Imprimitivity in Decomposable Economies

This note extends the analysis of imprimitive indecomosable economies (e.g.~Nikaido, 1968, 1970) to the case of economies represented by a decomposable matrix. Using graph theory we show that imprimitivity leads to cyclical production lags also in decomposable economies, although in such a case the property must not be referred to the matrix representing the economy but to its indecomposable sub-matrices along the block-diagonal. The structure of the overall flow of commodities depends on both the number of imprimitive sub-matrices and their imprimitivity index.

On the rationalizability of observed consumers’ choices when preferences depend on budget sets and (potentially) on anything else

We prove that defining consumers’ preferences over budget sets is both necessary and sufficient to make every fully informative and finite set of observed consumption choices rationalizable by a collection of preferences which are transitive, complete, and monotone with respect to own consumption. Our finding has two important theoretical consequences. First, assuming that preferences depend on budget sets is illegitimate under the scientific commitments of revealed preference theory. Second, as long as consumers’ preferences are not defined over budget sets, we can assume that preferences depend on observable objects other than own consumption without compromising the logical possibility to reject the model against observation. We however point out that, despite this logical possibility, in practice it can be almost impossible to reject a model where preferences are defined over objects that depend on budget sets. As an example of this we show that if preferences are defined over consumption choices of other individuals then rationalization fails only in cases of negligible practical interest.Revealed Preferences, Budget Sets, Rational Preferences, Rationalizability

On the Economic Interpretation of Imprimitive Leontiev-vonNeumann-Sraffa Matrices: Cyclical Input-Output Relationships

Starting from the known results of Perron (1907) and Frobenius (1912) I apply graph theory to give an economically intuitive characterization of imprimitivity. Such property implies cyclical vertical relationships among groups of industries which, either directly or indirectly, use each others’ products as inputs. More precisely, if the index of imprimitivity is h, then industries may be sorted in h groups such that i) each group produces the inputs of one and only one other group and ii) there is no direct flow of commodities between industries of the same group. A sufficient condition for primitivity is provided which offers some reasons to expect non-basic industries to have more vertical cyclical flows than basic ones.

Long-run Welfare under Externalities in Consumption, Leisure, and Production: A Case for Happy Degrowth vs. Unhappy Growth

In this paper we contribute to the debate on the relationship between growth and well-being by examining an endogenous growth model where we allow for externalities in consumption, leisure, and production. We analyze three regimes: a decentralized economy where each household makes isolated choices without considering their external effects, a planned economy where a myopic planner fails to recognize both leisure and consumption externalities but recognizes production externalities, and a planned economy with a fully informed planner. We first compare the balanced growth paths under the three regimes and then we numerically investigate the transition to the optimal balanced growth path. We provide a number of ndings. First, in a decentralized economy growth or labor (or both) are greater than in the regime with a fully informed planner, and hence are sub-optimal from a welfare standpoint. Second, a myopic intervention which overlooks consumption and leisure externalities leads to more growth and labor than in both the decentralized and the fully informed regime. Third, we provide a case for happy degrowth: a transition to the optimal balanced growth path that is associated with downscaling of production, a reduction in private consumption, and an ongoing increase in leisure and well-being.degrowth; endogenous growth; consumption externalities; leisure externalities; production externalities

Ordinal vs Cardinal Status: Two Examples

We demonstrate that in models where agents have concerns for status the model predictions can drastically change depending on whether status is modelled as an ordinal or cardinal magnitude. As a proof, we show that two well known theoretical findings are not robust to the substitution of ordinal status with cardinal status (Frank (1985)) and viceversa (Clark and Oswald (1998)).Status, Social Comparison, Ordinality, Cardinality

Single-Valuedness of the Demand Correspondence and Strict Convexity of Preferences: An Equivalence Result

If preferences are rational and continuous, then strict convexity implies that the demand correspondence is single-valued (e.g. Barten and B¨ohm, 1982, lemma 7.3). We show that if, in addition, preferences are strictly monotone then the converse is also true, namely single-valuedness of the demand correspondence implies strict convexity of preferences.Strict convexity; Strict monotonicity; Demand correspondence; Single-valuedness; Demand function

Preferences and Normal Goods: An Easy-to-Check Necessary and Sufficient Condition

We provide a necessary and sufficient condition for goods to be normal when utility functions are differentiable and strongly quasi-concave. Our condition is equivalent to the condition proposed by Alarie et al. (1990), but it is easier to check: it only requires to compute the minors associated with the border column (or row) of the bordered Hessian matrix of the utility function.normal goods; bordered hessian

Dynamic Adverse Selection and the Size of the Informed Side of the Market

In this paper we examine the problem of dynamic adverse selection in a stylized market where the quality of goods is a seller’s private information. We show that in equilibrium all goods can be traded if a simple piece of information is made publicly available: the size of the informed side of the market. Moreover, we show that if exchanges can take place frequently enough, then agents roughly enjoy the entire potential surplus from exchanges. We illustrate these findings with a dynamic model of trade where buyers and sellers repeatedly interact over time. More precisely we prove that, if the size of the informed side of the market is a public information at each trading stage, then there exists a weak perfect Bayesian equilibrium where all goods are sold in finite time and where the price and quality of traded goods are increasing over time. Moreover, we show that as the time between exchanges becomes arbitrarily small, full trade still obtains in finite time – i.e., all goods are actually traded in equilibrium – while total surplus from exchanges converges to the entire potential. These results suggest two policy interventions in markets suffering from dynamic adverse selection: first, the public disclosure of the size of the informed side of the market in each trading stage and, second, the increase of the frequency of trading stages.dynamic adverse selection; full trade; size of the informed side; frequency of exchanges; asymmetric information

Functional Distribution, Land Ownership and Industrial Takeoff

This paper investigates how the distribution of land property rights affects industrial take-off and aggregate income through the demand side. We study a stylized two sectors economy where the manufacturing sector is assumed to be constituted by a continuum of small markets producing distinct commodities. Following Murphy et al. [24] we model industrialization as the introduction of an increasing returns technology in place of a constant returns one. However, we depart from their framework by assuming income to be distributed according to functional groups’ membership (landowners, capitalists, workers). We carry out an equilibrium analysis for different levels of land ownership concentration proving that, under the specified conditions, there is a non-monotonic relation between the distribution of land property rights and both industrialization and income. We clarify that non-monotonicity arises because of the way land ownership concentration affects the level and the distribution of profits among capitalists. Our results suggest that i) both a too concentrated and a too diffused distribution of land property rights can be detrimental to industrialization, ii) landownership affects the economic performance of an industrializing country by determining industrial profits and iii) in terms of optimal land distribution there may be a tradeoff between income and industrialization.

A Comment On Gintis's "The Dynamics of General Equilibrium"

Gintis (2007, 'The Dynamics of General Equilibrium'', Economic Journal 117 (523) , 1280–1309) provides an agent-based model of a Walrasian economy where the tâtonnement is replaced by imitation. His simulations show that the economy converges to the Walrasian equilibrium. Gintis concludes that 1) his stability results provide some justification for the importance placed upon the Walrasian model, and 2) models allowing agents to imitate successful others lead to an economy with a reasonable level of stability and efficiency. Since these conclusions appear to be intended as general, we caution that Gintis''s findings can only be accepted for Walrasian models without capital goods in models with capital goods imitation-based adjustments alter the equilibrium''s data (which makes the demonstration of stability impossible) and raise other important problems (absent from Gintis''s simulations) still awaiting exploration.