Dynamic Economics: Optimization by the Lagrange Method

By Gregory C. Chow | Go to book overview

CHAPTER ONE Introduction

1.1 Dynamic Economics and Optimization

Dynamic economics is concerned with explaining economic behavior through time. Because economic behavior of individuals and enterprises always occurs through time, should all of economics be dynamic economics? No, because of the power of abstraction in scientific theorizing. Of course, all behavior occurs through time. Yet, without explicitly taking into account the temporal aspects of behavior, economists are able to explain a great deal of economic behavior. For example, static demand theory implies that if the price goes up, the quantity demanded goes down. The price and quantity referred to are supposed to be observed in the same time period. The price is the price on a certain Wednesday, and the quantity is the amount purchased on that same Wednesday. The term dynamic economics is used because there was a long period in its development when much of economic theorizing ignored the dynamic aspects of economic behavior and failed to explain the time paths of economic variables. Built on the method of comparative statics, economic theory explains only the directions of change of economic variables resulting from a change in the parameters, but it does not date the changes at each instance of time. Dynamic economics can explain the time paths of economic variables.

How do economists explain the time paths of economic variables? At an early stage of the development of dynamic economics in the 1950s and 1960s, a significant portion of dynamic theories is ad hoc. Starting with a static theory explaining a variable y by a variable x, delayed effects of x can be introduced by using distributed lags to obtain a dynamic theory. For example if yt at time t is assumed to equal βx + γyt-1, the time path yt for t = 1, 2, . . . is determined once the initial value y0 and the time path xt for t = 1, 2,. . . are given. Baumol ( 1951) is a good exposition of dynamic economics as it was known at the time, as is Allen ( 1956), which appeared a few years later. Many of the models introduced are based on ad hoc assumptions. The main tool of analysis was

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