21. A consumer has a utility function defined over two goods X and Y. Let the quantity of Good X be x ≥ 0 and the quantity of Good Y be y ≥ 0. The utility function is given below: u(x, y) = xy + 2y. Assume that the consumer has income m and that prices are px and Py. (a) Explain whether the preferences underlying this utility function satisfy completeness and transitivity.

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Chapter3: Preferences And Utility
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21. A consumer has a utility function defined over two goods X and Y. Let the quantity of
Good X be x ≥ 0 and the quantity of Good Y be y ≥ 0. The utility function is given
below:
u(x, y) = xy + 2y.
Assume that the consumer has income m and that prices are på and py.
(a) Explain whether the preferences underlying this utility function satisfy
completeness and transitivity.
(b) Explain whether the preferences underlying this utility function satisfy
monotonicity and convexity.
(c) Find the consumer's Marshallian demands for Good X and Good Y at prices px > 0
and Py
> 0.
(d) Show that goods X and Y are normal goods and explain whether either good is a
substitute for the other.
(e) Assume that px
10, Py
= 5 and m = 100. Suppose that px increases to px = 15,
how much of the change in demand for Good X is via the substitution effect and
how much is via the income effect?
Note: You may assume an interior solution (i.e. x > 0 and y> 0).
=
Transcribed Image Text:21. A consumer has a utility function defined over two goods X and Y. Let the quantity of Good X be x ≥ 0 and the quantity of Good Y be y ≥ 0. The utility function is given below: u(x, y) = xy + 2y. Assume that the consumer has income m and that prices are på and py. (a) Explain whether the preferences underlying this utility function satisfy completeness and transitivity. (b) Explain whether the preferences underlying this utility function satisfy monotonicity and convexity. (c) Find the consumer's Marshallian demands for Good X and Good Y at prices px > 0 and Py > 0. (d) Show that goods X and Y are normal goods and explain whether either good is a substitute for the other. (e) Assume that px 10, Py = 5 and m = 100. Suppose that px increases to px = 15, how much of the change in demand for Good X is via the substitution effect and how much is via the income effect? Note: You may assume an interior solution (i.e. x > 0 and y> 0). =
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