Question

Suppose that Omar’s marginal utility for cups of coffee is constant at 10 utils per cup no matter how many cups he drinks. On the other hand, his marginal utility per doughnut is 12 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 $2 each, and Omar has a budget that he can spend only on doughnuts, coffee, or both. If Omar has $12 to spend and if he spends the entire $12 budget on coffee and doughnuts, how many cups of coffee will he buy?

Answer 1

MU for cups of coffee = 10
So, MUcoffee/Pcoffee = 10/1 = 10

MU for first doughnut = 12
So, MU/Pdoughnut = 12/2 = 6

MU for 2nd doughnut = 10
So, MU/Pdoughnut = 10/2 = 5

And MU for doughnut goes on decreasing which means MU/Pdoughnut also decreases. Thus, we can see that MUcoffee/Pcoffee will always exceed MU/Pdoughnut. So, Omar will purchase only coffee with his entire budget.
Coffee purchased = Budget/Price of coffee = 12/1 = 12

He will buy 12 cups of coffee.