A Model of Firm Behaviour with Equity Constraints and Bankruptcy Costs

Based on Greenwald and Stiglitz (1988,1990), this work explores a simple model of microeconomic behaviour which incorporates the impact of capital markets imperfections generated by asymmetric information on firms’ optimal investment decision rules. In particular, this paper analyses how a specific form of asymmetric information problem (adverse selection) may imply lower investment than otherwise through the reduction of the firms’ ability to raise external financing – either in the form of credit rationing or the ‘voluntary’ reduction of firms’ borrowing activity. The natural follow-up to this work would be to formally show how a loan market where both contractual interest rates and loan sizes are (a priori) variable may be characterised by a credit rationing equilibrium.Asymmetric Information, Firm Behaviour, Investment Financing

p-symmetric fuzzy measures

In this paper we propose a generalization of the concept of symmetric fuzzy measure based in a decomposition of the universal set in what we have called subsets of indifference. Some properties of these measures are studied, as well as their Choquet integral. Finally, a degree of interaction between the subsets of indifference is defined.

Dominance of capacities by k-additive belief functions

In this paper we deal with the set of $k$-additive belieffunctions dominating a given capacity. We follow the lineintroduced by Chateauneuf and Jaffray for dominating probabilities and continued by Grabisch for general $k$-additive measures.First, we show that the conditions for the general $k$-additive case lead to a very wide class of functions and this makes that the properties obtained for probabilities are no longer valid. On the other hand, we show that these conditions cannot be improved.We solve this situation by imposing additional constraints on the dominating functions. Then, we consider the more restrictive case of $k$-additive belief functions. In this case, a similar result with stronger conditions is proved. Although better, this result is not completely satisfactory and, as before, the conditionscannot be strengthened. However, when the initial capacity is a belief function, we find a subfamily of the set of dominating $k$-additive belief functions from which it is possible to derive any other dominant $k$-additive belief function, and such that theconditions are even more restrictive, obtaining the natural extension of the result for probabilities. Finally, we apply these results in the fields of Social Welfare Theory and Decision Under Risk.Linear programming, decision analysis, capacity,dominance, k-additivity, belief functions

Axiomatic structure of k-additive capacities

In this paper we deal with the problem of axiomatizing the preference relations modelled through Choquet integral with respect to a $k$-additive capacity, i.e. whose Möbius transform vanishes for subsets of more than $k$ elements. Thus, $k$-additive capacities range from probability measures ($k=1$) to general capacities ($k=n$). The axiomatization is done in several steps, starting from symmetric 2-additive capacities, a case related to the Gini index, and finishing with general $k$-additive capacities. We put an emphasis on 2-additive capacities. Our axiomatization is done in the framework of social welfare, and complete previous results of Weymark, Gilboa and Ben Porath, and Gajdos.Axiomatic; Capacities; k-Additivity

Non-Equilibrium Random Matrix Theory : Transition Probabilities

In this letter we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large $N$ limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.Comment: REVTeX, 5 pages, 2 figure

Stylized Facts and Other Empirical Evidence on Firm Dynamics, Business Cycle and Growth

In this paper, we bring together in a systematised fashion the scattered empirical evidence relating firm dynamics and both short-run and long-run macroeconomic dynamics. There are numerous studies that focus on firm-level data while controlling for macroeconomic conditions, which cover a considerable range of variables, industries and countries. From these studies it has emerged what is by now a rather robust set of empirical regularities, or stylized facts, about entry, exit, growth and the size distribution of firms. On the contrary, the literature that focus explicitly on the interplay between firm dynamics and the business cycle is roughly confined to the US experience and to the cyclical properties of firm entry and exit, whereas systematic studies about the relationship between firm dynamics and economic growth are almost non-existent whatsoever.empirical evidence, firm dynamics, business cycle, economic growth

The Firm’s Perception of Demand Shocks and the Expected Profitability of Capital under Uncertainty

This paper revisits the results of the pioneering models of the firm under demand uncertainty and analyses the apparent disparity with respect to the signal of the investment-uncertainty relationship predicted by them. In the 1970’s-1980’s the modelling of demand uncertainty at the firm level taking into account the firm’s optimal choice of factor inputs constituted a cutting-edge research topic. But while setting the standards in the literature of the firm’s optimal behaviour under uncertainty, those models did not clarify the rationale behind the disparity of the results concerning the impact of increased uncertainty on the firm’s desired investment. In the context of an isoelastic stochastic demand function, where the shock variable may enter either linearly or non-linearly, we show it is the way the firm perceives the demand shocks that, by determining the shape of the profit function, establishes the signal of the investment-uncertainty relationship predicted by the model.Demand Uncertainty; Expected Profitability; Shock Perception; Jensen’s Inequality.

Animal Spirits and the Composition of Innovation in a Lab-Equipment R&D Model

We revisit the issue of self-fulfilling “waves of enthusiasm” as stationary rational expectations equilibrium outcomes in endogenous-growth models that merge the quality-ladders with the expanding-variety mechanism. By considering a lab-equipment specification with vertical-innovation intertemporal spillovers but no intersectoral spillovers, we extend previous results of a negative impact of animal spirits on both horizontal aggregate R&D and number of firms to a framework where decreasing returns to horizontal entry are not a necessary condition. In contrast, our general-equilibrium setting allows us to predict an effect of animal spirits on R&D composition impacting neither on aggregate growth nor on aggregate vertical R&D, as reduced outlays in “mature” industries compensate for the increased R&D intensity in newly-born industries.endogenous growth, horizontal and vertical R&D, stationary sunspot equilibria

Expected Profitability of Capital under Uncertainty – a Microeconomic Perspective

Hartman (1972) and Abel (1983) showed that when firms are competitive and there is flexibility of labour relative to capital, marginal profitability of capital is a convex function of the stochastic variable (e.g., price); by Jensen’s inequality, this means that uncertainty increases the expected profitability of capital, which increases the incentive to invest. We argue that, besides factor substitutability, the relevant assumption for the convexity property to hold is the implicit assumption about the choice variable in the representative firm’s maximisation problem: the assumption of perfect competition implies that the choice variable is output and that price is exogenous. However, in the case of a firm facing a downward-sloping demand curve, both output and output price emerge as the possible choice variable. We show that, when price is the choice variable, marginal profitability of capital is a concave function of the stochastic variable; hence, by Jensen’s inequality, an increase in uncertainty decreases the expected profitability of capital. We also show that keeping the assumption of factor substitutability but changing the share of labour in the production function has an important impact on the degree of concavity/convexity of the capital profit function.Expected Profitability; Uncertainty; Jensen’s Inequality.