Assume that strawberries cost $1 and apples cost $2. Which of the following combinations of strawberries and apples satisfies the following rule?
[tex]\frac{M U_x}{P_x}=\frac{M U_y}{P_y}[/tex]
| Strawberries Consumed | Total Utility |
| :-------------------- | :------------ |
| 0 | 0 |
| 1 | 7 |
| 2 | 13 |
| 3 | 18 |
| 4 | 22 |
| 5 | 25 |
| 6 | 27 |
| 7 | 28 |
| Apples Consumed | Total Utility |
| :-------------- | :------------ |
| 0 | 0 |
| 1 | 14 |
| 2 | 26 |
| 3 | 36 |
| 4 | 44 |
| 5 | 50 |
| 6 | 54 |
| 7 | 56 |
A. 3 strawberries and 2 apples
B. 6 strawberries and 7 apples
C. 6 strawberries and 5 apples
D. 2 strawberries and 4 apples
Answer (1)
Calculate the marginal utility for strawberries and apples at each consumption level.
For each combination, calculate the ratio of marginal utility to price for both goods.
Check if the ratios are equal for each combination.
Determine that none of the combinations satisfy the condition P s M U s = P a M U a , so the answer is that none of the combinations satisfy the condition. N o n e
Explanation
Understanding the Problem We are given a table of total utility for strawberries and apples at different consumption levels. We are also given the prices of strawberries and apples: Strawberries cost $1 and apples cost $2. The goal is to find which combination of strawberries and apples satisfies the condition P s M U s = P a M U a , where M U s is the marginal utility of strawberries, P s is the price of strawberries, M U a is the marginal utility of apples, and P a is the price of apples.
Calculating Marginal Utilities First, we need to calculate the marginal utility for each level of consumption for both strawberries and apples. Marginal utility is the change in total utility from consuming one additional unit of a good. M U ( n ) = T U ( n ) − T U ( n − 1 )
Listing Marginal Utilities Marginal Utility of Strawberries:
M U s ( 1 ) = 7 − 0 = 7
M U s ( 2 ) = 13 − 7 = 6
M U s ( 3 ) = 18 − 13 = 5
M U s ( 4 ) = 22 − 18 = 4
M U s ( 5 ) = 25 − 22 = 3
M U s ( 6 ) = 27 − 25 = 2
M U s ( 7 ) = 28 − 27 = 1
Marginal Utility of Apples:
M U a ( 1 ) = 14 − 0 = 14
M U a ( 2 ) = 26 − 14 = 12
M U a ( 3 ) = 36 − 26 = 10
M U a ( 4 ) = 44 − 36 = 8
M U a ( 5 ) = 50 − 44 = 6
M U a ( 6 ) = 54 − 50 = 4
M U a ( 7 ) = 56 − 54 = 2
Checking Combinations Now, we will check each combination to see if the condition P s M U s = P a M U a is satisfied.
Combination 1: 3 strawberries and 2 apples. M U s ( 3 ) = 5 , P s = 1 . P s M U s = 1 5 = 5 M U a ( 2 ) = 12 , P a = 2 . P a M U a = 2 12 = 6 Since 5 = 6 , this combination does not satisfy the condition.
Combination 2: 6 strawberries and 7 apples. M U s ( 6 ) = 2 , P s = 1 . P s M U s = 1 2 = 2 M U a ( 7 ) = 2 , P a = 2 . P a M U a = 2 2 = 1 Since 2 = 1 , this combination does not satisfy the condition.
Combination 3: 6 strawberries and 5 apples. M U s ( 6 ) = 2 , P s = 1 . P s M U s = 1 2 = 2 M U a ( 5 ) = 6 , P a = 2 . P a M U a = 2 6 = 3 Since 2 = 3 , this combination does not satisfy the condition.
Combination 4: 2 strawberries and 4 apples. M U s ( 2 ) = 6 , P s = 1 . P s M U s = 1 6 = 6 M U a ( 4 ) = 8 , P a = 2 . P a M U a = 2 8 = 4 Since 6 = 4 , this combination does not satisfy the condition.
Final Answer None of the given combinations satisfy the condition P s M U s = P a M U a .
Examples
This concept is used in everyday decision-making when allocating a budget between different goods or services. For example, when deciding how to spend your money on food and entertainment, you implicitly consider the marginal utility you'll receive from each dollar spent. If the marginal utility per dollar spent on food is higher than that of entertainment, you might choose to allocate more of your budget to food, and vice versa, until the marginal utility per dollar is equalized across all goods.
