Answer:a) To find Alice's optimal bundle of bread and butter in Town B, we need to maximize her utility given her budget constraint.
In Town B, Alice's utility function is given by u(x1, x2) = x1^a * x2^(1-a), where a is a parameter that represents her preferences between bread and butter.
Alice's budget constraint in Town B is given by p1x1 + p2x2 = m, where p1 and p2 are the prices of bread and butter, and m is her income.
Plugging in the values, we have p1 = 3, p2 = 1, and m = 12.
To find the optimal bundle, we can use the concept of marginal rate of substitution (MRS). The MRS measures the rate at which Alice is willing to trade one good for another while maintaining the same level of utility.
Mathematically, MRS = (∂u/∂x1) / (∂u/∂x2), which is the ratio of the partial derivatives of the utility function with respect to x1 and x2.
To find Alice's MRS at the optimal bundle in Town B, we can calculate the partial derivatives of the utility function with respect to x1 and x2, and then evaluate them at the optimal bundle.
b) If Alice is exactly as satisfied with her optimal bundle in Town B as she was with her optimal bundle in Town A, this implies that the MRS in Town B is equal to the MRS in Town A at their respective optimal bundles.
To compare the satisfaction levels, we need to determine the value of a, which represents Alice's preference parameter in the utility function u(x1, x2) = x1^a * x2^(1-a).
By finding the MRS in Town B and comparing it to the MRS in Town A, we can determine the value of a that satisfies the given condition.
In summary:
a) To find Alice's optimal bundle in Town B, maximize her utility function subject to the budget constraint.
b) Compare the MRS at the optimal bundle in Town B to the MRS at the optimal bundle in Town A to determine the value of a.
Explanation: