Chapter 4: Utility
1. Suppose that according to a consumer’s preferences a  b º c,
where a, b, and c are consumption bundles. (Since b º c then
either b  c or b ∼ c — we don’t know which.) Consider the
functions in the table below, .e.g., u assigns the number 12 to
bundle a.
bundle
u v
w
a
12 −2 8
b
12 −3 6
c
1 −4 6
(a) Could u be a utility function representing this consumer’s
preferences?
No because u(a)=u(b)
(b) Could v be a utility function representing this consumer’s
preferences?
yes
(c) Could w be a utility function representing this consumer’s
preferences?
yes
2. For each of the following utility functions, sketch the indiļ¬erence
curve for utility level 24. (Measure units of good 1 on the horizontal
axis.)
(a) u(x1 , x2 ) = 2x1 + x2 .
-du/dx1 / du/dx2
(b) u(x1 , x2 ) = min{3x1 , 4x2 }.
(c) u(x1 , x2 ) = max{3x1 , 4x2 }.
3x1=4x2=24
3x1=4x2=24
3. For each of the following utility functions, derive the marginal rate
of substitution.
(a) u(x1 , x2 ) = x1 + x2 .
-1
-x2/x1
1/4 3/4
x1 x2 .-1/4(x2^3/4)(x1)^-3/4 / 3/4(x1^1/4)(x2^ 1/4)=-1/3(x2/x1)
(b) u(x1 , x2 ) = x1 x2 .
(c) u(x1 , x2 ) =
MRS= -(a /b)(x2/x1)
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