Economics, 3rd Edition

OPTIMIZATION: WHAT THE CONSUMER CHOOSES

One of the working assumptions of the SEM is that the consumer will seek to maximize utility subject to 

the constraint of a limited income. This is an example of a constrained optimization problem. How is this 

constrained optimization problem solved?

The Consumer’s Optimal Choices

Using our cola and pizza example, the consumer would like to end up with the best possible combination 

of cola and pizza – that is, the combination on the highest possible indifference curve. But the consumer 

is constrained by the resources available to him – his income as shown by the budget constraint.

---

114  PART 2  SUPPLY AND DEMAND: HOW MARKETS WORK

Figure 5.11 shows the consumer’s budget constraint and three of his many indifference curves. The 

highest indifference curve that the consumer can reach (I

3

 in the figure) is the one that just barely touches 

the budget constraint. The point at which this indifference curve and the budget constraint touch is called 

the optimum. The consumer would prefer point A, but he cannot afford that point because it lies above 

his budget constraint. The consumer can afford point B, but that point is on a lower indifference curve 

and, therefore, provides the consumer less satisfaction. The combination of cola and pizza at point C is 

affordable being just on the budget constraint, but the consumer is not in equilibrium because there is 

an incentive for him to change his consumption choices and reach a higher indifference curve. What this 

means is that the consumer can reallocate his spending decisions and get more utility from his limited 

income. There is an incentive for him to reduce consumption of pizza and increase consumption of cola at 

point D on indifference curve I

2

. By doing this the consumer is getting more utility from an additional cent 

spent on more cola compared to the marginal utility spent on another pizza. This is entirely logical. If you 

could spend one cent on more cola and get an extra 7 utils of utility compared to an extra 5 utils you would 

get from more pizza with the same cent, it makes sense to buy more cola.

However, this is still not the optimum because the consumer can continue to reallocate his spending 

decisions reaching ever higher indifference curves (remember there are an infinite amount on the map) 

until the marginal utility of the last cent spent on cola is equal to the marginal utility of the last cent spent 

on pizza. The optimum represents the best combination of consumption of cola and pizza available to the 

consumer.