In spending all his income on beer and pizza, Fred finds that the marginal utility of the last pizza is currently 74, the marginal utility of the last bottle of beer is 45, and the price of a bottle of beer is R3.89. 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 on each good is equal.
Marginal utility per rand for pizza:
MUpizza / Pricepizza = 74 / Pricepizza
Marginal utility per rand for beer:
MUbeer / Pricebeer = 45 / 3.89
Setting these two equal to each other:
74 / Pricepizza = 45 / 3.89
Cross multiplying, we get:
74 * 3.89 = 45 * Pricepizza
288.86 = 45 * Pricepizza
Pricepizza = 288.86 / 45
Pricepizza = R6.42
Therefore, if Fred has maximized his utility, the price of a pizza should be R6.42.