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 doughnut he eats, 9 for the second doughnut he eats, 8 for the third he eats, and so on (that is declining 1 unit for each additional doughnut consumed). Suppose that coffee costs $1.00 per cup and doughnuts $1.00 each, and Omar has a budget that he can spend only on doughnuts and coffee. How large would his budget need to be before he would spend a dollar on coffee?

Answer 1

$6.5

Explanation:

The marginal utility per dollar of a commodity is obtained by:

Marginal utility of coffee = 5.5

Price of coffee = $1

The marginal utility of doughnut declines by 1 per additional unit of donut consumed :

10 / 1, 9 /1..... 1/1

Therefore , before a dollar can be spent on coffee, then the marginal. Utility of coffee should be greater than doughnut.

5.5 doughnuts will be purchased, at this time marginal utility of doughnut will be 5.5/1, the 6th doughnut will have a marginal utility of 5 which is less than that of coffee.

Cost of 5.5 donuts = $5.5

Cost of coffee = $1

Total = $(5.5 + 1) = $6.5