Suppose that Omar’s marginal utility for cups of coffee is constant at 3.5 utils per cup no matter how many cups he drinks. On the other hand, his marginal utility per doughnut is 10 for the first doughnut he eats, 9 for the second he eats, 8 for the third he eats, and so on (that is, declining by 1 util per additional doughnut). In addition, suppose that coffee costs $1 per cup, doughnuts cost $1 each, and Omar has a budget that he can spend only on doughnuts, coffee, or both. How big would that budget have to be before he would spend a dollar buying a first cup of coffee?
The marginal utility per dollar for a good is the marginal utility divided by the price of the good (=MU/P). For the first doughnut we have 10 (=10/$1), the second doughnut 9(=9/$1), third 8, fourth 7, fifth 6, sixth 5, seventh 4, eighth 3, ninth 2, tenth 1. The marginal utility per dollar for every cup of coffee is 3.5 (=3.5/$1). To determine how big the budget would have to be before Omar would spend a dollar buying his first cup of coffee, we compare the marginal utility per dollar values. Omar will purchase the first doughnut before he buys a cup of coffee because the marginal utility per dollar for the doughnut is greater than the marginal utility per dollar for the cup of coffee (10>1.5). The same is true for the second through the seventh doughnut. This implies Omar will buy 7 doughnuts at the price of $1 before he buys his first cup of coffee. Therefore, his budget will need to $8 before he buys his first cup of coffee, $7 on the doughnuts and $1 for the cup of coffee.