Question

Part 1:

Find the marginal utility of an additional unit of good x for a consumer with utility function
u (z, y) x-y-
when their current consumption level is and

Part 2:

Find the marginal rate of substitution between goods and for a consumer with utility function
u (z, y) x-y-
when their current consumption level is and

Answer 1

MUx = 2/3 (x) ^-1/3 y^1/3

x=2 and y=16

MUx = 2/3 (2)^-1/3 (16)^1/3

= 2/3 [16/2]^1/3

= 2/3 [8]^1/3

=2/3 (2) = 4/3 (Marginal utility of good x)

MUy = 1/3 (x)^2/3 (y)^-2/3

= 1/3 (2)^2/3(16)^-2/3

= 1/3 (2/16)^2/3

= 1/3 [1/8]^2/3

= 1/3 (1/2)²

= 1/3 (1/4) = 1/12 (Marginal utility of good y)

Marginal rate of substitution =MUx/ MUy

= (4/3) / (1/12)

= (4)(4)= 16