Asked by george brown on Apr 27, 2024
Verified
Ambrose's brother Bartholomew has an income of $114 and a utility function U(x1, x2) 32x1/21 x2.The price of good 1 (nuts) is $4 and the price of good 2 (berries) is $1.How many units of nuts will Bartholomew demand?
A) 26
B) 14
C) 16
D) 12
E) 30
Utility Function
A mathematical representation that ranks preferences or satisfaction levels consumers derive from consuming goods and services.
Nuts
Edible seeds enclosed in a hard shell, often characterized by their high fat and protein content.
Berries
Small, pulpy, and often edible fruits, typically juicy, rounded, brightly colored, and seed-containing.
- Investigate utility functions to calculate the suitable amounts of goods to be consumed.
- Scrutinize the effect of maximizing utility on the demand function for several products.
Verified Answer
SM
Stephanie ManningApr 30, 2024
Final Answer :
C
Explanation :
Bartholomew's demand for nuts can be found by maximizing his utility function with respect to the number of nuts he consumes. Taking the partial derivative of the utility function with respect to the number of nuts, setting it equal to 0 and solving for x1, we get:
16x1 = 114/4
x1 = 2.25
Since Bartholomew can only purchase whole units of nuts, he will demand 2 units of nuts, which is the closest integer value to 2.25. Therefore, the answer is C) 16.
16x1 = 114/4
x1 = 2.25
Since Bartholomew can only purchase whole units of nuts, he will demand 2 units of nuts, which is the closest integer value to 2.25. Therefore, the answer is C) 16.
Learning Objectives
- Investigate utility functions to calculate the suitable amounts of goods to be consumed.
- Scrutinize the effect of maximizing utility on the demand function for several products.