Question

Suppose that Sam allocates his income between milk and cereal. Milk costs $2.50 per gallon, and cereal costs $5.00 per box. Sam has $50 per week to spend on these two goods. The following table shows Sam's preference for consumption bundles, as well as how Sam's marginal utility (MU) for milk and cereal, respectively, varies as consumption varies.

MilkCerealMU MilkMU Creal2003---18141351625120143610512479010587586960671345481530291612010---8
Given the information provided here, how should Sam allocate his income between milk and cereal?
Sam should purchase the following, as this is his optimal consumption bundle:
_____ gallons of milk
_____ boxes of cereal

Answer 1

The exact allocation of Sam's budget between milk and cereal requires the complete table of marginal utilities. Still, Sam should aim to equate the marginal utility per dollar spent on milk with the marginal utility per dollar spent on cereal, without exceeding his $50 budget.

Step-by-step explanation:

To determine how Sam should allocate his income between milk and cereal, we need to equate the marginal utility per dollar spent on each good. Unfortunately, the table with Sam's marginal utility for each good is not fully visible in the question. However, we can use the concept of maximizing utility given the budget constraint.

Sam should choose the combination of milk and cereal where the marginal utility per dollar of milk (MU Milk / Price of Milk) is equal to the marginal utility per dollar of cereal (MU Cereal / Price of Cereal), and his spending on milk plus cereal equals his budget of $50.

Typically, a consumer like Sam would maximize utility by ensuring that the last dollar spent on each good provides the same marginal utility. Without the complete table data, we can't specify the exact quantities, but the theoretical approach would involve dividing the marginal utilities given for each good by their respective prices, finding the point where these ratios are equal, and checking that Sam's total expenditure does not exceed $50.

Answer 2

Sam should aim to equate the marginal utility per dollar for milk and cereal to maximize his utility, given his budget constraint. However, the incomplete data on marginal utilities for milk and cereal make it impossible to answer precisely how Sam should allocate his income.

Step-by-step explanation:

To determine how Sam should allocate his income between milk and cereal, we use the concept of marginal utility (MU) per dollar spent.

To maximize utility, Sam should equalize the MU per dollar spent on each good. Since the MU for milk and for cereal declines as more of each good is consumed, he will need to balance the two to reach this point. Unfortunately, your provided data for Sam's MU were incomplete.

With full MU data for both milk and cereal, you would divide the MU of each by its price to find the MU per dollar and then purchase up to the point where the MU per dollar for milk is equal to the MU per dollar for cereal, within Sam's budget constraint of $50.