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.