On the minimum degree of returns to scale in sunspot models of the business cycle

Bennett and Farmer (J. Econ. Theory 93 (2000) 118) claim that the degree of increasing returns to scale required for indeterminacy in a single sector growth model can be lowered by allowing for preferences that are non-separable in consumption and leisure. In this paper I show that the example they give violates concavity. In a more general setup, which does not impose specific functional forms on utility, I prove that there are no concave utility functions compatible with indeterminacy if the elasticity of scale is lower than the inverse of the labor share in production.     

Indeterminacy in a small open economy with endogenous labor supply

Summary. We establish conditions under which indeterminacy can occur in a small open economy business cycle model with endogenous labor supply. Indeterminacy requires small externalities in technologies with social constant returns to scale, independently of the intertemporal elasticities in both consumption and labor. Received: December 12, 2001; revised version: May 17, 2002 RID="*" ID="*"The paper has benefited from discussions with Jess Benhabib and Mark Weder, as well as from the comments of an anonymous referee. Correspondence to: Q. Meng     

Intertemporal production and intertemporal substitution in output supply and input demand

This article presents an intertemporal model of production with multiple inputs to investigate substitution opportunities facing firms over time. The firm’s intertemporal profit maximization problem is characterized with the familiar cost function, and various intertemporal substitution elasticities are delineated for output supply and input demand. The absence of intertemporal substitution in production can imply production smoothing, and allowance for intertemporal substitution in labour demand reinforces the prediction of the real business cycle model. For aggregate US manufacturing, we find substantial substitution in output supply and labour demand over time due to intertemporal changes in output price and wage rates.     

Determinants of business cycles in small scale macroeconomic models: the German case

We identify measures of shocks to total factor productivity and preferences from two real business cycle models and subject them to Granger causality tests to see whether they can be considered exogenous to other plausible sources of the German business cycle. For West German data from 1960.i to 1989.iv we conclude that our measures of shocks are indeed exogenous. This contrasts with similar studies for other countries that question the exogeneity of either productivity or preference shocks. For the period 70.i to 01.iv we find that M3 Granger causes all of our shock measures. We attribute this to the breaks in our time series associated with the German reunification in 1990 and the European Monetary Union in 1999.Earlier versions of this paper circulate as University of Augsburg economics discussion paper no. 213 and Kiel Institute for World Economics working paper no. 1158, respectively.     

A solution to the Lucas–Uzawa model with increasing returns to scale: Note

Chilarescu [2008, An analytical solutions for a model of endogenous growth, Economic Modelling.] claims that he determines a solution path to the Lucas–Uzawa model with increasing returns to scale. However, the path is not a closed-form since it depends on the initial consumption and the initial time for goods production, that are unknown. Moreover, the production function is nonconcave and then the first order conditions and the transversality conditions are not sufficient for the optimality. This note converts the model to a problem in which the Hamiltonian is available and derives a fully-closed form solution.