In a Walrasian economy, differences among agents in their attitudes towards risk do not constitute an inducement to trade. This is an outcome of the assumption of existence of a complete system of markets in contingent commodities.1 The assumption is, however, empirically unjustified. It is this observation that underlies the implicit theory of employment introduced by Baily (1974) and Azariadis (1975) and further elaborated by Baily (1975), Sargent (1975), Feldstein (1976), Negishi (1976) and Varian (1976). The assumptions and conclusions of the implicit contract theory can be briefly summarized as follows: It is assumed that a firm has a certain pool of workers associated with it and faces an uncertain price for its output. It is further postulated that the firm's objective function is the expected value of its profits, while workers desire to maximize the expected utility of their income, the latter characterized by risk aversion. The firm chooses the employment contract which maximizes its expected profit subject to the constraint that it provide the workers with a minimum of expected utility. The latter is supposed to reflect the opportunities open for workers elsewhere in the economy. Under these assumptions it can be demonstrated that the optimal contract involves full employment of the firm's labour pool at all states of nature, and a constant wage rate-i.e. a wage rate independent of the contingency realized. The above formulation involves a number of conceptual and empirical problems: It is assumed there is unanimity concerning the probability of occurrence of the various states of nature. Furthermore, not only are workers identical, but firms know the exact form of their utility function. The argument depends crucially on the risk neutrality of firms. In the absence of markets for contingent securities this assumption can only be justified in the very special case of perfect negative correlation between the profits of different firms. Otherwise one has to rely either on the superiority of firms vis-a-vis workers concerning the accessibility to capital markets, or in some Knightian distinction between the innate risk neutrality of entrepreneurs and risk aversion of workers. Workers are assumed to have an indirect utility function separable in income and prices. If this is not the case, even though firms behave parametrically with respect to the prices of goods, they must take into account portfolio-theoretic considerations on the part of workers. Since the only constraint faced by a firm is that the expected utility provided by the contract it offers be greater than or equal to some competitively determined level, it is implicitly assumed that workers cannot abandon the firm after the state of nature has been realized. Equivalently, the costs of movement for workers past the initial contracting period are assumed to be infinitely high. For otherwise, the constraints faced by a firm would take the form of a minimum wage to be paid at each state of nature. In the extreme case of costless labour mobility, this implies that firms are wage takers in the labour market.

[Under the assumption that demand behavior depends on intertemporal preferences as well as (point) expectations concerning future prices, it is demonstrated that under plausible conditions rationality imposes no observable restrictions on the demand function and expectations and preferences are observationally indistinguishable.]

Overlapping generations models with or without production or a portfolio demand for money display a fundamental indeterminacy. Expectations matter; and they are not, in the short run, constrained by the hypotheses of agent optimization, rational expectations, and market clearing. No short run policy analysis is possible without some explicit understanding of how agents expect the economy to respond to the policy. In this framework of perfect foresight and market clearing prices, it is possible to make Keynesian assumptions about the rigidity of money wages and the exogeneity of “animal spirits” of investors, to use the standard IS-LM apparatus, and to derive Keynesian conclusions about the short run effectiveness of policy. Alternatively, starting from different but no less rational expectations, one can derive the “new classical” neutrality propositions.

[We solve the problem of the restrictions imposed on the Jacobian A at prices p̄ of the aggregate excess demand function x(p) of m agents in an exchange economy with l commodities, under the assumption of individual rationality. Given an arbitrary differentiable function x(p) satisfying homogeneity and Walras' law, we attribute rational individual excess demand functions x^1 (p), ..., x^m (p) to the m agents such that at any arbitrarily specified vector p̄ aggregate excess demand is equal to x(p̄) and the following condition is satisfied: There exists a subspace M of dimension m such that the Jacobian at p̄ of x(p) and the Jacobian at p̄ of the aggregate excess demand function define the same linear function on M. If x(p̄) ≠ 0, M can be taken to have dimension (m+1). As an immediate consequence of our proof for m=1 we show that even if p̄, x(p̄), and Dx(p̄) are known for the excess demand function of a single agent, the substitution effect and the income effect cannot be unambiguously determined without knowledge of the utility function. We extend the results proved at a point to large open neighborhoods. We show that if x(p) is an arbitrary function which bounded from below and satisfies homogeneity and Walras' law, and if x(p̄) ≠ 0, then we can find an open neighborhood G of p̄ and (l-1) individually rational excess demand functions x^1(p), ..., x^l-l (p), such that Σ_k=1^l-1 x^k (p) = x(p) everywhere on G.]

J. Green, H. Polemarchakis; A Brief Note on the Efficiency of Equilibria with Costly Transactions, The Review of Economic Studies, Volume 43, Issue 3, 1 October

The transfer paradox may occur in a world with only two countri es ata dynamically stable intertemporal competitive equilibrium. In a framework of overlapping generations with production and investment, a transfer of income may immiserize the recipient while enriching thedonor. Away from the golden ru le, a transfer may result in a Paretoimprovement.