Unit Vs. Ad Valorem Taxes in Multi-Product Cournot Oligopoly

The welfare dominance of ad valorem taxes over unit taxes in a single-market Cournot oligopoly is well-known. This article extends the analysis to multi-market oligopoly. Provided all ad valorem taxes are positive, unit costs are constant, firms are active in all considered markets, and a representative consumer has convex preferences, it is shown that ad valorem taxes dominate in multi-product equilibrium. We discuss the role of unit cost covariances across multi-product firms in determining the extent of cost efficiencies arising under ad valorem taxation. The issue of merger under oligopoly is also considered. Conditions are identified under which a merger increases the sum of consumer and producer surpluses while also increasing the revenue yield from a set of unit taxes. If not all firms are active in all considered markets, then it is also shown that additional conditions are required to ensure the dominance of ad valorem taxes. In multi-input Cournot oligopsony, however, unit taxation welfare dominates. This is because ad valorem taxes on inputs reduce demand elasticities, amplifying market power distortions.ad valorem tax; imperfect competition; oligopoly merger; quantity-setting game; specific tax; tax efficiency; tax revenue

Cost Arrangement and Welfare in a Multi-Product Cournot Oligopoly

Welfare in a two-product Cournot oligopoly is shown to increase (decrease) with an increase in correlation between unit costs when the outputs complement (substitute) in demand. A more qualified correlation structure is required for the result to apply in a three-product Cournot oligopoly when products complement in demand.complementarity; arrangement increasing; invariance

When Different Market Concentration Indices Agree

Market concentration ratios are popular statistics for characterizing the extent of market dominance in an imperfectly competitive market, but these ratios may not agree when comparing two markets. Neither do they necessarily agree with the Herfindahl-Hirschman or entropy indices. This letter compares two Cournot oligopoly markets in which firms have constant unit costs. It is shown that the majorization pre-ordering on normalized marketing margin vectors is both necessary and sufficient for all aforementioned indices to agree on which is the more concentrated market.

Algebraic Theory of Multi-Product Decisions, An

The typical firm produces for sale a plural number of distinct product lines. This paper characterizes the composition of a firm?s optimal production vector as a function of cost and revenue function attributes. The approach taken applies mathematical group theory and revealed preference arguments to exploit controlled asymmetries in the production environment. Assuming some symmetry on the cost function, our central result shows that all optimal production vectors must satisfy a dominance relation on permutations of the firm?s revenue function. When the revenue function is linear in outputs, then the set of admissible output vectors has linear bounds up to transformations. If these transformations are also linear, then convex analysis can be applied to characterize the set of admissible solutions. When the group of symmetries decomposes into a direct product group with index K in N, then the characterization problem separates into K problems of smaller dimension. The central result may be strengthened ; when the cost function is assumed to be quasiconvex.

Taste Asymmetries and Trade Patterns

We study trade patterns in a pure exchange economy where preferences are symmetric up to taste intensity parameters. In a 2-person, 2-good endowment economy, then all endowments in a particular Edgeworth box rectangle require trading out of that rectangle. Under strictly quasi-concave preferences, trade will occur away from a larger area of initial endowments. The identified area is larger still when preferences are homothetic and identical up to taste intensity parameters. Implications for the factor price equalization theorem are explored.

Buying Ecological Services: Fragmented Reserves, Core and Periphery National Park Structure, and the Agricultural Extensification Debate

�Growing demand for cropland products has placed intense pressure on the abilityof land resources to support nature, straining public budgets to purchase environmental goods.Fixing overall agricultural output, two environmental policy options are whether to a) promotemore agricultural extensification and nature friendly farming practices or b) produce intensivelyon some land and leave the rest wild. Microeconomic models of the topic have not accounted forwidely recognized spatial externalities regarding fragmented reserves. This article does so, usingWirtinger’s inequality to also identify a third policy possibility. This is that ecological servicescan follow a smoothly varying spatial path chararacterized by harmonic functions. We use theresults to rationalize the core and periphery National Park structure put in place around theworld, i.e., versions of our third policy possibility have been implemented.Environmental policy; Land use; National Park management; Spatial externalities; Wirtinger’s inequality

Ordinal Approach to Characterizing Efficient Allocations, An

The invisible hand theorem relates nothing about the attributes of the optimal allocation vector. In this paper, we identify a convex cone of functions such that order on vectors of exogenous heterogeneity parameters induces component-wise order on allocation vectors for firms in an efficient market. By use of functional analysis, we then replace the vectors of heterogeneities with asymmetries in function attributes such that the induced component-wise order on efficient allocations still pertains. We do so through integration over a kernel in which the requisite asymmetries are embedded. Likelihood ratio order on the measures of integration is both necessary and sufficient to ensure component-wise order on efficient factor allocations across firms. Upon specializing to supermodular functions, familiar stochastic dominance orders on normalized measures of integration provide necessary and sufficient conditions for this component-wise order on efficient allocation. The analysis engaged in throughout the paper is ordinal in the sense that all conclusions drawn are robust to monotone transformations of the arguments in production.arrangement monotone; functional analysis; market structure; ordinal analysis; simplex; symmetry

Taste Asymmetries and Trade Patterns

We study trade patterns in a pure exchange economy where preferences are symmetric up to taste intensity parameters. In a 2-person, 2-good endowment economy, then all endowments in a particular Edgeworth box rectangle require trading out of that rectangle. Under strictly quasi-concave preferences, trade will occur away from a larger area of initial endowments. The identified area is larger still when preferences are homothetic and identical up to taste intensity parameters. Implications for the factor price equalization theorem are explored.general equilibrium

Statistical Moments Analysis of Production and Profits in Multi-Product Cournot Oligopoly

Our context involves N firms producing M products at constant marginal costs, and behaving as Cournot oligopolists. When preferences are quasi-linear, we study the relationships between second moments of unit costs and second moments of firm-level production. Larger variance in unit costs of a product increases own output variance and variance of any other output. We also investigate how second moments of unit costs affect the first and second moments of profit across firms. Larger variance in unit costs can reduce profit variance, even for a single product oligopoly.

Market Cycles for a Non-Storable Product Under Adjustment Costs

When adjustment costs are present, cyclical preference and technology heterogeneities in a product’s markets induce cycles in production. We exploit cyclic and dihedral group invariances in an industry’s cost technology to describe these patterns. We show when equilibrium cyclical pricing and production patterns are ordered according to demand patterns. Our approach allows us to identify periods when prices may fall below unit costs, net of adjustment costs. Social welfare preferences over cyclical demand and supply heterogeneities are identified. We study the particulars of cycle dynamics when demand is linear and adjustment costs are quadratic. The analysis is developed for when external trade is impossible and when it is possible.dihedral groups; production patterns; social welfare; external trade; group majorization