Question

A consumer has utility given by U(x,y) = ln(x) + ln(y) where ln is the natural logarithm function. The marginal utility of x is MUx = 1/x and the marginal utility of y is MUy = 1/y.

What is the MRS of good X for good Y of this consumer?

Answer 1

The Marginal Rate of Substitution (MRS) of good X for good Y is calculated as the ratio of the marginal utilities, which is MUx/MUy or y/x.

Step-by-step explanation:

The student is asking for the marginal rate of substitution (MRS) of good X for good Y based on their utility function U(x,y) = ln(x) + ln(y). The MRS reflects the rate at which a consumer can give up some amount of one good in exchange for another while maintaining the same level of utility. According to the information provided, the marginal utility of X (MUx) is 1/x and the marginal utility of Y (MUy) is 1/y. The MRS can be calculated by taking the ratio of the marginal utilities of the two goods, which is MUx divided by MUy. Therefore, MRS of good X for good Y is:

MRS = MUx / MUy = (1/x) / (1/y) = y / x

This ratio of y to x indicates how many units of good Y the consumer must give up to gain an additional unit of good X, holding utility constant. This ratio will be used to determine the utility-maximizing choice of goods based on their prices and the consumer's budget constraint.