In spending all his income on beer and pizza, Fred finds that the marginal utility of the last pizza is currently 88, the marginal utility of the last bottle of beer is 9, and the price of a bottle of beer is R12.65. If Fred has maximized his utility, the price of a pizza is:
To maximize his utility, Fred should allocate his income in such a way that the marginal utility per rand spent is equal for both goods.
Marginal utility per rand for pizza = 88 / P
Marginal utility per rand for beer = 9 / 12.65 = 0.712
To maximize utility, the marginal utility per rand spent on pizza should equal the marginal utility per rand spent on beer:
88 / P = 0.712
P = 88 / 0.712
P = 123.60
Therefore, the price of a pizza should be R123.60 for Fred to maximize his utility.