Answer :
The price of good Y, rounded to the fifth decimal, is approximately 3.01048.
Lan's utility function is U(x, y) = 4.2x^2.5y^1.2, where x is the quantity of good X and y is the quantity of good Y.
Lan's optimal bundle is x* = 1.3 units of good X and y* = 2.6 units of good Y.
To find the price of good Y, we need to calculate the marginal rate of substitution (MRS), which is the ratio of the marginal utility of X to the marginal utility of Y.
MRS = (MUx / MUy) = (dU/dx) / (dU/dy)
Taking the partial derivatives of the utility function with respect to x and y gives us:
MRS = (10.5x^1.5y^1.2) / (2.52.5x^2.5y^0.2)
Plugging in the values of x* = 1.3 and y* = 2.6 into the MRS equation:
MRS = (10.5 * (1.3)^1.5 * (2.6)^1.2) / (2.5 * 2.5 * (1.3)^2.5 * (2.6)^0.2)
Learn more about rounded here:
https://brainly.com/question/34045884
#SPJ11
