Mrs.Simpson buys loaves of bread and quarts of milk each week at prices of $1 and 80 cents, respectively. At present she is buying these products in amounts such that the marginal utilites from the last units purchased of the two products are 80 and 70 units, respectively. Is she buying the utility-maximizing combination of bread & milk? How should she reallocate her expenditures between the two goods?
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.
To determine if Mrs. Simpson is buying the utility-maximizing combination of bread and milk, we need to compare the marginal utilities (MU) per dollar spent on each product.
To calculate the MU per dollar, we divide the marginal utility by the price of each good.
For bread:
MU per dollar = MU of bread / Price of bread = 80 units / $1 = 80 units/dollar
For milk:
MU per dollar = MU of milk / Price of milk = 70 units / $0.80 = 87.5 units/dollar
Comparing the MU per dollar for both goods, we can see that the MU per dollar for milk (87.5 units/dollar) is higher than the MU per dollar for bread (80 units/dollar).
Since Mrs. Simpson is currently not allocating her expenditures in a way that maximizes her utility, she should reallocate her expenditure between the two goods. To do this, she should spend relatively more on milk and relatively less on bread.
By reallocating her expenditures, Mrs. Simpson can allocate her money in a way that equalizes the marginal utilities per dollar spent on each good. This means that the MU per dollar for both bread and milk should be equal.
In this case, since the MU per dollar for milk is higher, she should consider buying more milk and less bread until the MU per dollar for both goods are equalized. This will allow her to maximize her utility and get the most satisfaction from her expenditure.
To determine if Mrs. Simpson is buying the utility-maximizing combination of bread and milk, we need to compare the marginal utility per dollar spent on each product. This can be done by calculating the marginal utilities per dollar spent on bread and milk.
Marginal Utility per Dollar spent on Bread (MU/$ bread) = Marginal Utility of Bread (MU bread) / Price of Bread
MU/$ bread = 80 units / $1 = 80 units
Marginal Utility per Dollar spent on Milk (MU/$ milk) = Marginal Utility of Milk (MU milk) / Price of Milk
MU/$ milk = 70 units / $0.80 = 87.5 units
Since the marginal utility per dollar spent on milk (87.5 units) is higher than the marginal utility per dollar spent on bread (80 units), Mrs. Simpson should reallocate some of her expenditures from bread to milk.
To find the optimal reallocation, we need to equalize the marginal utility per dollar spent on both goods. This can be done by setting up the following equation:
MU/$ bread = MU/$ milk
80 = MU milk / $0.80
Solving for MU milk:
MU milk = 80 x $0.80 = $64
Given that the marginal utility of the last unit of milk purchased is 70 units, Mrs. Simpson is currently buying slightly more milk than is optimal. To achieve the utility-maximizing combination, she should reallocate some of her spending from milk to bread.
However, without additional information about Mrs. Simpson's preferences or budget, it is not possible to determine the exact reallocation of expenditures between the two goods.