Welfare Estimation In A General Equilibrium Model With Cites

We show that current measures of welfare changes which are all based on the compensated variation (CV) and the equivalent variation (EV) do not apply to an economy with cities. In addition, since these measures are utilized in a partial equilibrium analysis they capture only part of the effect of a welfare change. We then define measures appropriate for an urban economy in a general equilibrium framework. We first construct for each city a cost function from which we derive a city’s and, after aggregation, the economy’s, demand functions. These demands are functions of nationwide prices and of either the unearned incomes (Marshalian demand curves) or of the utility levels (compensated demand curves). From the same cost functions we also derive the Marshalian and compensated supply curves. Each point on a Marshalian demand curve is an allocation designated by the price vector and the unearned income vector. An allocation is either in perfect equilibrium, when the marginal cost in each market is equal to the market price or, if the marginal cost differs from the market price in some markets, the allocation is in imperfect equilibrium and is inefficient. Imperfect markets can be improved by moving to other allocations on the same Marshalian demand function. We construct modified versions, such as mCV and mEV, of the welfare measures CV and EV, from which we define the modified economic surplus (mES) as the ultimate welfare measure. The mES is equal to the willingness to pay for the added product produced (i.e., the area between the Marshalian demand curve and the quantity-axis), minus the added costs of production in current prices and wages, and plus the change in the differential land rents (DLR) in the cities producing the good. The analysis is then extended to cases in which more than one market price changes. We also estimate secondary effects in imperfect markets in which the market price remains constant while the price in the primary market changes.