Question

Optimal Choice of Milk and Honey. The price of milk is $2 per gallon, and the price of honey is $4 per jar. Hal's income is $16. Assuming that Hal spends all of his income on honey and milk, the combination of milk and honey that will maximize his total utility is _____ jars of honey and _____ gallons of milk.

Answer 1

Hal can afford various combinations of milk and honey within his $16 budget. The exact combination that maximizes utility cannot be determined without additional information on Hal's preferences. In theoretical terms, the optimal choice would depend on Hal's utility function.

Step-by-step explanation:

The student's question involves finding the combination of milk and honey that maximizes Hal's total utility given his budget constraints and the prices of milk and honey. Since milk costs $2 per gallon and honey costs $4 per jar, and assuming Hal spends all his income of $16 on these two goods, we'll use simple math to determine the possible combinations he can afford.

Let's calculate the possible combinations:

• If Hal buys 0 jars of honey ($0), he can buy 8 gallons of milk ($16).
• If Hal buys 1 jar of honey ($4), he can buy 6 gallons of milk ($12).
• If Hal buys 2 jars of honey ($8), he can buy 4 gallons of milk ($8).
• If Hal buys 3 jars of honey ($12), he can buy 2 gallons of milk ($4).
• If Hal buys 4 jars of honey ($16), he can buy 0 gallons of milk ($0).

Without further information about Hal's preferences or the utility he derives from each good, we cannot definitively say which combination maximizes his total utility. In practice, Hal would choose the combination that gives him the most satisfaction based on his personal preferences.

Answer 2

Assuming that Hal spends all of his income on honey and milk, the combination of milk and honey that will maximize his total utility is 2 jars of honey and 4 gallons of milk.

Step-by-step explanation:

This question is missing a table that should be as follows:

quantity total util. marginal quantity total util. marginal

of milk from milk utility per $ of honey from honey utility per $

1 32 16 1 44 11

2 60 14 2 84 10

3 84 12 3 120 9

4 104 10 4 152 8

5 120 8 5 180 7

6 132 6 6 204 6

7 140 4 7 224 5

8 144 2 8 240 4

We should purchase quantities that yield the same marginal utility per dollar spent, options are:

• 4 gallons of milk and 2 jars of honey ⇒ total cost = $8 + $8 = $16
• 5 gallons of milk and 4 jars of honey ⇒ total cost = $10 + $16 = $26
• 6 gallons of milk and 6 jars of honey ⇒ total cost = $12 + $24 = $36
• 7 gallons of milk and 8 jars of honey ⇒ total cost = $14 + $32 = $46