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Annie is faced with three alternative consumption baskets: Basket A contains ...

Oct 10, 2024

Annie is faced with three alternative consumption baskets: Basket A contains 2 pairs of shoes, 3 bottles of wine and 1 movie ticket. Basket B contains 9 pairs of shoes, 3 bottles of wine and 2 movie tickets. Basket C contains 2 pair of shoes, 3 bottle of wine and 3 movie tickets. If Annie's preferences satisfy the more-is-better assumption then, When comparing baskets A and B, choose your answer... Annie is indifferent between A and B Annie prefers B over A Annie's preferences cannot be determined from the information provided Annie prefers A over B

Key Concept

More-is-better assumption

Explanation

According to the more-is-better assumption, if one basket contains more of at least one good without having less of another, it is preferred. Basket B has more shoes and more movie tickets compared to Basket A, making it the preferred choice.

Annie is faced with three alternative consumption baskets: Basket A contains 2 pairs of shoes, 3 bottles of wine and 1 movie ticket. Basket B contains 9 pairs of shoes, 3 bottles of wine and 2 movie tickets. Basket C contains 2 pair of shoes, 3 bottle of wine and 3 movie tickets. If Annie's preferences satisfy the more-is-better assumption then, When comparing baskets A and C, choose your answer... Annie is indifferent between A and B Annie prefers B over A Annie's preferences cannot be determined from the information provided Annie prefers A over B

Key Concept

More-is-better assumption

Explanation

According to the more-is-better assumption, if one basket contains more of at least one good without having less of another, it is preferred. Comparing baskets A and C, both have the same number of shoes and wine, but C has more movie tickets, making C preferable to A. Thus, Annie prefers C over A.

Annie is faced with three alternative consumption baskets: Basket A contains 2 pairs of shoes, 3 bottles of wine and 1 movie ticket. Basket B contains 9 pairs of shoes, 3 bottles of wine and 2 movie tickets. Basket C contains 2 pair of shoes, 3 bottle of wine and 3 movie tickets. If Annie's preferences satisfy the more-is-better assumption then, When comparing baskets B and C, choose your answer... Annie is indifferent between A and B Annie prefers B over A Annie's preferences cannot be determined from the information provided Annie prefers A over B

Key Concept

More-is-better assumption

Explanation

According to the more-is-better assumption, if one basket contains more of at least one good without having less of another, it is preferred. Basket B has 9 pairs of shoes and 2 movie tickets, while Basket C has 2 pairs of shoes and 3 movie tickets. Thus, Basket B is preferred over Basket C. However, since the question asks to compare B and C directly, we cannot definitively say Annie prefers one over the other without additional information about her utility function. Hence, the correct answer is that Annie's preferences cannot be determined from the information provided.

After paying for his necessities (rent, utilities, food), Kim has

173 a month left over to spend on beer (good x) and petrol (good y). The price of a beer is Px =

6.0. The price of petrol is Py = $2.05 per litre. At what height does Kim's budget line intersects the y-axis? (Report your answer to 2 decimal places.)

Solution

Budget Constraint: Kim's budget constraint can be expressed as

P_x \cdot x + P_y \cdot y = I

, where

I

is the income left after necessities. Here,

I = 173

P_x = 6.0

(price of beer), and

P_y = 2.05

(price of petrol)

Finding the y-intercept: To find the height at which the budget line intersects the y-axis (where

x = 0

), we set

x = 0

in the budget constraint equation:

P_y \cdot y = I

. Thus,

y = \frac{I}{P_y} = \frac{173}{2.05}

Calculation: Performing the calculation gives

y = 84.39

(rounded to two decimal places)

Answer

84.39

Key Concept

Budget Line Intersection with the Y-axis

Explanation

The height at which the budget line intersects the y-axis represents the maximum quantity of petrol Kim can purchase if he spends all his remaining income on petrol.

Zoe loves apples and coffee. Apples cost

2.3 per kilogram. Coffee costs

8.3 per cup. After a late night, Zoe decides that she needs an extra cup of coffee. If Zoe is currently spending all of her budget, how many kilograms of apples must she give up? (Report your result to 2 decimal places.)

Solution

Budget Constraint: Zoe's budget constraint can be expressed as

P_a \cdot a + P_c \cdot c = I

, where

I

is her total budget,

P_a = 2.3

(price of apples per kilogram), and

P_c = 8.3

(price of coffee per cup)

Additional Coffee Cost: Since Zoe decides to buy an extra cup of coffee, the cost of this additional coffee is

P_c = 8.3

Apples to Give Up: To find out how many kilograms of apples Zoe must give up, we can rearrange the budget constraint to find the equivalent amount in apples:

\text{kg of apples} = \frac{P_c}{P_a} = \frac{8.3}{2.3} \approx 3.61

Answer

3.61

Key Concept

Budget Constraint and Opportunity Cost

Explanation

Zoe must give up approximately 3.61 kilograms of apples to afford an additional cup of coffee, reflecting the trade-off in her budget.

Match the following characteristics of a consumer's optimal consumption basket to the conditions that describes them. Prompt 1A consumer spends all of their available income. Interior optimum condition First-order condition Partial derivative condition Tangency condition Budget line condition

Solution

Budget Constraint Condition: A consumer spends all of their available income when they are at their optimal consumption basket. This is represented by the budget line condition, which states that the total expenditure on goods equals the income available

First-Order Condition: The first-order condition for optimal consumption occurs when the marginal utility per dollar spent on each good is equal, ensuring that the consumer maximizes their utility given their budget constraint

Tangency Condition: The tangency condition occurs when the budget line is tangent to the highest indifference curve, indicating that the consumer cannot increase their utility without exceeding their budget

Answer

Budget line condition

Key Concept

The optimal consumption basket is achieved when a consumer spends all their income, satisfying the budget line condition.

Explanation

This condition ensures that the consumer is maximizing their utility given their budget constraints.

Match the following characteristics of a consumer's optimal consumption basket to the conditions that describes them. A consumer cannot improve their welfare by reallocating their expenditure from one item to another.. Interior optimum condition First-order condition Partial derivative condition Tangency condition Budget line condition

Solution

Definition of Optimal Consumption: A consumer cannot improve their welfare by reallocating their expenditure from one item to another when they are at an optimal consumption basket. This is represented by the first-order condition, which states that the marginal utility per dollar spent on each good must be equal

Answer

First-order condition

Key Concept

First-order condition in consumer theory

Explanation

At the optimal consumption basket, reallocating expenditure does not increase utility, indicating that the consumer is maximizing their satisfaction given their budget.

Tracy's preferences over consumption baskets containing food (good x) and clothing (good y) are represented by the utility function: U = 3x + y What utility does tracy receive from a basket containing 7 meals and 9 items of clothing?

Solution

Utility Calculation: Tracy's utility function is given by

U = 3x + y

. To find the utility from a basket containing 7 meals (good x) and 9 items of clothing (good y), we substitute

x = 7

and

y = 9

into the utility function:

U = 3(7) + 9

Final Calculation: Performing the calculation gives

U = 21 + 9 = 30

Answer

Key Concept

Utility Function

Explanation

The utility function represents the satisfaction a consumer derives from consuming goods, and in this case, Tracy receives a utility of 30 from the specified basket.