Individual consumer surplus in the Edgeworth Box

Subject. The consumer surplus conception is an important part of the modern microeconomic theory at the introductory and intermediate levels. Consumer surplus measures the change in the consumer’s real welfare. The article addresses the peculiarities of generation and the main property of the generalized individual consumer surplus, using the Edgeworth Box case. Objectives. The purpose is to find the main property of individual consumer surplus in the Edgeworth Box economy. Methods. The study draws on methods of logical and mathematical analysis. The generalized consumer surplus is correctly constructed, using the mathematical theory of curve integrals of the second type (the theory of line integrals in the Western mathematics). Results. The generalized individual consumer surplus is defined through the respective curve integral along some admissible trajectory in the simple exchange economy (Edgeworth Box). The paper also introduces the notion of the marginal individual consumer surplus, and demonstrates that consumer surplus is a correct individual welfare measure in the Edgeworth Box, and that consumer surplus is zero along any given indifference curve. I consider the numerical example of individual surplus calculation and presentation in the Edgeworth Box. Conclusions. The generalized individual consumer surplus is a correct measure of consumer’s utility change along monotone (weakly monotone) trajectories in the Edgeworth Box. Geometrically, the consumer surplus is presented as an area limited by the reservation price curve from the top and by the reallocation line (curve) from the bottom.

Incentive Constrained Risk Sharing, Segmentation, and Asset Pricing

Incentive problems make securities’ payoffs imperfectly pledgeable, limiting agents’ ability to issue liabilities. We analyze the equilibrium consequences of such endogenous incompleteness in a dynamic exchange economy. Because markets are endogenously incomplete, agents have different intertemporal marginal rates of substitution, so that they value assets differently. Consequently, agents hold different portfolios. This leads to endogenous markets segmentation, which we characterize with optimal transport methods. Moreover, there is a basis going always in the same direction: the price of a security is lower than that of replicating portfolios of long positions. Finally, equilibrium expected returns are concave in factor loadings. (JEL D51, D52, G11, G12)

Economy Through Orders

Ordoliberals studied the manifestations of power through a “morphological” lens (opposing the centrally administered economy to the economy of exchange), leading Eucken to take a stand in relation to two of the great international discussions of the discipline in the interwar years: the feasibility of a socialist calculation and the debate over imperfect/monopolistic market structures. The theoretical substance of these two debates is closely related to a political quest for stability of the economic and social order. The centrally administered economy is characterized by the strong influence of what ordoliberals saw as illegitimate powers on the economic process. But ordoliberals considered that, within the exchange economy system itself, markets were not free from power relations. The contribution of Stackelberg to the analysis of unbalanced market structures is therefore indispensable for understanding the literary marginalism of the ordoliberals.

Equity Premium with Habits, Wealth Inequality and Background Risk

In an exchange economy with endowment inequality, we investigate how preferences with external habits affect the equity risk premium. We show that the dynamics of external additive habits with wealth inequality are complex when a background risk is present. It is ambiguous whether wealth inequality will increase or decrease the equity premium even when the income uncertainty is low. This result extends literature by suggesting that wealth inequality has a small role in explaining asset pricing puzzles.

Fairness and fuzzy coalitions

In this paper, we study the problem of a fair redistribution of resources among agents in an exchange economy á la Shitovitz (Econometrica 41:467–501, 1973), with agents’ measure space having both atoms and an atomless sector. We proceed by following the idea of Aubin (Mathematical methods of game economic theory. North-Holland, Amsterdam, New York, Oxford, 1979) to allow for partial participation of individuals in coalitions, that induces an enlargement of the set of ordinary coalitions to the so-called fuzzy or generalized coalitions. We propose a notion of fairness which, besides efficiency, imposes absence of envy towards fuzzy coalitions, and which fully characterizes competitive equilibria and Aubin-core allocations.

States, Institutions, and Literacy Rates in Early-Modern Western Europe

The purpose of the paper is to develop the theory that structural or procedural changes in institutions precede changes in education in a society. It examines the development of pre-modern institutions in Western Europe in the 16th and 17th centuries and the influences this had on growth in literacy rates within these states. Literacy rates in Western European countries during the Middle Ages were below twenty percent of the population. For most countries, literacy rates did not experience significant increases until the Enlightenment and industrialization. Two early exceptions to this broad trend were the Netherlands and England, which had achieved literacy rates above fifty percent of their populations by the mid-seventeenth century. The explanations for these divergent trends are the structural changes in formal institutions that embodied capital markets, protected private property, and overall established the initial steps in developing modern political institutions. This created incentives to invest more in schools per capita as well as incentives for a middle class to invest more in literacy and numeracy skills for a market-exchange economy that was becoming more specialized in division of labor.

An Experimental Comparison of Two Exchange Economies: Long-Lived Asset vs. Short-Lived Asset

The Lucas tree model [Lucas RE Jr (1978) Asset prices in an exchange economy. Econometrica 46(6):1429–1445.] lies at the heart of modern macrofinance. At its core, it provides an analysis of the equilibrium price of a long-lived asset in an exchange economy where consumption is the objective and the sole purpose of the asset is to smooth consumption through time. Experimental tests of the model use a particular instantiation of the Lucas model. Here we adopt a different instantiation to the first two, extending their analyses from a two-period oscillating world to a three-period cyclical world; this is partly to test the robustness of their results. We also go one step further and compare this solution (to a consumption-smoothing problem), in which consumption claims are traded via the long-lived asset, with the alternative solution provided by a market, in which agents can directly trade (short-lived) consumption claims between periods. We find that the latter exchange economy is more efficient in encouraging consumption smoothing than the economy with the long-lived asset. We find evidence of uncompetitive trading in both markets. This paper was accepted by Yan Chen, decision analysis.