Answer to Question #168045 in Microeconomics for Sophia Nyborg

Question

Suppose that Omar's marginal utility for each additional cup of coffee is 6.5 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?

 

Answer 1

marginal utility for coffee is a constant 6.5 utils.

but the marginal utility per doughnut is diminishing at the rate of 1 util per doughnut.

doughnuts will be bought till its marginal utility falls below 6.5 utils.

it can be seen that doughnuts will be bought using $4.

coffee can be bought using $1.

Budget to have before he would spend a dollar buying a first cup is $4+$1 =>$5.