Suppose that Omar\'s marginal utility for cups of coffee is constant at 1.5 util

Question

Suppose that Omar's marginal utility for cups of coffee is constant at 1.5 utils per cup no matter how many cups he drinks. On the other hand, his marginal utility per doughnut is 10 for the first he eats, 9 for the second, 8 for the third, and so on (declining by 1 until per additional doughnut). Suppose that coffee cost $1 per cup, and so do the doughnuts and Omar has a budget that he can only spend on coffee, doughnuts, or both. How big would that budget have to be before he would spend a dollar buying a first cup of coffee?

Explanation / Answer

He would buy 9 doughnuts (at which point the marginal utility of an additional doughnut would be 2, the 10th would only be 1). He would then buy a cup of coffee, since the marginal utility of coffee is higher than the 10th doughnut. So he would need a budget of $10 before he bought the first cup of coffee

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