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.     

Multiple equilibrium in the overlapping generations model revisited

Bliss [Bliss, C., 2008. Multiple equilibrium in the Diamond capital model. Economics Letters 100, 143-145] finds numerically that the Diamond OLG model can have uncountably many steady states. We use log preferences and show analytically that a continuum of steady states can still exist.     

A note on the closed-form solution to the Lucas–Uzawa model with externality

Ruiz-Tamarit [2008. The closed-form solution for a family of four-dimension nonlinear MHDS. Journal of Economic Dynamics and Control 32, 1000–1014] provides a closed-form solution to the two-sector model of endogenous growth with externalities. He assumes that the coefficient of the relative risk aversion is equal to the physical capital share, but this assumption is empirically and theoretically implausible. This note uses the result of Boucekkine and Ruiz-Tamarit [2008. Special functions for the study of economic dynamics: the case of the Lucas–Uzawa model. Journal of Mathematical Economics 44, 33–54] and derives a closed-form solution without setting the parametric assumption. The solution path is expressed in terms of the Gauss hypergeometric functions.     

Calculations of the shares of financial resources paid by actual payers for transportation improvements

In this paper we identify and quantitatively describe the actual providers of financial resources, termed “actual payers”, for transportation improvements in some advanced countries, using various statistical data. The theoretical framework on which the concept of actual payers is based was presented in our earlier paper (Transport Policy, April 1998). The current study presents the results of calculations performed according to that concept. Because of the complexity and variety of the financial resources drawn on by transportation systems, the means of financial support for transportation have not been made clear when superficial classifications such as “National expenditures”, “Local expenditures”, “Owners/operators' funds” and “Debt” are used. In the present study, the financial support for transportation is calculated on the basis of what is spent by actual payers, such as users, payers of national taxes and payers of local taxes. This approach allows us to show that the shares of actual payers are quite different in each country. In addition, we indicate the characteristics of the shares of the actual payers in each country by calculating the ratio of the users' burden or the dependence of debt, etc.     

A note on the competitive search model of Azariadis and Pissarides

In this short note, I reinvestigate a recent paper of Azariadis and Pissarides (Unemployment dynamics with international capital mobility, European Economic Review, 2007(51), 27–48) where wages are determined in a competitive search setting. I show that their equation on the equilibrium wage rate is incorrect. I derive a correct wage equation and perform the numerical analysis. The correction does not change their result and high capital mobility still raises the variability of the unemployment rate.     

On the optimality of the Friedman rule in a New Monetarist model

We study a monetary model in which buyers choose search intensity and prices are considered as given in a decentralized market. We indicate that the Friedman rule may not be optimal.     

A two-country model of trade and growth with intersectoral knowledge spillovers

We formulate a two-country, two-good, two-factor endogenous growth model with learning by doing and intersectoral knowledge spillovers. Our model exhibits no transitional dynamics because of constant returns to capital, the existence of only one state variable for each country, and the factor price equalization theorem. By applying our model to the problem of aid and growth, we show that a permanent increase in untied aid raises the common growth rate if and only if the propensity to consume the capital-intensive good in the recipient country is larger than in the donor country.     

A two sector endogenous growth model with habit formation

In this paper, we study an endogenous growth model with physical and human capital in which consumption habits enter the utility function multiplicatively. We show that although the utility function with multiplicative habits is nonconcave and unbounded, an interior optimal growth path still exists, it is uniquely determined and it converges to a balanced growth path. We also find that habit formation in consumption lowers the convergence speed of the optimal path toward the balanced growth path.     

Dynamics of a two-sector endogenous growth model with intersectoral knowledge spillovers

In a two-sector endogenous growth model with learning by doing and intersectoral knowledge spillovers, we associate local dynamics with the slope of the excess demand curve for a consumption good. Factor intensity determines the income effect, which governs dynamics. We are grateful to an anonymous referee for his/her helpful comments and suggestions.