Question

U (x, y) = 3x^3/4 + 3y

a)Calculate MUx and MUy.

b) Do the consumer’s preferences exhibit a diminishing marginal utility for each good?

c) Calculate MRS_x,y.

d) Do the consumer’s preferences exhibit a diminishing marginal rate of substitution of x?

Answer 1

Answer

a) Formula:

Hence MU_x = (9/4)x^-1/4

MU_y = 3

b) Diminishing Marginal utility for x occurs when MUx is decreases as x increases

Here MUx = (9/4)x^-1/4

d(MUx)/dx = -(9/16)x^-5/4 < 0

Hence, MUx is decreases as x increases. Hence. consumer’s preferences exhibit a diminishing marginal utility for Good x.

Diminishing Marginal utility for y occurs when MUy is decreases as y increases

Here MUy = 3

d(MUx)/dx = 0

Hence, MUy does not decreases as x increases. Hence. consumer’s preferences will not exhibit a diminishing marginal utility for Good y.

Hence, consumer’s preferences will exhibit a diminishing marginal utility for Good x but not for Good y

c)

MRS_xy = MUx/MUy = ((9/4)x^-1/4)/3 = (3/4)x^-1/4

d)

The consumer’s preferences exhibit a diminishing marginal rate of substitution of x If MRS_xy decreases as x increases

MRS_xy = (3/4)x^-1/4

dMRS_xy /dx = -(3/16)x^-5/4 < 0

Hence MRS decreases as x increases.

So, The consumer’s preferences exhibit a diminishing marginal rate of substitution of x