Problem 1 (25pts) Benjamin spends his time either watching movies (x1) (he uses "on demand" option, cable TV) or listening to songs MP3 downloaded from the Internet (x2). His preferences are described by - U(x1, x2) = ln(x1) + In(x2) - a) Derive Benjamin's demand for movies and MP3 files as a function of prices p1, p2 and his income m. (do not use Cobb Douglas formula but rather derive demand using "two secrets of happiness"). b) Fix the price of MP3 at p2 = 1, and income on m = 10. Find the price offer curve (give an exact formula x2 = f(x1)) and plot it in the commodity space. Find the demand curve x1 = f(p1) and plot it in the graph (with p₁ on vertical axis and x1 on horizontal axis). == c) Is x1 an ordinary good or a Giffen good? Explain. d) Now fix p₁ = 1 and p2 = 1. In the commodity space, plot the income offer curve. In addition, in two separate graphs, plot Engel curves for both movies and MP3 files. Argue that the two commodities are normal (not inferior). e) For the demand functions from point a), determine whether the two goods are gross complements, substitutes or neither.
Problem 1 (25pts) Benjamin spends his time either watching movies (x1) (he uses "on demand" option, cable TV) or listening to songs MP3 downloaded from the Internet (x2). His preferences are described by - U(x1, x2) = ln(x1) + In(x2) - a) Derive Benjamin's demand for movies and MP3 files as a function of prices p1, p2 and his income m. (do not use Cobb Douglas formula but rather derive demand using "two secrets of happiness"). b) Fix the price of MP3 at p2 = 1, and income on m = 10. Find the price offer curve (give an exact formula x2 = f(x1)) and plot it in the commodity space. Find the demand curve x1 = f(p1) and plot it in the graph (with p₁ on vertical axis and x1 on horizontal axis). == c) Is x1 an ordinary good or a Giffen good? Explain. d) Now fix p₁ = 1 and p2 = 1. In the commodity space, plot the income offer curve. In addition, in two separate graphs, plot Engel curves for both movies and MP3 files. Argue that the two commodities are normal (not inferior). e) For the demand functions from point a), determine whether the two goods are gross complements, substitutes or neither.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Problem 1 (25pts)
Benjamin spends his time either watching movies (x1) (he uses "on demand" option, cable TV) or listening
to songs MP3 downloaded from the Internet (x2). His preferences are described by
-
U(x1, x2) = ln(x1) + In(x2)
-
a) Derive Benjamin's demand for movies and MP3 files as a function of prices p1, p2 and his income
m. (do not use Cobb Douglas formula but rather derive demand using "two secrets of happiness").
b) Fix the price of MP3 at p2 = 1, and income on m = 10. Find the price offer curve (give an exact
formula x2 = f(x1)) and plot it in the commodity space. Find the demand curve x1 = f(p1) and plot it
in the graph (with p₁ on vertical axis and x1 on horizontal axis).
==
c) Is x1 an ordinary good or a Giffen good? Explain.
d) Now fix p₁ = 1 and p2 =
1. In the commodity space, plot the income offer curve. In addition, in
two separate graphs, plot Engel curves for both movies and MP3 files. Argue that the two commodities
are normal (not inferior).
e) For the demand functions from point a), determine whether the two goods are gross complements,
substitutes or neither.
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