price ones, regardless of the chosen consumption category. Although we explicitly allow for time-variability of elasticities via a state space model, our results show that the demand elasticities are independent of the business cycle, both across states and across the considered consumption categories. Consumption trajectories obviously exhibit some secular tendencies and are insensitive to transitory shocks.    

We consider price-dependent demand and develop an integrated inventory and transportation policy with strategic pricing to maximize the total profit for a ubiquitous enterprise. The proposed policy provides the optimal ordering, shipment and pricing decision. We first assume that demand for a product is a linear function of the price. A mathematical model for the total profit under quantity based dispatch is developed in consideration of ordering, shipment and pricing variables. Optimality properties for the model are then obtained and an efficient algorithm is provided to compute the optimal parameters for ordering, shipment and pricing decision. Finally, we extend our results to a more general case where demand for the product is a convex or a concave function of the price.

\"This paper calculates the effects of immigration on the wages of native US workers of various skill levels in two steps. In the first step we use labor demand functions to estimate the elasticity of substitution across different groups of workers. Second, we use the underlying production structure and the estimated elasticities to calculate the total wage effects of immigration in the long run. We emphasize that a production function framework is needed to combine own-group effects with cross-group effects in order to obtain the total wage effects for each native group. In order to obtain a parsimonious representation of elasticities that can be estimated with available data, we adopt alternative nested-CES models and let the data select the preferred specification. New to this paper is the estimate of the substitutability between natives and immigrants of similar education and experience levels. In the data-preferred model, there is a small but significant degree of imperfect substitutability between natives and immigrants which, when combined with the other estimated elasticities, implies that in the period from 1990 to 2006 immigration had a small effect on the wages of native workers with no high school degree (between 0.6% and +1.7%). It also had a small positive effect on average native wages (+0.6%) and a substantial negative effect (-6.7%) on wages of previous immigrants in the long run.\" (Author's abstract, IAB-Doku). Die Untersuchung enthält quantitative Daten. Forschungsmethode: empirisch-quantitativ; empirisch; Längsschnitt. Die Untersuchung bezieht sich auf den Zeitraum 1990 bis 2006.

The welfare effects of third-degree price discrimination are analyzed when demand in one market is an additively shifted version of demand in the other market and both markets are served with uniform pricing. Social welfare is lower with discrimination if the slope of demand is log concave or the convexity of demand is nondecreasing in the price. The demand functions commonly used in models of imperfect competition satisfy at least one of these sufficient conditions.

The traffic assignment problem (TAP) with elastic demands can be formulated as an optimization problem, the objective of which is the sum of a congestion function and a disutility function. We propose to use a variant of the analytic center cutting plane method to solve this problem. We test the method on TAP instances with the Bureau of Public Roads congestion function and different demand functions (constant elasticity and linear). The results of the numerical experiments show that it is possible to solve large instances with high accuracy.

We consider a dynamic pricing problem with an unknown and discontinuous demand function. There is a seller who dynamically sets the price of a product over a multiperiod time horizon. The expected demand for the product is a piecewise continuous and parametric function of the charged price, allowing for possibly multiple discontinuity points. The seller initially knows neither the locations of the discontinuity points nor the parameters of the demand function but can infer them by observing stochastic demand realizations over time. We measure the seller’s performance by the revenue loss relative to a clairvoyant who knows the underlying demand function with certainty. We construct a dynamic estimation-and-pricing policy that accounts for demand discontinuities, derive the convergence rates of discontinuity- and parameter-estimation errors under this policy, and prove that it achieves near-optimal revenue performance. We also extend our analysis to the cases of time-varying demand discontinuities and inventory constraints. This paper was accepted by Noah Gans, stochastic models and simulation .