The shape of an indifference curve will depend upon the utility function of the individual concerned. One likely shape for an indifference curve is shown in Figure 3.3. By definition, as the two points labeled 1 and 2 both lie on one indifference curve, they yield an equal utility level, . Indeed, all points along the indifference curve yield that amount of utility. The reason why the term “indifference curve” is used is as follows: since each combination yields the same amount of utility, a rational consumer will be indifferent between alternative bundles along any one such curve.
An indifference curve demonstrates that the individual is confronted with trade-offs in consumption. In moving from point 1 to point 2, for example, the consumer can give up some of good y in return for more of good x, without changing the amount of utility he or she attains. If an indifference curve were linear – that is, it could be drawn as a straight line – the terms of this trade-off would not alter as the individual changes the proportions in which the two goods are consumed. However, the indifference curve shown in Figure 3.3 is not linear, and so the terms of this trade-off are not constant. As we have drawn it, an individual has to give up increasingly large amounts of y in return for additional units of x if utility is to remain unchanged.
For any utility function, there will be an indifference curve for each feasible utility level. We show three indifference curves in Figure 3.4. These correspond to the different utility levels, , and , such that > and <. The individual is indifferent between the combinations at points 1 and 2 as they confer the same utility level (). Similarly, the individual is indifferent between the combinations at points 3 and 4 as they confer equal utility (). However, the combinations shown by 3 and 4 are preferred to those at 1 and 2. Any combination on the indifference curve for utility level is preferred to any combination on that for .