SIZE AND COMPOSITION OF PUBLIC SPENDING IN A NEOCLASSICAL GROWTH MODEL

This paper analyses the effect of public expenditures in a modified Solow model of capital accumulation with optimizing agents. The model identifies optimal government size and composition of public expenditures which maximize the rate of growth in the dynamics to the steady state and the long‐run level of per capita income. Different allocations of public resources lead to different growth rates in the transitional dynamics depending on their elasticities. However effects from fiscal policy are only temporary. Finally we argue that neglecting the non‐linear nature of the relationship between government spending and growth may lead empirical studies to biased results.     

ENDOGENOUS FLUCTUATIONS OF ACTUAL PRICES NEAR NATURAL ONES IN A CLASSICAL GROWTH MODEL

This paper re-examines dynamics of the Hosoda classical growth model. We identify the existence of endogenous fluctuations, applying the celebrated Hopf bifurcation theorem. It is shown that the proposition of divergence of actual prices from natural ones of classical economists is valid, even if there are no exogenous forces upon the economic system.     

REPRODUCTION AND TEMPORARY DISEQUILIBRIUM: A CLASSICAL APPROACH

We build a bisector reproduction model with Classical features in which the capitalists aim at maximizing accumulation. At variance with gravitation models, it is assumed that they invest their profits in their own industry. Their plans are based on actual productions and expected prices. Effective prices and effective allocations of resources are determined by a market‐clearing mechanism. A law on the formation of expectations allows us to define the dynamics of disequilibria, which let appear endogenous self‐sustained fluctuations around a long‐run path. The long‐run rate of growth and the amplitude of the fluctuations depend on the initial conditions.     

ON A GENERALIZED VON NEUMANN MODEL

The main aim of the paper is to give a constructive proof to an existence theorem concerning the generalized von Neumann model à la Morishima in a particular case which arises by dropping and replacing a strong continuity assumption of Morishima, whose existence theorem does not work (as the appendix example shows) when all of Morishima's other assumptions but that continuity assumption hold. In particular, the paper proves that the generalized von Neumann model à la Morishima has a solution when all people consume the same commodities in the same proportions, with a substitution effect equal to zero, even if some commodities are never consumed and not all processes require labour. Moreover, it shows a way to construct a solution by solving a Linear Complementarity Problem with Lemke's complementarity pivot algorithm.     

MATURITY,STAGNATION AND CONSUMER DEBT: A STEINDLIAN APPROACH

This paper extends a Steindlian model of growth and income distribution to incorporate borrowing by consumers. It shows that borrowing by consumers can improve growth prospects in the short run by increasing consumer demand. However, in the longer run the effects of increasing consumer borrowing are ambiguous because, by increasing consumer debt, it redistributes income towards the rich who have a higher propensity to save, thereby possibly depressing aggregate demand and growth despite the borrowing‐induced expansion. The problem may be exacerbated by financial considerations involving the increase of the interest rate due to greater borrowing, but these considerations are not necessary for it. The problem is more likely to occur when autonomous investment demand is weak, i.e. when borrowing‐induced consumption increases are most required to counter tendencies towards stagnation.     

ECONOMIC POLICY IN A GROWTH CONTEXT: A CLASSICAL SYNTHESIS OF KEYNES AND HARROD

This paper clarifies key differences between Harrodian and Keynesian theories and policies, and develops a classical alternative to both. The stability of the Harrodian warranted path is proved, and the Keynesian paradox of thrift is shown to be transient. Distinct Harrodian fiscal policies are derived, and Post‐Keynesian debates about Harrodian dynamics are addressed. Finally, it is argued that business and household savings are fundamentally different, and it is shown that if the business savings rate responds at all to the investment–savings gap, it becomes possible to have both profit‐driven accumulation as in Keynes and normal capacity growth as in Harrod.     

A FIRST‐ORDER BSPDE FOR SWING OPTION PRICING: CLASSICAL SOLUTIONS

In a companion paper, we studied a control problem related to swing option pricing in a general non‐Markovian setting. The main result there shows that the value process of this control problem can uniquely be characterized in terms of a first‐order backward stochastic partial differential equation (BSPDE) and a pathwise differential inclusion. In this paper, we additionally assume that the cash flow process of the swing option is left‐continuous in expectation. Under this assumption, we show that the value process is continuously differentiable in the space variable that represents the volume in which the holder of the option can still exercise until maturity. This gives rise to an existence and uniqueness result for the corresponding BSPDE in a classical sense. We also explicitly represent the space derivative of the value process in terms of a nonstandard optimal stopping problem over a subset of predictable stopping times. This representation can be applied to derive a dual minimization problem in terms of martingales.     

A NOTE ON THE FORMAL TREATMENT OF EXPLOITATION IN A MODEL WITH HETEROGENOUS LABOR

The paper presents a formal generalization of Marx's analysis of exploitation and prices in economies in which categories of labor are distinguished according to their unequal ability to create exchange value. Measures of exploitation of categories of labor which are consistent with both the Price of Net Product‐Unallocated Purchasing Power (PNP‐UPP) (New Interpretation) and the traditional interpretation of Marx's theory of value are defined which aggregate consistently over labor categories and sectors. In order to measure rates of exploitation from real economic data some additional assumption about relative rates of exploitation (which Marx often explicitly assumes to be equal) is required.     

CRITICAL PRICE NEAR MATURITY FOR AN AMERICAN OPTION ON A DIVIDEND-PAYING STOCK IN A LOCAL VOLATILITY MODEL

We consider an American put option on a dividend-paying stock whose volatility is a function of the stock value. Near the maturity of this option, an expansion of the critical stock price is given. If the stock dividend rate is greater than the market interest rate, the payoff function is smooth near the limit of the critical price. We deduce an expansion of the critical price near maturity from an expansion of the value function of an optimal stopping problem. It turns out that the behavior of the critical price is parabolic. In the other case, we are in a less regular situation and an extra logarithmic factor appears. To prove this result, we show that the American and European critical prices have the same first-order behavior near maturity. Finally, in order to get an expansion of the European critical price, we use a parity formula for exchanging the strike price and the spot price in the value functions of European puts.     

COMMODITY CONTENT IN A GENERAL INPUT–OUTPUT MODEL: A COMMENT

This paper critically analyses the approach to the determination of values, or commodity contents, developed by Fujimoto and Opocher in 2009. Even setting aside various problematic definitional issues, the broader implications of the approach for classical theory are unclear. First, the value‐theoretic definitions of skill differentials and bads capture at best necessary conditions and it is unlikely that such definitions can be provided by focusing only on the technological data of the economy. Second, the approach has various interesting implications concerning the relation between productiveness and exploitation that directly contradict some of the authors' claims.     

HEURISTIC EXPECTATION FORMATION AND BUSINESS CYCLES: A SIMPLE LINEAR MODEL

We develop a Keynesian business cycle model to study how extrapolative and regressive expectation formation rules may affect fluctuations in economic activity. We find that simple expectation formation rules may have an impact on the level and the stability of the equilibrium income, the size of the multiplier and the resulting adjustment process after an exogenous shocks. Our model also reveals that national income may be influenced by how agents perceive their long‐run average income.     

THE 4/2 STOCHASTIC VOLATILITY MODEL: A UNIFIED APPROACH FOR THE HESTON AND THE 3/2 MODEL

We introduce a new stochastic volatility model that includes, as special instances, the Heston (1993) and the 3/2 model of Heston (1997) and Platen (1997). Our model exhibits important features: first, instantaneous volatility can be uniformly bounded away from zero, and second, our model is mathematically and computationally tractable, thereby enabling an efficient pricing procedure. This called for using the Lie symmetries theory for partial differential equations; doing so allowed us to extend known results on Bessel processes. Finally, we provide an exact simulation scheme for the model, which is useful for numerical applications.     

ON THE IMPORTANCE OF THE RETENTION RATIO IN A KALECKIAN DISTRIBUTION AND GROWTH MODEL WITH DEBT ACCUMULATION—A COMMENT ON SASAKI AND FUJITA (2012)

In a paper published in Metroeconomica, Sasaki and Fujita (2012) argue that an earlier paper of mine (Hein, 2007 ; Metroeconomica, 57, pp. 310–39), which introduces interest payments and corporate debt into a post‐Kaleckian distribution and growth model, leads to empirically implausible and unusual results from a Keynesian/Kaleckian perspective. The major reason for the presumed shortcomings is found in the overly restrictive assumption of a retention ratio equal to unity. However, in the alternative model presented by Sasaki and Fujita either perfect capital gains have to be assumed or firms have to be allowed to issue equity in the accumulation process. The latter variant yields results which are again close to Hein ( 2007 ).     

MODELING SOVEREIGN RISKS: FROM A HYBRID MODEL TO THE GENERALIZED DENSITY APPROACH

Motivated by the European sovereign debt crisis, we propose a hybrid sovereign default model that combines an accessible part taking into account the evolution of the sovereign solvency and the impact of critical political events, and a totally inaccessible part for the idiosyncratic credit risk. We obtain closed‐form formulas for the probability that the default occurs at critical political dates in a Markovian setting. Moreover, we introduce a generalized density framework for the hybrid default time and deduce the compensator process of default. Finally, we apply the hybrid model and the generalized density to the valuation of sovereign bonds and explain the significant jumps in long‐term government bond yields during the sovereign crisis.