Asked by Allissa Jenkins on Jun 21, 2024
Verified
Ambrose has the utility function U(x1, x2) 4x1/21 x2.If Ambrose is initially consuming 25 units of nuts and 17 units of berries, then what is the largest number of berries that he would be willing to give up in return for an additional 39 units of nuts?
A) 8
B) 12
C) 25
D) 6
E) 3
Utility Function
A mathematical representation of a consumer's preference ranking over a set of goods or outcomes.
Units Of Nuts
A measure used to quantify a quantity of nuts, often used for nutritional or commercial purposes.
Units Of Berries
Units of berries refer to the quantified portions or measurements used to define an amount of berries, typically used in contexts of production, sale, or consumption.
- Assess the influence of changes in consumption on utility metrics.
- Investigate consumer selections and the necessary exchanges through the application of marginal rate of substitution (MRS) and indifference curves.
Verified Answer
MT
Melexi ThomasJun 26, 2024
Final Answer :
B
Explanation :
To find the answer, we need to determine the marginal rate of substitution (MRS) between nuts and berries.
MRS = MU of nuts / MU of berries
Taking the partial derivatives of the utility function with respect to nuts and berries, we get:
MU of nuts = 2x1/21 4x22
MU of berries = 4x1/22 x1
Plugging in the initial consumption bundle of (25,17), we get:
MU of nuts = 9.8
MU of berries = 6.5
Therefore, MRS = 1.5.
This means that Ambrose is willing to give up 1.5 units of berries for each additional unit of nuts. To get an additional 39 units of nuts, he would be willing to give up:
39 * 1.5 = 58.5 units of berries.
He cannot give up 58.5 units of berries, so he would give up the largest integer value less than or equal to 58.5, which is 12.
Therefore, the answer is (B).
MRS = MU of nuts / MU of berries
Taking the partial derivatives of the utility function with respect to nuts and berries, we get:
MU of nuts = 2x1/21 4x22
MU of berries = 4x1/22 x1
Plugging in the initial consumption bundle of (25,17), we get:
MU of nuts = 9.8
MU of berries = 6.5
Therefore, MRS = 1.5.
This means that Ambrose is willing to give up 1.5 units of berries for each additional unit of nuts. To get an additional 39 units of nuts, he would be willing to give up:
39 * 1.5 = 58.5 units of berries.
He cannot give up 58.5 units of berries, so he would give up the largest integer value less than or equal to 58.5, which is 12.
Therefore, the answer is (B).
Learning Objectives
- Assess the influence of changes in consumption on utility metrics.
- Investigate consumer selections and the necessary exchanges through the application of marginal rate of substitution (MRS) and indifference curves.