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.
Micro Economics For Today
10th Edition
ISBN:9781337613064
Author:Tucker, Irvin B.
Publisher:Tucker, Irvin B.
Chapter6: Consumer Choice Theory
Section: Chapter Questions
Problem 3SQ
Related questions
Question
AI-Generated Solution
AI-generated content may present inaccurate or offensive content that does not represent bartleby’s views.
Unlock instant AI solutions
Tap the button
to generate a solution
Recommended textbooks for you