Two extensions of consumer surplus

We study consumer surplus in a single market when (a) there is a lower bound in the consumption of the outside good and (b) the weights in the social welfare function given to consumers and firms are different. We assume quasilinear utility. When the lower bound constraint on the consumption of the outside good is binding, income effects arise in demand. In some cases, Cournot equilibrium output is below equilibrium output without this constraint because the constraint makes demand less elastic. When the weights given to consumers and firms are not identical, social welfare is not necessarily concave and profits might be negative at the unrestricted optimum. We characterize social welfare optimum with a bound on maximum losses in a class of utility functions. We offer a formula to find the percentage of welfare losses due to oligopoly in this case.

Quasilinear Utility and Two Market Monopoly

The use of quasilinear utility functions in economic analyses is widespread. This paper presents an overdue clarification on the implications of quasilinear utility for two market monopoly. The paper begins by deriving the demands facing a two market monopoly from a representative consumer with quasilinear utility. Expressions are derived for the profit margins expressed solely in terms of the own and cross-price elasticities of demand. The paper also analyzes the implications of quasilinear utility for other issues in two market monopoly: pricing below marginal cost in a market, third-degree price discrimination when the monopoly products are substitutes and pricing in the inelastic region of demands.

Surplus Maximization and Optimality

Expected consumer's surplus rarely represents preferences over price lotteries. Still, I give sufficient conditions for policies which maximize aggregate expected surplus to be interim Pareto Optimal. Besides two standard partial equilibrium conditions, I assume that feasible prices satisfy a single-crossing property; and each consumer's indirect utility satisfies increasing differences in the price and income. I use the result to extend well-known welfare conclusions beyond the knife-edge quasilinear utility case. Since increasing differences puts no upper bound on risk aversion, the result is useful for applications in which risk aversion is important. (JEL D11, D24, D42, D81, D83, L42)

The linearised Hamiltonian as comprehensive NDP

For guidance in determining which items should be included in comprehensive NDP (net domestic product) and how they should be included, reference is often made to the linearised Hamiltonian from an optimal growth problem. The paper gives a rigorous interpretation of this procedure in terms of a money-metric utility function linked to familiar elements of standard welfare theory. A key insight is that the Hamiltonian itself is a quasilinear utility function, so imposing the money-metric normalisation is simply equivalent to using Marshallian consumer surplus as the appropriate measure of welfare when there are no income effects. The twin concepts of the ‘sustainability-equivalence principle’ and the ‘dynamic welfare-comparison principle’ are explained, and it is indicated why these two principles are important for the theory of national income accounting.

Verallgemeinerungen einfacher quasilinearer Nutzenfunktionen / Generalization of Simple Quasilinear Utility Functions

ZusammenfassungQuasilineare Nutzenfunktionen oder Nutzenfunktionen ohne (partiellen) Einkommens- oder Vermögenseffekt spielen in der modernen Ökonomik eine wichtige Rolle. Sie liefern nicht nur nützliche Approximationen, sondern sind häufig notwendige Restriktionen bei der Ableitung zentraler Theoreme. Die verwendete funktionale Form spezifiziert eine Funktion, für die additive Separabilität gilt, und bei der die Variable, die den Einkommens- oder Vermögenseffekt trägt, als linearer Term erscheint. Die Funktion ist also quasilinear. Gezeigt wird zunächst, daß sich die Annahme der strengen Additivität durch die schwächere Annahme der strengen Separabilität ersetzen läßt. In einem weiteren Schritt wird die Analyse auf den Fall vieler Variablen verallgemeinert. Zwei Gruppen von Variablen sind streng separabel in eine Nutzenfunktion einbezogen. Der Einkommens- bzw. Vermögenseffekt läßt sich für die erste Gruppe von Variablen eliminieren, wenn die zweite Gruppe von Variablen sich als eine linear homogene Funktion schreiben läßt. Die erste Gruppe von Variablen muß demgegenüber als streng konkave Funktion geschrieben werden. Der Ausgangspunkt der Überlegungen waren jeweils die Bedingungen 1. und 2. Ordnung.