2. Suppose Matt has $20 to spend on movies and books. The price of one unit...
2. Suppose Matt has $20 to spend on movies and books. The price of one unit of movie and the price of one unit of book are both $2. Assume movies and books are normal goods.
a) Draw Matt’s budget line (Draw Movies on the X-axis). Suppose Matt optimally consumes 6 movies and 4 books. Label this bundle as point A on your graph, and draw the indifference curve associated with this bundle.
b) Consider the bundle (5 movies, 5 books) and label this bundle as point B on your graph. What can you say about the slope of the indifference curve that passes through this point? Is it steeper, flatter or the same as the slope of the budget line?
c) suppose Matt’s income goes up to $30, draw the new budget line on your graph. Show the region where the new optimal bundle will lie.
d) Suppose Matt’s income goes up to $30 but the price of books also increases to $4. Suppose Matt now chooses the bundle (5 movies, 5 books). What can we conclude about Matt’s preferences?
Homework Answers
a. The consumer's budget equation is:
where x is the quantity of movies and y is the quantity of books.
Plotting this budget line along with the optimal choice:
b.
Since the consumer did not choose point B as his optimal bundle,
the slope of the indifference curve cannot be the same as the slope
of the budget line at B. The slope of the budget line is greater
than the slope of the indifference curve at point B.
c.
The new optimal bundle will lie on the new budget line.
d.
This proves that the consumer's preferences satisfy WARP. At the
original prices and income, the consumer chose A over B. At the new
prices and income, the consumer couldn't afford A and chose B.
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