You are deciding what apartment to rent in a somewhat hip neighborhood. There are two goods you care about: Square feet of housing space (H), and pupusas (F). You can rent an apartment for $2/square foot/month, and can purchase pupusas for $2/pupusa'. Your monthly budget is $1,600. a. Write down the equation for your budget constraint. Draw your budget constraint, with square feet of housing on the horizontal axis and pupusas per month on the vertical axis. b. Suppose that your preferences can be represented by the utility function: U(H,P) = 4H³pÅ Determine your optimal choice of housing and pupusas given your budget constraint. Label this point on your budget constraint, and draw an indifference curve through this point representing your preferences (your indifference curve should have the correct shape, and should show that your optimal point is, indeed, optimal, but it does not need to exactly correspond to your utility function). c. A media frenzy over the availability of excellent vegan street food results in an increase in rent. You can now rent an apartment for $6/square foot/month. Because you're a renter, you get no increase in income from this price change. Write down the equation for your new budget constraint, and graph it on the same graph from part a. Label this BC3. d. Determine your optimal choice of housing and pupusas given your new budget (BC2). Label this point on your new budget constraint, and draw an indifference curve through this point representing your preferences. e. Graphically decompose your change in housing from part b to part d into an income and substitution effect. Note: While you don't need to get exact answers for this decomposition, you should correctly identify the direction of each effect.
You are deciding what apartment to rent in a somewhat hip neighborhood. There are two goods you care about: Square feet of housing space (H), and pupusas (F). You can rent an apartment for $2/square foot/month, and can purchase pupusas for $2/pupusa'. Your monthly budget is $1,600. a. Write down the equation for your budget constraint. Draw your budget constraint, with square feet of housing on the horizontal axis and pupusas per month on the vertical axis. b. Suppose that your preferences can be represented by the utility function: U(H,P) = 4H³pÅ Determine your optimal choice of housing and pupusas given your budget constraint. Label this point on your budget constraint, and draw an indifference curve through this point representing your preferences (your indifference curve should have the correct shape, and should show that your optimal point is, indeed, optimal, but it does not need to exactly correspond to your utility function). c. A media frenzy over the availability of excellent vegan street food results in an increase in rent. You can now rent an apartment for $6/square foot/month. Because you're a renter, you get no increase in income from this price change. Write down the equation for your new budget constraint, and graph it on the same graph from part a. Label this BC3. d. Determine your optimal choice of housing and pupusas given your new budget (BC2). Label this point on your new budget constraint, and draw an indifference curve through this point representing your preferences. e. Graphically decompose your change in housing from part b to part d into an income and substitution effect. Note: While you don't need to get exact answers for this decomposition, you should correctly identify the direction of each effect.
Chapter10: Consumer Choice Theory
Section: Chapter Questions
Problem 9P
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Transcribed Image Text:You are deciding what apartment to rent in a somewhat hip neighborhood. There are two goods
you care about: Square feet of housing space (H), and pupusas (F). You can rent an apartment
for $2/square foot/month, and can purchase pupusas for $2/pupusa'. Your monthly budget is
$1,600.
a. Write down the equation for your budget constraint. Draw your budget constraint, with
square feet of housing on the horizontal axis and pupusas per month on the vertical axis.
b. Suppose that your preferences can be represented by the utility function:
U(H,P) = 4H³pÅ
Determine your optimal choice of housing and pupusas given your budget constraint.
Label this point on your budget constraint, and draw an indifference curve through this
point representing your preferences (your indifference curve should have the correct
shape, and should show that your optimal point is, indeed, optimal, but it does not need to
exactly correspond to your utility function).
c. A media frenzy over the availability of excellent vegan street food results in an increase
in rent. You can now rent an apartment for $6/square foot/month. Because you're a
renter, you get no increase in income from this price change. Write down the equation
for your new budget constraint, and graph it on the same graph from part a. Label this
BC3.
d. Determine your optimal choice of housing and pupusas given your new budget (BC2).
Label this point on your new budget constraint, and draw an indifference curve through
this point representing your preferences.
e. Graphically decompose your change in housing from part b to part d into an income and
substitution effect. Note: While you don't need to get exact answers for this
decomposition, you should correctly identify the direction of each effect.
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