Mrs. Wilson buys loaves of bread and quarts of milk...?

Question

each week at prices of $1 and 80 cents, respectively. At present she is buying these products in amounts such that the marginal utilities from the last units purchased of the two products are 80 and 70 utils, respectively. Is she buying the utility-maximizing combination of bread and milk? If not, how should she reallocate her expenditures between the two goods?

Answer 1

When buying bread, she's getting 80 utils for a dollar.

When she's buying milk, she's getting 70 utils for 80 cents, which is equivilent to 87.5 utils for a dollar (division).

With milk, she's getting more for her money.  So she should allocate more money towards milk.  :)

Answer 2

She is not doing the right thing to maximize her utility from the consumption of  bread and milk. If the last dollar spent on bread gives her 80 utils of satisfaction, the last dollar spent on milk should give her the same utility of 80. This is the utlity maximization rule of equating the marginal utility per unit of money spent on the different products/ goods. But in this case she spend 80 cents to get 70 utils from the last quart of milk. In other words she roughly gets 87.5 utils by spending the last dollar on milk. So by reducing her spending of one dollar on bread, she would lose 80 utils but would get 87.5 utils by reallocating that dollar withdrwan from bread to milk purchase. So, to maximize utiliy she should increase the consumption of milk a little more.

Answer 3

I believe the utility maximizing number can be found by dividing the marginal utility by the price of the good.

For example:

The marginal utility of the bread divided by the price is

MUbread/1=    80/1     =80

For the milk it would be

MUmilk/80=    70/.80    =87.5

This means she gets 80 units per dollar spent on the bread.

She gets 87.5 units per dollar spent on the milk.

Obviously, she is getting more units per dollar with the milk.