In classical Computable General Equilibrium (CGE) models all decisions are about continuous quantities, represented by non-negative real numbers. In a spatial framework it is however natural to allow for discrete choices, like choice location of residence and/or and location of work. Another case in point is the choice of mode for transporting a certain commodity between locations. A common practice in the literature is to embed a logit choice model into the general equilibrium, with prices and possibly some other determinants of choice as arguments in the logit function. In this paper I discuss the problems inherent in this approach and how to solve them. I first deal with the case of households choosing locations. An obvious way of handling this case is to replace representative agents by sets of such agents. An individual in the set is an element of a probability space, with varying preferences or technologies across the probability space. Under an appropriate assumption regarding the distribution of preferences one obtains a logit model in which the logs of real income appear as arguments, as in Anas? urban models. One has to be careful, however, to specify welfare effects of shocks in a theoretically consistent way for this case. I show that basing welfare measures on expected real income may lead to perverse cases where welfare declines though no real income goes down. I show how to fix this problem by defining a theoretically consistent Hicksian Equivalent Variation measure defined as the minimal amount of money needed at the reference state to make all individuals in the above mentioned probability space as well off as in the alternative state which is to be evaluated. Though this measure cannot be obtained in closed form, it is nevertheless easily calculated by Monte-Carlo simulation to any desired accuracy. I compare this measure with measures used in practice for a set of artificial examples. I then treat the case where firms discretely choose between inputs. In this case it is assumed that there exists a probability distribution over qualities of a given commodity stemming from different sources. If the logs of qualities follow a Gumbel-distribution and the discrete choice is embedded into a CES demand system, then a nested CES system is obtained. This generalises a famous result of Anderson, De Palma and Thisse (Ec. Letters 24: 1987).
