ABSTRACT
A familiar progression from the standard theory of consumer behaviour is that to the analysis of welfare economics in the simplest context of given endowments of consumption commodities. One studies Paretoefficient allocations of those commodities and considers their relationship to competitive equilibria in a pure exchange economy. Having developed a somewhat different approach to consumer theory, we should therefore ask whether it has any implications for elementary welfare economics. (It has.)
Before entering into the (simple) technicalities of the argument, we should perhaps emphasize an obvious but fundamental point. We must not allow our focus on time to lead us astray into speaking of welfare economics as now involving an ‘allocation of time amongst agents’, rather than an allocation of commodities (as in the familiar analysis). There is no ‘stock of time’ to be allocated amongst the agents. If our analysis pertains to a time period of length T then each and every agent (who does not die in the interim) will, willy-nilly, spend time T doing one thing or another. Not even the most powerful Allocating Angel can give Smith an extra 10 hours per week by giving Schmidt 10 fewer hours per week. No matter how strongly we focus our attention on the use of time, the Allocating Angel can only allocate commodities, not time. It is for this reason that ‘commodity space’ features prominently in what follows. (It is of course true that some commodity allocations could influence agents’ abilities to modify T; for example, the allocations of rice or of penicillin. But we shall find quite enough to discuss whilst taking T to be exogenously given!)
The basic case We naturally begin with the case of two uses of time, two commodities and two agents, Agamemnon and Clytemnestra. For each agent, i, xi=Cti and stiT; rates of consumption are taken to be fixed and the same for both agents. Figure 4.1 shows the possible consumption quantities, and for Agamemnon along the ‘lower’ solid line. The ‘upper’ solid line, which is parallel to the lower one and exactly twice as ‘far out’ from the origin, shows the only combinations of commodity endowments that are capable of being allocated exactly between Agamemnon and Clytemnestra in such a way that each can satisfy the time constraint on individual consumption. Endowments within the feasible region, F, but off the solid line can, with free disposal, be reduced to endowments on that line; note that there is no welfare gain to be had from the endowment point’s being above the line. In Figure 4.2 the endowment point, e, is thus taken to be indeed on the line; it is also the origin for Clytemnestra’s consumption time constraint diagram, which is just like Agamemnon’s except that it has been rotated by 180°. (If e were moved along its line then Clytemnestra’s triangle would slide along Agamemnon’s.) Only commodity allocations lying along the common part of the two triangles, KL, are possible; at all other allocations at least one of our dramatis personae will be violating the consumption-time constraint. Note how very restricted are these permissible allocations relative to all
(otherwise) possible allocations in the box; in the standard diagram every point in the box is permitted but here only the points on a line within the area of the box are allowed, so that permitted allocations have been restricted by an order of magnitude. Moreover, if the best time use should imply a commodity allocation between K and L, for either agent, then the Pareto-efficient allocations of commodities will be still further restricted. (The Paretian Angel will never so allocate commodities that a move along KL could make both Agamemnon and Clytemnestra better off!) Consideration of consumption-time has certainly forced us to modify the familiar ‘contract curve’ within the endowment box.
