Final answer:
Ann's expenditure function is given by e(u, px, py) = (px)(x) + (py)(y), where u is the utility, px is the price of good x, and py is the price of good y. The expenditure function calculates the minimum amount of money Ann needs to spend to achieve a specific level of utility. In this case, the expenditure function is derived from Ann's utility function u(x, y) = 4xy.
Step-by-step explanation:
Ann’s Utility Function
To find Ann’s expenditure function, we need to first determine her marginal utility for each good/variable. The marginal utility of a good represents the additional utility gained from consuming an additional unit of that good. To find the marginal utility, we take the partial derivatives of the utility function with respect to each variable.
For Ann’s utility function u(x, y) = 4xy, the marginal utility of x, denoted as MUx, is equal to 4y, and the marginal utility of y, denoted as MUy, is equal to 4x.
Next, we need to determine the ratio of the marginal utilities, which represents the rate at which Ann is willing to trade one good for another while keeping the level of utility constant. In this case, the marginal rate of substitution (MRS) is equal to (MUx)/(MUy) = (4y)/(4x) = y/x.
Ann's expenditure function, denoted as e(u, px, py), gives us the minimum amount of money Ann has to spend to obtain a certain level of utility u at prices px and py. Using the MRS, we can express the expenditure function as e(u, px, py) = (px)(x) + (py)(y) = (px)(x) + (py)(x(y/x)), which simplifies to e(u, px, py) = (px)(x) + (py)(y).