Nonlinear dynamics in economic modelling

Decisions in Economics and Finance -     

Delay two-sector economic growth model with a Cobb–Douglas production function

Decisions in Economics and Finance - This study demonstrates the possibility of cyclic capital accumulation in the case in which there are delays in capital implementation and estimation of capital...     

Neoclassical growth model with two fixed delays

“Delay” has been considered as one of destabilizing factors in economic dynamics for a long time. Dynamic macroeconomics is concerned with explaining growth and fluctuations. This paper shows how various dynamics involving cyclic fluctuations can emerge in the standard neoclassical growth model when two distinct delays, a delay in production and a delay in depreciation, are explicitly taken into account. We first confirm that the production delay has a stabilizing effect and the depreciation delay has a destabilizing effect in a one‐delay model. We then determine the stability switching curve analytically in the two delay model. It is shown that cyclic fluctuations emerge via Hopf bifurcation when stability is lost. It is also found that stability loss and gain repeatedly occur. Numerical examples verify the theoretical results when the Cobb‐Douglas production function is adopted.     

Contributions to Cournot oligopoly theory

This work contributes to a number of questions concerning oligopoly models. In particular, uniqueness of the Cournot equilibrium point is demonstrated under the assumption that either the unit price function is differentiable and the derivative is strictly negative or the cost functions are strictly convex. Also, under the assumption of either strictly decreasing unit price function or strictly convex cost functions, it is shown that (a) the total production level at equilibrium increases with entry of additional players, (b) that cooperation between some of the players necessarily entails profit for the others, and (c) cooperative grouping causes decrease in production levels.     

CHANGES IN DEMAND FUNCTION IN COURNOT OLIGOPOLY

Abstract.  The effects of change in the market (inverse) demand function are systematically analysed for Cournot oligopoly without product differentiation. The general comparative-static results are stated using the original data on firms' cost functions and inverse demand function. Three special models are examined in light of our results. The stability condition is shown to be insufficient for determinate comparative statics.     

Petroleum spreads and the term structure of futures prices

We employ the term structure of gasoline and heating oil prices, proxied by convenience yields, to explain the variation in the spread between the prices of gasoline and crude oil and the prices of heating oil and crude oil. We demonstrate that the marginal convenience yields in the gasoline and heating oil markets explained much of the variation in the spreads between 1986 and 1999. The evidence indicates the importance of a disaggregated treatment of the term structure of prices: the convenience yield is found to explain a substantially higher amount of the variation in the spread when it is decomposed by maturity, even after controls for seasonality and inventory levels are implemented. These findings support the notion that the futures term structure contains information beyond what can be garnered via obvious or easily available proxies of current supply and demand. The findings are also supported in an alternate specification that tests for the origins of information spillover (leadership) between the commodities: it is demonstrated that decomposed convenience yields explain a substantial portion of the volatility spillover from the gasoline and heating oil markets to the crude market.     

Delay dynamics in nonlinear monopoly with gradient adjustment

Decisions in Economics and Finance - Two types of boundedly rational monopolists are considered, when they are unable to determine the profit maximizing output levels. In the first case, the...     

Delay Dynamics in a Classical IS‐LM Model with Tax Collections

An IS‐LM model is developed for the dynamics of income, interest rate and money stock with delay in tax revenue. The main aim is to show that the delay matters in macro dynamics. Two different delays, fixed time delays and continuously distributed time delays, are considered explicitly and described by delay‐differential equations and integro‐differential equations, respectively. Conditions for the local stability of the two models are derived and compared. The destabilizing effects caused by the delay are numerically examined. Appearance of wide spectrum of dynamics ranging from simple cyclic oscillations to complex dynamics is described through Hopf bifurctions.