Abstract

AbstractWe 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.

Highlights

  • Since Dupuit (1844) consumer surplus has become a popular method for measuring the social optimality of allocations

  • 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

  • In this paper we study two extensions of standard consumer surplus; namely, the consideration of a nonnegativity constraint (NNC) in the consumption of the outside good and different weights for the consumer and the firm

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Summary

Introduction

Since Dupuit (1844) consumer surplus has become a popular method for measuring the social optimality of allocations. We study the effect of a lower bound on the consumption of the outside good on the consumer’s decision problem, and, on the other, the effect of different weights of consumers surplus and producers surplus on social welfare. Let us take these two points in turn. A common procedure is to plug the budget constraint in the utility function and getting rid of income to obtain 2x1/2 − px Maximizing this concave function, first-order condition (FOC) yields the inverse demand function x−1/2 = p. This paper is organized in the following manner: Sect. 2 spells the model, Sect. 3 tackles nonnegativity constraint; Sect. 4 studies social welfare when consumers and firms have different weights; and lastly Sect. 5 spells possible applications of our results and suggests new paths of research

The model
Nonnegativity of the consumption of the outside good
Monopoly equilibrium
Several firms
Social welfare when consumers and firms have different weights
When the regulator chooses prices
Conclusions
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