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Research Article Open access CC BY 3.0

Price Dynamics of Maize in Ghana: An Application of Continuous –Time Delay Differential Equations

Martin Anokye, Francis T. Oduro

Journal of Advances in Mathematics and Computer Science · pp. 3427–3443 · Published 1 Oct 2014

10.9734/BJMCS/2014/13484

Abstract

This paper seeks to study the price dynamics of maize in Ghana, in the context of mathematical modelling using continuous-time cobweb models derived from linear and nonlinear delay differential equations. The stability conditions of two cobweb models: continuous-time linear and nonlinear models are discussed. The data is obtained from the Ministry of Food and Agriculture, Statistical Directorate Kumasi-Ghana, from 1994 to 2013. The models performed on the assumptions that, maize has no equal substitutes and there are no exogenous shocks needed to generate price fluctuations so that market price would be determined by only the available supply in a single market. From the results of the analysis performed on the real economic price and production data using numerical approach, the nonlinear delay differential model (formulated from linear demand and quadratic supply functions) showed oscillations between and around two equilibrium points and would neither converge. This result seems realistic as it appears to reflect real market conditions since an equilibrium price would not be compatible with the prevailing situation of high inflation, food insufficiency and/or producers’ sensitivity towards price. The linear model (formulated from linear demand and linear supply functions) on the other hand showed little oscillations and then converged towards an equilibrium point (zero equilibrium price). However, this seems quite unrealistic. Effects of delay parameter on oscillations are also discussed. It is observed that oscillations (price fluctuations) are suppressed for ≤0.5, using the nonlinear delay equation. This is an indication that price fluctuations are reduced, if and only if, factors affected by time lag, such as the time necessary for increasing supply, buying new inputs, hiring workers or transporting commodities to market centres, building warehouse and reducing effects of natural constraints on crop yields are improved. On the contrary, the linear delay differential equation, for >0.5 or ≤0.5, would still be in stable equilibrium. We draw inferences from this study that researchers should rather use nonlinear models instead of linear models in solving most real-life economic problems to avoid misleading conclusions.

Cobweb model delay differential equations and price stability.

References (36)

  1. 1 A Rational Route to Randomness [DOI]
  2. 2 Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL [DOI]
  3. 3 Gaussian Estimation of Single-Factor Continuous Time Models of The Term Structure of Interest Rates [DOI]
  4. 4 Commodity price fluctuations: Price dependent delays and nonlinearities as explanatory factors [DOI]
  5. 5 FITTING A CONTINUOUS TIME AUTOREGRESSION TO DISCRETE DATA [DOI]
  6. 6 Adaptive learning and roads to chaos [DOI]
  7. 7 Serial Correlation in Unequally Spaced Longitudinal Data [DOI]
  8. 8 A Poverty Profile for Ghana, 1987–1988 [DOI]
  9. 9 Homoclinic solution and chaos in [DOI]
  10. 10 E&F Chaos: A User Friendly Software Package for Nonlinear Economic Dynamics [DOI]
  11. 11 Modelling with Differential and Difference Equations [DOI]
  12. 12 Cournot oligopoly models with time delays [DOI]
  13. 13 Analysis of Foodstuff Price Volatility in Ghana: Implications for Food Security
  14. 14 Threshold autoregressive modelling in continuous time
  15. 15 Delay differential equations [DOI]
  16. 16 Global dynamics in a commodity market model [DOI]
  17. 17 Complex Dynamics in a Nonlinear Cobweb Model for Real Estate Market [DOI]
  18. 18 Delay induced transitions in an asymmetry bistable system and stochastic resonance [DOI]
  19. 19 On continuous-time threshold ARMA processes [DOI]
  20. 20 On continuous-time threshold autoregression [DOI]
  21. 21 Food and nutritional adequacy in Ghana.
  22. 22 CONTINUOUS TIME THRESHOLD AUTOREGRESSIVE MODELS
  23. 23 Contagion effects in a chartist–fundamentalist model with time delays [DOI]
  24. 24 Cobweb Model with Buffer Stock for the Stabilization of Tomato Prices in Ghana [DOI]
  25. 25 A comparison of continuous- and discrete- time three-state models for rodent tumorigenicity experiments. [DOI]
  26. 26 Mathematics for Economics and Finance [DOI]
  27. 27 Dynamics of Maize Price in Ghana: Linear versus Nonlinear Cobweb Models
  28. 28 An Introduction to Mathematics for Economics [DOI]
  29. 29 Dynamics of price cooperating model in commodity market
  30. 30 Theory Analysis of Model for Price Fluctuations in a Single Commodity Market
  31. 31 Delay Differential Equations [DOI]
  32. 32 Modelling with differential and difference equations [DOI]
  33. 33 Fundamentals of Price Analysis in Developing Countries' Food Systems: A Training Manual to Accompany the Microcomputer Software Program 'MSTAT' [DOI]
  34. 34 Nonlinear Dynamics in Economics: A Theoretical and Statistical Approach to Agricultural Markets
  35. 35 A simple model for price fluctuations in a single commodity market [DOI]
  36. 36 Hopf Bifurcation Analysis in a Chartist-Fundamentalist Model with Time-Delays [DOI]

Cited by 3

Modelling price volatility of three major cereals in the Northern Region of Ghana

Yakubu Amadu, Shamsu-Deen Mohammed Salim, Ibn Imoro Abdul-Rahaman · African Journal of Agricultural Research · 2025

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