[Paper Review] Multi-Dimensional Pass-Through and Welfare Measures under Imperfect Competition

Takanori Adachi, Michal Fabinger|arXiv (Cornell University)|Feb 16, 2017

Fiscal Policy and Economic Growth4 citations

TL;DR

This paper develops a general framework for analyzing welfare effects under imperfect competition when firms face multiple policy interventions, introducing multi-dimensional pass-through as a key determinant of marginal cost of public funds (MCF) and tax incidence. It derives empirically relevant sufficient statistics—unit and ad valorem tax pass-through and demand elasticity—for MCF, and shows how these depend on demand curvature and market structure in price or quantity competition settings.

ABSTRACT

This paper provides a comprehensive analysis of welfare measures when oligopolistic firms face multiple policy interventions and external changes under general forms of market demands, production costs, and imperfect competition. We present our results in terms of two welfare measures, namely, marginal cost of public funds and incidence, in relation to multi-dimensional pass-through. Our arguments are best understood with two-dimensional taxation where homogeneous firms face unit and ad valorem taxes. The first part of the paper studies this leading case. We show, e.g., that there exists a simple and empirically relevant set of sufficient statistics for the marginal cost of public funds, namely unit tax and ad valorem pass-through and industry demand elasticity. We then specialize our general setting to the case of price or quantity competition and show how the marginal cost of public funds and the pass-through are expressed using elasticities and curvatures of regular and inverse demands. Based on the results of the leading case, the second part of the paper presents a generalization with the tax revenue function specified as a general function parameterized by a vector of multi-dimensional tax parameters. We then argue that our results are carried over to the case of heterogeneous firms and other extensions.

Motivation & Objective

• To extend the welfare analysis of government interventions beyond single-policy settings to multi-dimensional tax and regulatory changes.
• To develop a general framework for measuring the marginal cost of public funds (MCF) under imperfect competition with multiple policy instruments.
• To identify empirically relevant sufficient statistics for MCF, particularly unit and ad valorem tax pass-through and industry demand elasticity.
• To examine how MCF and pass-through vary under different market structures, such as price (Bertrand) and quantity (Cournot) competition.
• To generalize results to heterogeneous firms and broader policy interventions, including regulations and reporting requirements.

Proposed method

• Formalizes multi-dimensional pass-through as a vector or matrix of price responses to infinitesimal changes in multiple tax or regulatory parameters.
• Derives MCF using a general equilibrium model with general demand and cost functions under oligopolistic competition.
• Applies comparative statics to link MCF to pass-through rates of unit and ad valorem taxes, and to demand elasticity and curvature.
• Specializes the model to price and quantity competition, expressing MCF and pass-through in terms of elasticities and curvatures of demand and inverse demand functions.
• Uses a two-dimensional taxation framework (unit and ad valorem taxes) as a leading case to derive closed-form expressions.
• Generalizes results to multi-dimensional tax vectors and extends to heterogeneous firms and non-tax interventions such as sales restrictions and labor regulations.

Experimental results

Research questions

• RQ1 How does multi-dimensional pass-through influence the marginal cost of public funds under imperfect competition?
• RQ2 What are the sufficient statistics for MCF in the presence of multiple policy instruments like unit and ad valorem taxes?
• RQ3 How do pass-through rates for unit and ad valorem taxes relate under different market structures such as Bertrand or Cournot competition?
• RQ4 How do demand curvature and market competitiveness affect the pass-through of taxes and the resulting welfare costs?
• RQ5 To what extent can the framework be generalized to heterogeneous firms and non-tax policy interventions?

Key findings

• The marginal cost of public funds (MCF) can be expressed using a simple set of sufficient statistics: unit tax pass-through, ad valorem tax pass-through, and industry demand elasticity.
• In price competition, pass-through increases with the curvature of the inverse demand function, and this effect is not mitigated by the degree of market competitiveness.
• For quantity competition, the pass-through of unit and ad valorem taxes depends on the curvature of the demand function and the degree of product differentiation.
• The relationship between unit and ad valorem tax pass-through is analytically derived and shown to depend on market structure and demand curvature.
• The framework generalizes to multi-dimensional tax vectors and applies without change to symmetric multi-product oligopolies.
• The results extend to non-tax interventions such as sales restrictions, labor regulations, and reporting requirements, with pass-through serving as a key welfare determinant.