Suppose that Omar’s marginal utility for cups of coffee is constant at 5.5 utils per cup no matter how many cups he drinks. On the other hand, his marginal utility per doughnut is 11 for the first doughnut he eats, 10 for the second he eats, 9 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?
Utility has everything to do with satisfaction and not price.The decision rule for utility maximization is to purchase items that give you the greatest marginal utility per dollar and are affordable or within the budget.For this case,the marginal utility per dollar of coffee is @$5.5\over 1@$ which is 5.5 while the marginal utility per dollar of doughnut is@$10\over1@$ which is 10. Omar budget has to be of at least 1 dollars for doughnuts before he can allocate the next amount to tea.This is because doughnut have a higher utility per dollar than tea. To get the number of units you can allocate within the budget is the intercept point of the budget get constraint = income/price.