Question

Assume that an individual’s preferences is represented by the following utility function: ?(?, ?) = (?^1/3)*(y^2/3)

a. What could you tell about the type of x and y? (“good” , “bad” or a “neuter”)

b. Derive the equation for his/her indifference curve for utility level of 100?

c. Derive marginal utility of x and marginal utility of y as a function of x,y.

d. Does goods x and y exhibit diminishing marginal utility, constant marginal utility, or increasing marginal utility?

e. Are goods x and y perfect substitutes or imperfect substitutes? f. Calculate marginal utility of x and y when original consumption level is (125, 125)

Answer 1

U = x^1/3y^2/3

(a)

The utility function is of Cobb-Douglas form which signifies that x and y are "good".

(b)

When U = 100,

x^1/3y^2/3 = 100

y^2/3 = 100 / (x^1/3)

Raising both sides to the power of (3/2),

y = [100 / (x^1/3)]^3/2

y = 1000 / (x^1/2) [Indifference curve equation]

(c)

Marginal utility of x (MUx) = Y/x = (1/3).(y/x)^2/3

Marginal utility of y (MUy) = Y/y = (2/3).(x/y)^1/3

(d)

From MUx function, when x increases, [(y/x)^2/3] decreases, therefore MUx is diminishing in x.

From MUy function, when y increases, [(x/y)^1/3] decreases, therefore MUy is diminishing in y.

NOTE: As per Chegg Answering Policy, 1st 4 parts have been answered.