Inverse Demand Curve Research Articles

Nonlinear inverse demand curves in electricity market modeling

In large-scale energy market models, the price–demand relationship is usually represented by a linear function. In this paper, nonlinear demand functions are fitted to electricity market bid data; in particular, exponential and polynomial (cubic) functions are estimated from EPEX day-ahead data (i.e. Central Western European market area). The corresponding game-theoretic, large-scale electricity models were successfully solved using the Extended Mathematical Programming framework after a suitable adaptation for conjectural variations. Additionally, sufficient conditions for the existence of equilibrium solutions are tested. Numerical results show that nonlinear demand curves lead to an improved modeling especially in high price (peak) load periods and to lower levels of implied market power, which can be considered to be more realistic for markets that have strong transparency measures.

Parallel inverse aggregate demand curves in discrete choice models

This paper highlights a previously unnoticed property of commonly-used discrete choice models, which is that they feature parallel demand curves. Specifically, we show that in additive random utility models, inverse aggregate demand curves shift in parallel with respect to variety if and only if the random utility shocks follow the Gumbel (Type 1 Extreme Value) distribution. Using results from Extreme Value Theory, we provide conditions for other distributions to generate parallel demands asymptotically, as the number of varieties increases. We establish these results in the benchmark case of symmetric products, illustrate them using numerical simulations and show that they hold in extended versions of the model with correlated tastes and asymmetric products. Lastly, we provide a “proof of concept” of parallel demands as an economic tool by showing how to use parallel demands to identify the change in consumer surplus from an exogenous change in product variety.

Managers’ and Employees’ Judgment and Decision Making: New Theoretical Developments

The quality of managers’ and employees’ decision making is one of the most important antecedents of organizations’ efficiency — if employees and managers make suboptimal decisions, their company’s performance would suffer (Ceschi, Demerouti, Sartori, & Weller, 2017; Dane & Pratt, 2007; Dean Jr & Sharfman, 1996; Schwenk, 1995). This symposium brings together groundbreaking research on judgment and decision making that advances scholarship in managerial decision making and cognition, human resources, and organizational behavior. Four presentations will illustrate how people’s judgment and decision making biases lead managers and employees to make suboptimal decisions in diverse organizational contexts, such as overtime work, bonus allocation, job selection, and pay disparity. Further, the research discussed in this symposium not only highlights how decision making biases lead people to make irrational decisions, but also identifies interventions to rectify people’s biases, thereby making the current findings useful to both management researchers and practitioners. Inverse Demand Curves in the Workplace: Asking Employees to Work Longer When They are Unproductive Presenter: Siran Zhan; U. of New South Wales Presenter: Krishna Savani; Nanyang Technological U. Equity Bias in Bonus Allocation to Teams: Giving Too Much to Larger but Unproductive Teams Presenter: Yun Bai; Xi'an Jiaotong U. Presenter: Krishna Savani; Nanyang Technological U. Should You Join a Large Team or a Small Team? Role of Employee Qualifications on Team Selection Presenter: Zhiyu Feng; Nanyang Technological U. Presenter: Krishna Savani; Nanyang Technological U. Does the Cause of Inequality Influence Perceptions of Fairness? Presenter: Simone Tang; Cornell U. Presenter: Kin Fai Ellick Wong; Hong Kong U. of Science and Technology

Parallel Inverse Aggregate Demand Curves in Discrete Choice Models

This paper highlights a previously unnoticed property of commonly-used discrete choice models, which is that they feature parallel demand curves. Specifically, we show that in additive random utility models, inverse aggregate demand curves shift in parallel with respect to variety if and only if the random utility shocks follow the Gumbel (Type 1 Extreme Value) distribution. Using results from Extreme Value Theory, we provide conditions for other distributions to generate parallel demands asymptotically, as the number of varieties increases. We establish these results in the benchmark case of symmetric products, illustrate them using numerical simulations and show that they hold in extended versions of the model with correlated tastes and asymmetric products. Lastly, we provide a “proof of concept” of parallel demands as an economic tool by showing how to use parallel demands to identify the change in consumer surplus from an exogenous change in product variety.

Cournot competition in wholesale electricity markets: The Nordic power exchange, Nord Pool

Horizontal shifts in bid curves observed in wholesale electricity markets are consistent with Cournot competition. Quantity competition reduces the informational requirements associated with evaluating market performance because the price-cost margins of all producers then depend on the same inverse residual demand curve instead of one for each firm. We apply the model to the day-ahead market of the Nordic power exchange, Nord Pool, for the years 2011-13. We reject the null hypothesis of perfect competition in all specifications. Results suggest that the average price-cost margin across the sample period was around four percent.

Welfare‐enhancing Trade Unions in an Oligopoly with Excessive Entry

Trade unions are often argued to cause allocative inefficiencies and to lower welfare. We analyze whether this evaluation is also justified in a Cournot‐oligopoly with free but costly entry. If input markets are competitive and output per firm declines with the number of firms (business stealing), there is excessive entry into such oligopoly. If trade unions raise wages above the competitive level, output and profits per firm decline, which could deter entry and thus improve welfare. We find that an increase in the union’s bargaining power raises welfare if the (inverse) demand curve is (sufficiently) concave. We also show that collective bargaining loosens the linkage between business stealing and excessive entry.

Ranking Supply Function and Cournot Equilibria in a Differentiated Product Duopoly with Demand Uncertainty

In this paper, we provide a welfare ranking for the equilibria of the supply function and quantity competitions in a differentiated product duopoly with demand uncertainty. We prove that the expected consumer surplus is always higher under the supply function competition, irrespective of whether the (duopolistic) products are substitutes, complements, or independent. Numerical simulations suggest that if the products are either complements or independent, or if they have an extremely low degree of substitution, then the supply function competition can always be Pareto superior to the quantity competition in terms of the producers’ and consumers’ welfares. Moreover, if the degree of product substitution is not extremely low, then the supply function competition can be Pareto superior to the quantity competition if and only if the size of the demand uncertainty is sufficiently large to exceed a critical level. We find that this critical level of demand uncertainty becomes higher when the duopolistic products are less differentiated. Additionally, this critical level is nonincreasing both in the marginal cost of producing a unit output and in the own-price sensitivity of each inverse demand curve when all other parameters are fixed. Our results imply that in electricity markets with differentiated products, the regulators should not intervene to impose the quantity competition in favor of the supply function competition unless the degree of product substitution is sufficiently high and the predicted demand fluctuations are sufficiently small.

Effect of government quality grade labels on consumer demand for pork chops in the short and long run

Despite ample evidence of pork quality variability, at present there are few signals that would incentivize growers to produce higher quality pork. Using split-sample, choice experiment data from a nationwide online survey of U.S. pork chop eaters, this research determines changes in pork chop demand in response to a potential change in U.S. government policy that would introduce a new pork quality grading system based on color scores. Our simulations include novel short-run projections in which the conditional and latent class logit models are inverted to yield inverse demand curves. The inverse demand curves are used to calculate equilibrium prices and pork revenue given a fixed supply of different pork qualities. We supplement these calculations with a more traditional “long run” analysis in which prices are fixed and quantities of different qualities adjust. Compared to the status quo (control) of no quality grades, we find that two grading systems based on alternative nomenclatures (Select, Choice, Prime vs. Good, Better, Best) both have the potential to increase pork chop sales and revenue to the pork industry; however, we also find that if only the highest quality is labeled, revenue could fall as the increase in demand for the higher quality is offset by the fall in demand for the lower qualities. Results also highlight important heterogeneity in consumer preferences, and although sensory studies strongly suggest redder pork chops are more highly preferred, there remains a non-trivial share of consumers who prefer whiter pork even after quality grade labeling. Overall, this study offers several insights that can help inform labeling and quality grading policies.

Ranking Supply Function and Cournot Equilibria in a Differentiated Product Duopoly With Demand Uncertainty

In this paper, we provide a welfare ranking for the equilibria of the supply function and quantity competitions in a differentiated product duopoly with demand uncertainty. We prove that the expected consumer surplus is always higher under the supply function competition. By numerical simulations, we also show that if the degree of product substitution is extremely low, then the supply function competition can become a superior form of competition for the duopolistic producers, as well. However, if the degree of product substitution is not extremely low, then the expected producer profits under the supply function competition can be lower than under the quantity competition in situations where the size of the demand uncertainty is below a critical level. We find that this critical level is non-decreasing in the degree of product substitution, while non-increasing both in the marginal cost of producing a unit output and in the own-price sensitivity of each inverse demand curve. Our results imply that in electricity markets with differentiated products, the regulators should not intervene to impose the quantity competition in favor of the supply function competition unless the degree of product substitution is sufficiently high and the predicted demand fluctuations are sufficiently small.

Cournot Competition in Wholesale Electricity Markets: The Nordic Power Exchange, Nord Pool

Horizontal shifts in bid curves observed in wholesale electricity markets are consistent with Cournot competition. Quantity competition reduces the informational requirements associated with evaluating market performance because the markups of all producers then depend on the same inverse residual demand curve instead of one for each firm. We apply the model to the day-ahead market of the Nordic power exchange, Nord Pool, for the years 2011-2013. Results suggest that mark-ups were 8-11 percent. We find some support for the hypothesis that the division of Sweden into price areas in 2011 increased the exercise of market power.

The size of the critical mass as a function of the strength of network externalities: a mobile telephone estimation

The amount of financial incentives required to stimulate network growth depends on the size of the critical mass which, in its turn, depends on the intensity with which network externalities play their role in the diffusion process. The measurement of the strength of network effects and all that can enforce or depress them is fundamental for forecasting the diffusion of new goods. Looking at the mobile telephone network for the OECD countries surveyed between 1989 and 2006, we propose a new methodology which allows us to estimate the size of the critical mass through the estimation of the parameters which determines the concavity degree of the inverse demand curve for mobiles. We found that socio-demographic variables, as well as variables which proxy the efficiency of fixed-line operators or the availability and cost of alternative services, affect the strength of network effects and, therefore, the critical mass size.

Capacity Investment with Dynamic Operation and Intertemporal Budget Balance

AbstractWe characterize the optimal investment and production path in a project characterized by indivisible capacity and stochastic inverse demand curve. At first best (without budget requirements), the investment is made earlier the lower the price elasticity of demand, causing the trajectory of production to be below the trajectory of capacity. At second best (when the investor is required to break even), the investment delay is upward distorted, the distortion being larger the lower the price elasticity of demand. Moreover, in the particular case of constant elasticity demand, investment is delayed but production remains at its first‐best level.

An Existence Theorem for Cournot-Walras Equilibria in a Monopolistically Competitive Economy

We establish an existence theorem for the Cournot-Walras equilibria in the model which consists of a representative consumer and n-monopolistically competitive firms. Instead of the traditional approach which depends on Kakutani’s fixed point theorem, we employ the theory of the relationship between games with monotone best responses and potential games. We show that, under some conditions on a utility function and production technologies, the profit maximization game is the (pseudo) best reply potential game and hence, the existence of the equilibria is proved independently of the well known convexvalued assumption on best responses. The key property is the separability of the utility function. We exclude neither cost-diminishing technologies nor the existence of fixed costs. In addition, in our framework, the rationality of each monopolistically competitive firm can be alleviated in the sense that it can figure out the inverse demand curve from less information than is required in existing studies.

Direct network effects, small-world networks, and industry formation

This paper addresses the formation of industries that involve direct network effects. Using two concepts from the literature on network effects (critical mass and inverse demand curves) and descriptive data from the formation of five telecommunication-related industries, this paper argues that a critical mass of users was created multiple times in these industries where multiple critical masses of users can be represented as local maximums in an inverse demand curve. The existence of these multiple local maximums reflects the existence of different sub-populations of users within a total population of potential users where these populations of users can be considered small-world networks. Initially the different sub-populations represent fragmented networks of users that are served by fragmented networks of firms. Over time connected networks of both firms and users emerge.

Comparison of four contingent valuation methods to estimate the economic value of a pneumococcal vaccine in Bangladesh

To compare four contingent valuation elicitation methods as a means to estimate the value of a pneumococcal vaccine in Bangladesh and to test if the elicitation methods are subject to bias and if they produce valid responses. Three hundred sixty-one households with at least one child under 5 years of age were recruited in Dhaka, Bangladesh. Subjects were cluster-randomized to various elicitation methods: open-ended, dichotomous choice (at one of two asking prices), payment card (one of two cards with differing ranges). The dichotomous choice method was then followed up with a bidding game methodology, with the dichotomous choice price acting as the starting price for the bidding game. Analysis focused on summary statistics, demand curve estimation and multivariate regression analysis to test for validity and bias. Thirty-one households refused to participate, leaving a total of 330 participating households (a 91.4 percent response rate). Willingness to pay estimates varied significantly across the methods (p < .001), with average estimates varying between $2.34 and $18 (US). The open-ended elicitation method was found to produce highly inflated values that were insensitive to construct validity tests. The dichotomous choice method produced quantity (demand) estimates rather than value estimates, and there was some evidence of yea-saying. The payment card elicitation method was found to be affected by range bias. The bidding game elicitation method was found to be less sensitive to starting point bias and yea-saying. Different elicitation format do give rise to different demand curves; however, this may be partially due to the fact that they do not measure the same outcome. For example, the dichotomous choice format produces a demand curve, while the payment card, open-ended and bidding game produce inverse demand curves. All formats are prone to multiple biases. When choosing an elicitation format, it is important to first consider the purpose and use of the data. Each elicitation method has strengths and weaknesses and can be used for different purposes in technology assessment.

Auction hosting site pricing and market equilibrium with endogenous bidder and seller participation

This paper characterizes the payoffs and pricing policies of auction hosting sites when both the bidders’ and the sellers’ participation is endogenous. Sellers have heterogeneous opportunity costs and make a listing decision depending on the listing fee and the expected revenue from the sale. On the other side of the market, factors such as facility in navigating an interface layout and prior bidding experience result in bidder heterogeneity with respect to participation costs. Bidders participate if their ex ante expected payoff from searching the site exceeds their participation costs. The auction site earns revenue by setting positive listing fees, trading off the increased revenue per seller resulting from a higher fee with the revenue reduction from the loss of sellers. Though this appears to be a classic monopoly problem, there are important differences. The reduction in the number of sellers participating in a site has feedback effects, as it affects the number of bidders who choose to visit that site, which in turn again affects the attractiveness of the site to sellers, and thus further reduces seller participation. In this environment the monopolist’s ability to extract rents is severely limited, even if one considers rent extraction from the seller side of the market only. It is demonstrated that the inverse demand curve is flatter than the demand curve obtained from the (inverse) distribution of seller costs. Moreover, the inverse demand curve has at least one and possibly multiple flat segments, leading to discontinuities in the profit function. Thus, small changes in the environment can lead to large changes in the optimal fee and market participation.

Auction Hosting Site Pricing and Market Equilibrium with Endogenous Bidder and Seller Participation

This paper characterizes the payoffs and pricing policies of auction hosting sites when both the bidders' and the sellers' participation is endogenous. Sellers have heterogeneous opportunity costs and make a listing decision depending on the fee and the expected revenue from the sale. On the other side of the market, factors such as interface layout and prior bidding experience result in bidder heterogeneity with respect to participation costs. Bidders participate if their ex ante expected payoff from searching the site exceeds their participation costs. The auction site earns revenue by setting positive listing fees, trading off the increased revenue per seller resulting from a higher fee with the revenue reduction from the loss of sellers. Though this appears to be a classic monopoly problem, there are important differences. The reduction in the number of sellers participating in a site has feedback effects, as it affects the number of bidders who would choose to visit that site, which in turn again affects the attractiveness of the site for seller, and thus further reduces seller participation. In this environment, the monopolist's ability to extract rents is severely limited, even if one considers rent extraction from the seller side of the market only. It is demonstrated that the inverse demand curve is flatter than the demand curve obtained from the (inverse) distribution of seller costs. Moreover, the inverse demand curve has at least one and possibly multiple flat segments, leading to discontinuities in the profit function. Thus, small changes in the environment can lead to large changes in the optimal fee and market participation.

EXPORT SUBSIDIES VERSUS EXPORT QUOTAS WITH INCOMPLETELY INFORMED POLICY MAKERS

This paper analyses export subsidies (price incentives) and export quotas (quantity controls) in the Brander-Spencer (1985) model when policy makers have limited information on demand and cost structures. We examine necessary or sufficient information for policy makers to determine welfare-enhancing policies. It is crucial that they know the elasticity value of the slope of the inverse demand curve and the market share. It is also shown that for policy makers, export quotas are superior to export subsidies under certain conditions.

Long-Run Substitutability Between More and Less Educated Workers: Evidence from U.S. States, 1950–1990

We estimate the aggregate long-run elasticity of substitution between more educated workers and less educated workers (the slope of the inverse demand curve for more relative to less educated workers) at the U.S. state level. Our data come from the (five) 1950–1990 decennial censuses. Our empirical approach allows for state and time fixed effects and relies on time- and state-dependent child labor and compulsory school attendance laws as instruments for (endogenous) changes in the relative supply of more educated workers. We find the aggregate long-run elasticity of substitution between more and less educated workers to be around 1.5.

Horizontal mergers and exit in declining industries

Previous work on exit in declining industries has neglected mergers. This paper examines a simple model that illustrates how mergers can affect the order of exit. The model also predicts which declining industries experience horizontal mergers. Mergers are more likely if (1) the inverse demand curve is steep at high levels of output and flat at low levels of output; (2) the industry declines slowly early on and rapidly later on; and (3) market concentration is high. The conditions that make mergers privately profitable also tend to make them socially optimal.