Question

Jack consumes only Bread (good x) and Cheese (good y). His utility function is given by U(x, y) = ln(x) + ln(y) (a) Find Jack’s marginal rate of substitution (MRS) at bundle (x, y).

(b) The price of good x is $6 and the price of good y is $3. Jack has an income of $120. Find his utility maximising consumption bundle.
(c) Calculate Jack’s utility from the bundle you have solved in part (b).

Answer 1

To find the MRS, find the partial derivatives of the utility function with respect to x and y. For utility maximization, compare the ratio of marginal utility to price for the two goods. The utility can be calculated by substituting the values of x and y into the utility function.

Step-by-step explanation:

To find Jack's marginal rate of substitution (MRS) at bundle (x, y), we need to find the derivative of the utility function with respect to x and y. The utility function is U(x, y) = ln(x) + ln(y).

To find the MRS, we need to find the partial derivative ∂U/∂x and ∂U/∂y.

The marginal rate of substitution (MRS) is the ratio of the marginal utility of x to the marginal utility of y: MRS = ∂U/∂x / ∂U/∂y.

(b) To find Jack's utility maximizing consumption bundle, we can use the approach of comparing the ratio of the marginal utility to price of good 1 with the marginal utility to price of good 2 and applying the rule that at the optimal choice, the two ratios should be equal.

(c) To calculate Jack's utility from the bundle solved in part (b), we can substitute the values of x and y into the utility function U(x, y) = ln(x) + ln(y) and evaluate it.