Atkinson-Stiglitz and Ramsey Reconciled: Pareto Efficient Taxation and Pricing Under a Break-Even Constraint

35 Pages Posted: 6 Jun 2013

See all articles by Helmuth Cremer

Helmuth Cremer

University of Toulouse (GREMAQ & IDEI); Centre for Economic Policy Research (CEPR); CESifo (Center for Economic Studies and Ifo Institute)

Firouz Gahvari

University of Illinois at Urbana-Champaign - Department of Economics; CESifo (Center for Economic Studies and Ifo Institute)

Date Written: May 31, 2013

Abstract

The Ramsey tax problem examines the design of linear commodity taxes to collect a given tax revenue. This approach has been seriously challenged by Atkinson and Stiglitz (1976) who show that (under some conditions) an optimal income tax makes commodity taxes redundant. In the meantime, the Ramsey setting has had a second life as model of regulatory pricing. Boiteux (1956) studies linear pricing of a regulated multi-product monopoly that has to cover some "fixed cost" through markups on the different products (equivalent to taxes). While the scope of regulation has declined, Ramsey-Boiteux pricing continues to play an important role. This paper examines if the optimal tax and regulatory pricing approaches to Ramsey pricing can be reconciled. We incorporate the two objectives of revenue raising for financing the government's expenditures and a regulated firm's fixed cost into a single framework. The first major lesson is that the existence of a break-even constraint not only requires taxation of goods produced by the regulated firm, but also the taxation of other goods. Next, we consider the cases of independent Hicksian and Marshallian demand curves. In both the Ramsey solution imply so-called inverse elasticity rules. In the separable Hicksian demand case, the private goods (not included in the break-even constraint) continue to go untaxed as in the Atkinson and Stiglitz setting. In the case where Marshallian demands are independent, the effect of the break-even constraint spills over to the other goods which no longer go untaxed. We continue to get inverse elasticity rules; however, there is no covariance (or similar) term that captures redistributive considerations. Finally, we study the most celebrated general result obtained in the Ramsey model; namely, the (un)equal proportional reduction in compensated demands property. We find that the redistributive considerations are once again replaced by tax revenue terms.

Keywords: Atkinson-Stiglitz theorem, Ramsey, Pareto efficient taxation, break-even constraint

JEL Classification: H210

Suggested Citation

Cremer, Helmuth and Gahvari, Firouz, Atkinson-Stiglitz and Ramsey Reconciled: Pareto Efficient Taxation and Pricing Under a Break-Even Constraint (May 31, 2013). CESifo Working Paper Series No. 4248, Available at SSRN: https://ssrn.com/abstract=2274637

Helmuth Cremer (Contact Author)

University of Toulouse (GREMAQ & IDEI) ( email )

Toulouse, 31000
France
+33 1 6112 8606 (Phone)
+33 1 6112 8637 (Fax)

Centre for Economic Policy Research (CEPR)

London
United Kingdom

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

Firouz Gahvari

University of Illinois at Urbana-Champaign - Department of Economics ( email )

313 David Kinley Hall, 1407 West Gregory Drive
Urbana, IL 61801
United States

HOME PAGE: http://www.economics.illinois.edu/people/fgahvari

CESifo (Center for Economic Studies and Ifo Institute) ( email )

Poschingerstr. 5
Munich, DE-81679
Germany

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