Question

1. What is the formula for the indifference curve associated with U = xy3 = 8?

2.Given the utility function U = x 1 3 y, what is the slope of the indifference curve at the point (x, y) = (2, 3)?

3.Question 1 Suppose U = x 3 4 y 1 4 . What is the marginal utility of x? What is the marginal utility of y?

Answer 1

1)

U = xy³

8 = xy³

8/x = y³

(8/x)^1/3 = y

y = 2/x^1/3  

Indifference curve is

y = 2/x^1/3  

2)

U = x^1/3y

U/x = MUx = 1/3x^{1/3 - 1}y

MUx = 1/3x^{- 2/3}y

U/y = MUy = x^1/3  

MUy = x^1/3  

slope of IC = MRS = MUx/MUy

=   1/3x^{- 2/3}y / x^1/3  

= 1/3(y/x)

= y/3x

at point (x,y) = (2,3)  

slope of IC = MRS = y/3x = 3/3(2) = 1/2  

Thus slope of IC at point (x,y) = (2,3) is MRS = 1/2

3)

U = x^3/4y^1/4  

U/x = MUx = (3/4)x^{3/4 - 1} y^1/4  

MUx = (3/4)x ^-1/4 y^1/4  

U/y = MUy = (1/4)x^3/4y^{1/4 - 1}  

MUy = (1/4)x^3/4y ^{- 3/4}

Therefore

MUx = (3/4)x ^-1/4 y^1/4  

MUy = (1/4)x^3/4y ^{- 3/4}