In this section we will examine the conditions of social welfare maximisation in the simple two-factor, two-commodity, two-consumer model.
The assumptions of our analysis are listed below:
1. There are two factors, labour L, and capital K, whose quantities are given (in perfectly inelastic supply). These factors are homogeneous and perfectly divisible.
2. Two products, X and Y, are produced by two firms. Each firm produces only one commodity. The production functions give rise to smooth isoquants, convex to the origin, with constant returns to scale. Indivisibilities in the production processes are ruled out.
3. There are two consumers whose preferences are represented by indifference curves, which are continuous, convex to the origin and do not intersect.
4. The goal of consumers is utility maximisation and the goal of firms is profit maximisation.
5. The production functions are independent. This rules out joint products and external economies and diseconomies in production.
6. The utilities of consumers are independent. Bandwagon, snob and Veblen effects are ruled out. There are no external economies or diseconomies in consumption.
7. The ownership of factors, that is, the distribution of the given L and K between the two consumers, is exogenously determined.
8. A social welfare function, W=ƒ (UA, UB), exists. This permits a unique preference-ordering of all possible states, based on the positions of the two consumers in their own preference maps. This welfare function incorporates an ethical valuation of the relative deservingness or worthiness of the two consumers.
The problem is to determine the welfare-maximising values of the following variables:
(a) The welfare-maximising commodity-mix, that is the total quantity of X and Y (production problem).
(b) The welfare-maximising distribution of the commodities produced between the two consumers, XA, XB, YA, YB (distribution problem).
(c) The welfare-maximising allocation of the given resources in the production of X and Y, LX, Ly, Kx, Ky (allocation problem).