Market Demand Functions in the CAPM

Dynamic Pricing in an Evolving and Unknown Marketplace

The empirical content of Cournot competition

Most modern financial research can be characterized as theoretical or empirical, or a mix of the two. Theoretical finance can be divided in the way that theoretical economics is. Neoclassical research stems from the neoclassical economics of perfectly competitive markets that have no imperfections or frictions, such, as taxes, transaction costs, externalities, or information asymmetries. By definition, imperfect markets research includes all other topics, such as the study of taxes, institutions, and topics stemming from information economics. Darrell Duffie's new book is an introduction to neoclassical finance that emphasizes topics in the intersection of theoretical finance and the mathematical economics of general equilibrium. The book is designed to take the student from first principles to the frontiers of finance-oriented general equilibrium theory. The book contains a rigorous introduction to the necessary topics in probability and stochastic control and is a good source for that material. It also contains a good summary of general equilibrium theory, including the required background mathematics. Each theorem from the general equilibrium literature is presented in a form that is general enough to be applicable to continuous-time models in finance but is as simple as possible given that level of generality. Other variations are mentioned in the literature reviews at the end of each section.

A marketing system is efficient if it is able to deliver production results to consumers at the lowest possible cost and relatively even margins to the actors involved. But in reality, when production is in surplus while demand is not, it causes the market mechanism to produce price distortions. This study aims to analyze the rice marketing system with an organizational approach and market demand (market trends, market demand functions, and price elasticity). The data is obtained from the relevant authorities as well as from observations and internet searches. The results showed that the marketing actors for unhusked rice/rice consisted of collectors, rice millers, inter-district traders, and retailers where almost half of the profits were enjoyed by rice mills. The results of the market demand function analysis show that rice consumption will tend to decrease if there is an increase in rice prices. Consumers will divert some of their consumption expenditure on rice substitute products. The results of market trend analysis show that rice consumption has a positive trend over time. Keywords: Market Demand, Market Trends, Organizational Approach, Price Elasticity, Rice Marketing System.

This paper discusses the Sonnenschein–Mantel–Debreu (SMD) theorems in general equilibrium theory. It argues that the SMD results were related to the previous literature on the integrability of demand. The integrability question involved rationalizing individual demand functions, and the SMD theorems asked the same question about aggregate (market) excess demand functions. The paper’s two goals are to demonstrate how the SMD results followed naturally from the earlier work on integrability, and to point out that the profession’s reception was quite different; the integrability results were considered a success story, while the SMD results were quite negative.

OVER THE PAST THIRTY YEARS OR SO, the problem of the stability of a competitive general equilibrium system has been extensively studied by many economists. The first efforts at formulating the problem date back to Hicks [10], though it is well known that his analysis was purely static in nature. Taking off from Hicks' work, a number of authors (e.g., Samuelson [18], Metzler [14]) considered the dynamic stability of a linearized general equilibrium system and related their stability conditions to those obtained by Hicks. More recently, the stability of nonlinear general equilibrium systems has received a good deal of attention, and this more modern treatment originated primarily with the work of Arrow and Hurwicz [1].1 While these works indicate very clearly that major advances have been achieved in the study of stability, they all suffer from one serious defect in that they do not permit stochastic elements to be present. Therefore, the objective of the present paper is to introduce random shocks into a general equilibrium model and to investigate the resulting stability properties of such a system. This is obviously an important extension of the theory since random disturbances can enter the system in a number of ways, and in doing so possibly introduce destabilizing elements. For example, both the supply and demand functions may be subject to random shifts both in position and slope due to unforeseen exogenous factors such as changes in taste or technological uncertainties. Alternatively, the random element may be introduced because the process tatonnment which describes the adjustment to equilibrium (to be described presently) does not hold exactly. We shall interpret our results from both these standpoints. When confronted with the task of making choices in a world which is both dynamic and stochastic, individual decision makers will tend to base their behavior not only on current values of relevant variables, but also on their expected future values. For example, their expectations concerning future price movements are likely to be a very important determinant of their actions during the current period, since they will indicate how desirable it is to make a particular purchase now rather than later. Furthermore, since the current price is only a short run market equilibrium, it is quite likely to change in response to random disturbances and cannot be relied upon to provide accurate information about what future equilibrium prices are likely to be. Hence we shall assume that the excess demand functions (to be introduced in Section 2) depend on both current and expected future prices. In

In the literature on labor-managed firms, competitive or monopolistic or oligopolistic firms are assumed to produce only one homogeneous good. Therefore, the firms try to maximize the surplus per worker net of the competitively determined wage by adjusting output levels, and the sum of the firms' equilibrium outputs determines uniquely the equilibrium market price of the product through the market demand function. If product differentiation exists as is universally observed in modern economies, the labormanaged oligopolistic firms can maximize the surplus per worker by optimally adjusting either output levels ?r prices of their products. In the profit maximizing oligopoly with product differentiation, different sets of equilibrium prices emerge depending on whether firms choose outputs or prices as their strategic variables. Take a simple example of duopoly where two firms have the following demand functions.

A New Approach for General Equilibrium with Discontinuous Excess Demand Function

A novel perspective on closed-loop supply chain coordination: Product life-cycle approach

The article presents a dynamic stochastic general equilibrium model (DSGE-model) for the Russian economy. The model describes the behavior of the following macroeconomic agents: households, real sector, banking sector, Central Bank, as well as the interactions between them and the world. Household modeling uses the external habit formation approach to account for the inertia of preferences. To model the real sector, we abandoned the most common approach which assumes that the decision on investments is made by the households as the owners of production factors. Instead, we took the firm-specific capital approach which assumes that the decision on investment is made by the firms themselves. The study also considers that in Russia, fixed assets are mostly invested from the firms' own funds. To account for the investment inertia in the fixed asset in a real sector model, the expenditures are transferred to the commissioning of new facilities, the Calvo model is applied to describe the price setting under the monopolistic competition. A banking sector which defines the loan and debt interest rates to the key Central Bank interest rate is chosen to be a link between the households and firms in the model. The Taylor equation is used to describe the monetary policy of the Bank of Russia under the inflation targeting, while an inertia factor is included into the equation with the uncovered interest parity for the budget rule which regulates the purchases (or sales) of the currency by the National Welfare Fund. The final linearized model is a system of 23 difference equations with rational expectations. Based on the proposed model, calculations were made and key macroeconomic indicators were forecasted for 2020–2021 on a quarterly basis for the Russian economy. The calculations account for the relevant recessionary factors: oil price fall, oil production cut in OPEC+ deals, quarantine measures aimed to prevent the spread of the corona virus infection, anti-recessionary measures of the RF Government. The findings show that the economic downturn in 2020 can be from 5 to 7% under COVID-19 pandemic. Growth in 2021 is estimated to be within 3–5%. The developed model can be used for scenario projecting for the Russian economy, upgrading the monetary policy of the Bank of Russia, and for developing applied quarterly projection models (QPM). The model could be further modified by including more elements: decomposing the household sector into the Ricardian and non-Ricardian ones, identifying the resources industries and industries in the real sector which manufacture the invested goods, including the key taxes and budget expenses into the model. One more promising area is to analyze the equilibrium of the interest rates when large firms could accumulate their own financial resources. This prerequisite decreases the demand for the bank loans from the real sector and, thus, leads to lower, including the negative, interest rates. The proposed approach enhances the quality of a DSGE model as a predictive tool for making the political and managerial decisions.

A recent paper by Capozza and Van Order (CVO) (1977) proposed a generalization of the Greenhut-Hwang-Ohta (GHO) (1975) analysis of pricing under three alternative types of spatial competition. The GHO analysis was based on a short-run model in which the locations of firms are assumed to be fixed. CVO accordingly proposed relaxation of this rigid assumption to examine if the GHO results also apply to the long-run zero-profit industry equilibrium. They confirmed the GHO results, which, however, they also contended, require certain particular modifications as well in the light of their own models. The CVO contribution lies in their simple model analysis of long-run industry equilibrium conditions-a generalization of the GHO analysis. However, they failed to recognize that the GHO analysis is based on another restrictive assumption regarding the form of the demand function. Moreover, they assumed even more restrictive demand conditions and misled themselves to a conclusion that L6schian competition never results in a lower price than spatial monopoly. Their conclusion is invalid since Loschian competition can be shown to result in a lower (not higher) mill price if only the demand function is assumed to be sufficiently convex to the origin (Ohta (1980)). This calls for a more general examination of conditions under which the firm's f.o.b. mill price may rise or fall due to spatial entry of rival firms. The present paper presents selected results of such examination. Section 2 briefly reviews the theory of spatial monopoly. Initially some fundamental assumptions are set forth. This is followed by derivation of the market demand function for the spatial monopolist. The market demand in turn is shown to be more or less elastic than the assumed basic demand function depending on the curvature of the latter curve. We also comment on the so-called paradox of spatial monopoly, which we claim is a misnomer. The analytical framework of Section 2 is employed in Section 3 as we generalize previous analyses and present a concise cataloguing of comparative static results of spatial competition.1 Again the basic demand characteristics, in combination with alternative types of spatial competition, are shown to play an important role in yielding the distinct elasticity results, and for that matter competitive equilibrium prices. In the process a counter-example to CVO's aforementioned argument on L6schian pricing is presented. Also discussed is the conceptual distinction between perceived and realized elasticities of demand under spatial competition, which CVO also failed to recognize. As a result, they erred in speculating that equilibrium mill prices would be the same under alternative types of spatial competition, given the size of the market area. We will show that they in fact are not. Section 4 concludes the paper by summarizing the basic results of our analysis.

This paper studies the monotonicity of individual and market demand with the aid of the indirect utility function. We identify sufficient (and in a sense, necessary) conditions on an agent's indirect utility which will guarantee that he has a monotonic demand function. Our conditions also point to a natural way of extending the result of Hildenbrand (1983). Hildenbrand showed that market demand is monontonic if the income distribution has a downward sloping density, even though individual agents' demand function might violate monotonicity. Using the indirect utility function, we introduce a measure of violations of individual monotonicity that allows us to identify a larger class of density functions that will generate a monotonic market demand.

Assessing the economic impact of public investment in Malaysia: a case study on MyRapid Transit project using a dynamic computable general equilibrium model

In this paper the possibility of computing equilibrium in pure exchange and production economies by a homotopy method is investigated. The performance of the algorithm is tested on examples with known equilibria taken from the literature on general equilibrium models and numerical results are presented. In computing equilibria, economy will be specified by excess demand function.

We investigate the welfare properties of the one-sector neoclassical growth model with uninsurable idiosyncratic shocks. We focus on the notion of constrained efficiency used in the general equilibrium literature. Our characterization of constrained efficiency uses the first-order condition of a constrained planner's problem. This condition highlights the margins of relevance for whether capital is too high or too low: the factor composition of income of the (consumption-)poor. Using three calibrations commonly considered in the literature, we illustrate that there can be either over- or underaccumulation of capital in steady state and that the constrained optimum may or may not be consistent with a nondegenerate long-run distribution of wealth. For the calibration that roughly matches the income and wealth distribution, the constrained inefficiency of the market outcome is rather striking: it has much too low a steady-state capital stock.