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Basic Mathematics for Economists - Rosser - Chapter 13

13 Dynamics and difference equations Demonstrate how a time lag can affect the pattern of adjustment to equilibrium in some basic economic models. Construct spreadsheets to plot the time path of dependent variables in economic models with simple lag structures. Set up and solve linear first-order difference equations. | 13 Dynamics and difference equations Learning objectives After completing this chapter students should be able to Demonstrate how a time lag can affect the pattern of adjustment to equilibrium in some basic economic models. Construct spreadsheets to plot the time path of dependent variables in economic models with simple lag structures. Set up and solve linear first-order difference equations. Apply the difference equation solution method to the cobweb Keynesian and Bertrand models involving a single lag. Identify the stability conditions in the above models. 13.1 Dynamic economic analysis In earlier chapters much of the economic analysis used has been comparative statics. This entails the comparison of different static equilibrium situations with no mention of the mechanism by which price and quantity adjust to their new equilibrium values. The branch of economics that looks at how variables adjust between equilibrium values is known as dynamics and this chapter gives an introduction to some simple dynamic economic models. The ways in which markets adjust over time vary tremendously. In commodity exchanges prices are changed by the minute and adjustments to new equilibrium prices are almost instantaneous. In other markets the adjustment process may be a slow trial and error process over several years in some cases so slow that price and quantity hardly ever reach their proper equilibrium values because supply and demand schedules shift before equilibrium has been reached. There is therefore no one economic model that can explain the dynamic adjustment process in all markets. The simple dynamic adjustment models explained here will give you an idea of how adjustments can take place between equilibria and how mathematics can be used to calculate the values of variables at different points in time during the adjustment process. They are only very basic models however designed to give you an introduction to this branch of economics. The mathematics required to analyse