On resource-oriented multi-commodity market computations

Ambiguity in Fama's Market Equilibrium?

We introduce credit frictions motivated by moral hazard in a general equilibrium model of international trade with two dimensions of heterogeneity and endogenous investments. Firms’ competitiveness consists of capabilities to conduct process and quality innovations at low costs, whereas investment outlays have to be financed by external capital. We show that the scope for vertical product differentiation in a sector determines how credit tightening affects investment and price setting. Consistent with recent empirical evidence, our model rationalizes positive as well as negative correlations of firm-level FOB prices with financial frictions and variable trade costs. Faced with an increase in the borrowing rate, producers reduce both types of innovation resulting in opposing effects on marginal production costs and prices. In general equilibrium, financial frictions intensify quality-based (cost-based) sorting of firms if the scope for vertical product differentiation is high (low). Consequently, credit tightening leads to firm exit, increased innovation activity among existing suppliers, and welfare losses that are larger in sectors with low investment intensity.

On the Foreign Exchange Risk Premium in Stick-Price General Equilibrium Models

The existence, determination, and effects of competitive market equilibrium for unit commitment power pool auctions are investigated in this paper. When an equilibrium does not exist, under specific situations conflictive multiple optimal primal solutions may exist. When an equilibrium exists, multiple primal solutions do not represent conflicts of interest. The existence or nonexistence of competitive equilibrium can be determined if the dual problem is solved to optimality. If equilibrium does not exist, there is excess supply at the optimal dual solution, which can be used to define priority orders and price-setting altematives to determine a final schedule, and avoid the conflicts of interest and revenue deficiency. Under disequilibrium, the optimal dual variables are not market clearing prices; a nonuniform pricing rule that avoids the flaws and complications of other pricing rules, such as maximum average cost and price minimization auctions, is proposed in the paper. The proposed scheduling and price-setting alternatives show that unit commitment models can be used in a market environment.

Promotions are a critical decision for supermarket managers, who must decide the price promotions for a large number of items. Retailers often use promotions to boost the sales of the different items by leveraging the cross-item effects. We formulate the promotion optimization problem for multiple items as a nonlinear integer program. Our formulation includes several business rules as constraints. Our demand models can be estimated from data and capture the postpromotion dip effect and cross-item effects (substitution and complementarity). Because demand functions are typically nonlinear, the exact formulation is intractable. To address this issue, we propose a general class of integer programming approximations. For demand models with additive cross-item effects, we prove that it is sufficient to account for unilateral and pairwise contributions and derive parametric bounds on the performance of the approximation. We also show that the unconstrained problem can be solved efficiently via a linear program when items are substitutable and the price set has two values. For more general cases, we develop efficient rounding schemes to obtain an integer solution. We conclude by testing our method on realistic instances and convey the potential practical impact for retailers. This paper was accepted by Yinyu Ye, optimization.

The search for equilibrium in a two-stage traffic flow model reduces to the solution of a special nonsmooth convex optimization problem with two groups of different variables. For numerical solution of this problem, it is proposed to use the accelerated block-coordinate Nesterov–Stich method with a special choice of block probabilities at each iteration. Theoretical estimates of the complexity of this approach can appreciably improve the estimates of previously used approaches. However, in the general case they do not guarantee faster convergence. Numerical experiments with the proposed algorithms are carried out.

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.

Price setting under uncertainty about inflation

Abstract. The purpose of the article is to substantiate the concept and to build a model of partial economic equilibrium of the automotive products market by market segments (cars, trucks and buses) on the basis of the Walras and Errow-Debre equilibrium models. The provisions and limitations of the Walras equilibrium model are considered and analyzed. The market of automobile products of Ukraine is researched, trends of its change are identified and the main types of restrictions regarding its functioning are identified. The possibility of applying a modified model of the general market equilibrium to describe the functioning of the automotive market is established, as well as the substantive conceptual provisions for the construction of the partial economic equilibrium model are substantiated. The developed model describes the interaction of market economy actors in the production and consumption of automotive products during the annual cycle. The conditions of equilibrium of demand and supply of automobile products in the domestic market are outlined, taking into account the openness of the Ukrainian economy, and the restrictions on the solvent demand of the population are shown. The role of the state as an influential side of interaction, aiming to obtain maximum budget revenues through the formation of an adequate tax policy, is argued. Given the role and importance of the development of the automotive industry as one of the strategic sectors of the Ukrainian economy, modeling of the economic equilibrium of the automotive market is of particular importance. The developed model of partial economic equilibrium is based on the formed conceptual provisions on the conditions of functioning of the market of automobile products of Ukraine and describes the market interaction of its three participants - consumers, manufacturers and the state. It can be interpreted as an analytical reflection of the process of production and consumption of automobile products during a one-year cycle of interaction between market economy actors. Reflection in the model of institutional constraints, which describe the role of the state in the process of seeking economic equilibrium, helps to increase its adequacy to real market conditions. Keywords: general equilibrium model, partial economic equilibrium, market conditions, supply and demand, interaction, automotive market, optimal solution. Formulas: 15; fig.: 0; tabl.: 1; bibl.: 16.

Price Dispersion in a Model with Middlemen and Oligopolistic Market Makers: A Theory and an Application to the North American Natural Gas Market

A quais-equilibrium is a set of prices that results in a balanced inflation. This paper sets forth a simpale general equilibrium model with money and proves the existence of a quasi-equibrium.

We construct experimental economies, populated with human subjects, with a structure based on a nonlinear version of the New Keynesian Dynamic Stochastic General Equilibrium (DSGE) model. We analyze the behavior of firms' pricing decisions in four different experimental economies. We consider how well the experimental data conform to a number of accepted empirical stylized facts. Pricing patterns mostly conform to these patterns. Most price changes are positive, and inflation is strongly correlated with average magnitude, but not the frequency, of price changes. Prices are affected negatively by the productivity shock and positively by the output gap. Lagged real interest rate has a negative effect on prices, unless human subjects choose the interest rate, or firms sell perfect substitutes in the output market. There is inertia in price setting, firms integrate wage increases into their prices, and there is evidence of adaptive behavior in price-setting in our laboratory economy. The hazard function for price changes, however, is upward-sloping, in contrast to most empirical studies.

We develop a framework to study implications of Quality of service (QoS)-sensitive users on market equilibrium. We consider multiple competing providers each offering a queued service. Each provider posts a price and expected delay. Arriving users then pick the queue with the smallest price plus expected delay cost. We first consider the case where the providers are strategic and compete on price, when their capacity is fixed. We obtain conditions for existence of Nash equilibrium in such a game. We then consider the case where the providers invest in capacity and set price simultaneously. We intend to extend this to queues with multiple classes of service as a framework to study differentiated services in networks.

Consider a retailer, stocking a seasonal item facing a stochastic demand. The retailer places orders before the start of the season and in-season reorders are impossible. A question frequently asked is: How should one set prices throughout the selling season to optimize profits? Applications include the production of fashion goods, hotel rooms, airline seats, and car rentals. The objective function is typically non-concave, so finding an optimal solution is computationally challenging and heuristic approaches are often employed. For a T period dynamic pricing model with the expected profit objective, it was shown in the literature that the problem reduces to solving T single variable optimization problems. We extend the result by incorporating holding costs. We obtain similar simple solutions for the special cases of deterministic demands and nonnegative holding costs proportional to selling prices. For the general case, we introduce heuristics using simply structured policies.

Economists have long been interested in the functioning of forward (futures) markets. Keynes and Hicks were the first to write persuasively in support of the theory of backwardation. This theory says the futures price is biased downward relative to the expected future spot price as a means of compensating for taking long futures positions [12; 8]. In this theory, speculators are viewed as providing insurance to hedgers who desire to take short futures positions to reduce the riskiness of their commodity holdings. In addition to there are theories of unbiasedness and contango.' The unbiasedness theory says that the futures price equals the expected spot price while the contango theory says that the futures price exceeds the expected spot price [4; 19; 21]; however, the controversy over the three theories has not been entirely resolved. It has been suggested [4; 19] that each of the three theories could be applicable at various points during the planting-harvesting-processing cycle of a crop as the net hedging demand shifts from a large number of hedgers who desire to be short in the futures market to a large number of individuals who are long hedgers. Nonetheless, the traditional theories of futures markets have been criticized because they are not grounded in a general equilibrium model where participants' tastes, endowments, and beliefs interact so as to generate a market equilibrium incorporating both speculative and non-speculative transactions [9]. It is the purpose of this paper to provide a framework within which normal contango, normal backwardation, and unbiasedness can each occur for commodities which have certain well-specified characteristics, independent of the relative numbers of participants on each side of the futures market. In the spirit of [9], we consider the major source of uncertainty to be technological in nature (quantity risk) and argue that the commonly used definitions of hedger (one who sells forward some fraction of his crop yield) and speculator are not very useful for economic analysis. Instead, the more generally applicable concept of hedger as one who trades mean income for reductions in risk (in the Rothschild-Stiglitz sense [17]) is supported because it