Economics, 3rd Edition

Constrained Optimization

Throughout this book we will look at situations where consumers, firms and governments are assumed 

to exhibit maximizing or minimizing behaviour. Consumers might be assumed to want to maximize the 

satisfaction (utility) they get from consumption, firms might be assumed to want to maximize profits but 

minimize costs, and governments might want to maximize tax revenue, for example. In most cases, there 

will be factors which will limit the extent to which this maximizing or minimizing behaviour can be carried 

out such as time, income and resources. In the case of consumers, the ability to maximize utility will be 

subject to a constraint – their income. Firms might want to minimize costs but subject to the constraint of 

their income (revenue) or the factor inputs that they have at their disposal.

Economists will often carry out analysis under conditions of constrained optimization. Typically this might 

take the form: maximize 

x subject to the existence of y constraint. Usually, the constraint is assumed to 

be fixed and so a calculation can be made which shows the optimizing (maximum or minimum) behaviour 

given the constraint which exists. We can then change the constraint to see how behaviour would differ 

and what the outcome would be. You will probably learn some of the mathematical techniques for solving 

constrained optimization problems in the quantitative methods modules that you will take alongside your 

Principles of Economics module.