Question

Suppose utility is given by the following function: u(x, y) = xy³ Use this utility function to answer the following questions:

(d) What is the marginal rate of substitution implied by this utility function? What does this mean in words?

(e) How much of each good would this individual need to have to be willing to trade 1 unit of good x for 1 unit of good y (i.e. for the MRS to be equal to 1)?

(f) Suppose we squared utility, so that u(x, y) = (xy³ ) ² . Would this affect the marginal utilities? Would this affect the MRS? (

Answer 1

u(x, y) = xy³

(d) MRS =
It means y/3x units of y needs to be given up in order to get an additional unit of x.

(e) MRS = 1 = y/3x
So, y = 3x
So when x = 1 then y = 3*1 = 3
Thus, MRS = 3/(3*1) = 3/3 = 1
So, individual needs to have y = 3x or for an example x = 1 and y = 3 to be willing to trade 1 unit of good x for 1 unit of good y.

(f) MUx =

MUy =

Thus, marginal utilities would be affected

MRS = MUx/MUy = 2xy⁶/6x²y⁵ = y/3x
Thus, MRS wouldn't be affected.