(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 121

96 PART • Producers, Consumers, and Competitive Markets down an indifference curve in Figure 3.8 (page 79) The additional consumption of food, ⌬F, will generate marginal utility MUF This shift results in a total increase in utility of MUF ⌬F At the same time, the reduced consumption of clothing, ⌬C, will lower utility per unit by MUC, resulting in a total loss of MUC ⌬C 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, = MUF(⌬F) + MUC(⌬C) Now we can rearrange this equation so that -(⌬C/⌬F) = MUF/MUC But because −(⌬C/⌬F) 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 or MUF/PF = MUC/PC • equal marginal principle Principle that utility is maximized when the consumer has equalized the marginal utility per dollar of expenditure across all goods (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, suppose 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 satisfied 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 reappear in different forms throughout our analysis of consumer and producer behavior