In Section 3.3, we showed graphically how a consumer can maximize his or her satisfaction, given a budget constraint. We do this by finding the highest indifference curve that can be reached, given that budget constraint. Because the highest indifference curve also has the highest attainable level of utility, it is natural to recast the consumer ’s problem as one of maximizing utility subject to a budget constraint.
The concept of utility can also be used to recast our analysis in a way that provides additional insight. To begin, let’s distinguish between the total utility obtained by consumption and the satisfaction obtained from the last item consumed. Marginal utility (MU) measures the additional satisfaction obtained from consuming one additional unit of a good. For example, the marginal utility associated with a consumption increase from 0 to 1 unit of food might be 9; from 1 to 2, it might be 7; from 2 to 3, it might be 5.
These numbers imply that the consumer has diminishing marginal utility: As more and more of a good is consumed, consuming additional amounts will yield smaller and smaller additions to utility. Imagine, for example, the consumption of television: Marginal utility might fall after the second or third hour and could become very small after the fourth or fifth hour of viewing.
We can relate the concept of marginal utility to the consumer ’s utility-maximization problem in the following way. Consider a small movement down an indifference curve in Figure 3.8 (page 79). The additional consumption of food, AF, will generate marginal utility MUr This shift results in a total increase in utility of MUF AF. At the same time, the reduced consumption of clothing, AC, will lower utility per unit by MUC, resulting in a total loss of MUC AC.
Because all points on an indifference curve generate the same level of utility, the total gain in utility associated with the increase in F must balance the loss due to the lower consumption of C. Formally,
0 = MUf(AF) + MUc(AC)
Now we can rearrange this equation so that
– (AC/AF) = MUf/MUc
But because -(AC/AF) is the MRS of F for C, it follows that
MRS = MUF/MUc (3.5)
Equation (3.5) tells us that the MRS is the ratio of the marginal utility of F to the marginal utility of C. As the consumer gives up more and more of C to obtain more of F, the marginal utility of F falls and that of C increases, so MRS decreases.
We saw earlier in this chapter that when consumers maximize their satisfaction, the MRS of F for C is equal to the ratio of the prices of the two goods:
MRS = PF/PC (3.6)
Because the MRS is also equal to the ratio of the marginal utilities of consuming F and C (from equation 3.5), it follows that
MUf/MUc = PF/PC
muF/fF = MUC/PC (3.7)
Equation (3.7) is an important result. It tells us that utility maximization is achieved when the budget is allocated so that the marginal utility per dollar of expenditure is the same for each good. To see why this principle must hold, sup- pose that a person gets more utility from spending an additional dollar on food than on clothing. In this case, her utility will be increased by spending more on food. As long as the marginal utility of spending an extra dollar on food exceeds the marginal utility of spending an extra dollar on clothing, she can increase her utility by shifting her budget toward food and away from clothing. Eventually, the marginal utility of food will decrease (because there is diminishing marginal utility in its consumption) and the marginal utility of clothing will increase (for the same reason). Only when the consumer has sat- isfied the equal marginal principle—i.e., has equalized the marginal utility per dollar of expenditure across all goods—will she have maximized utility. The equal marginal principle is an important concept in microeconomics. It will reap- pear in different forms throughout our analysis of consumer and producer behavior.
Source: Pindyck Robert, Rubinfeld Daniel (2012), Microeconomics, Pearson, 8th edition.