Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Question
Chapter 3, Problem 3.13P
(a)
To determine
To find:The MRS of the given function.
(b)
To determine
To analyze:Whether the function is quasi-concave.
(c)
To determine
To find:The equation of an Indifference curve.
(d)
To determine
To compare:The
(e)
To determine
To provide:A situation for a similar function.
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A utility function is called separable if it can be written as
U(x, y) = U (x) + U,(y),
where U > 0, U" < 0, and U1, U, need not be the same
function.
a. What does separability assume about the cross-partial
derivative U„? Give an intuitive discussion of what word
this condition means and in what situations it might be
plausible.
b. Show that if utility is separable then neither good can be
inferior.
c. Does the assumption of separability allow you to con-
clude definitively whether x and y are gross substitutes or
gross complements? Explain.
d. Use the Cobb-Douglas utility function to show that
separability is not invariant with respect to monotonic
transformations. Note: Separable functions are examined
in more detail in the Extensions to this chapter.
Hi, what does it mean if the utility function is ordinal and not cardinal.
Suppose a consumer purchases food X and clothing Y. The utility function of the consumeris given by: U(X,Y ) = XY + 5Y and the budget /income/ of the consumer is 200 ETB. Andalso the price of food is X P and the price of clothing is Y P . Then drive the equation ofconsumer’s demand function for food and clothing.
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