Problem 3. José gets earns $100 per week from his YouTube videos. He spends all of it on concert tickets and paintball. His preferences over the two goods are u(c, p) = 2c + p where c is the number of concerts he attends and p is the number of paintball sessions in which he participates. Currently concert tickets and paintball sessions both cost $25 each. a) What is José's Marginal Rate of Substitution as a function of c and p? b) It turns out we can't solve for José's demand functions using calculus. Why? (Try setting Marginal Rate of Substitution equal to relative price.) c) Draw José's budget set in (c, p) space. Indicate the horizontal and vertical intercepts of the budget line and sketch the u = 4,6,8, and 10 indifference curves. d) What is José's optimal bundle at these prices? e) Next week, José's favorite paintball location is offering a special where members can purchase sessions for $10 each. If Jose is already a member, how many sessions will he buy? f) If the paintball location charges a fee to become a member, what is the maximum fee José is willing to pay? (Assume the special in part e) is for one week only.)
Problem 3. José gets earns $100 per week from his YouTube videos. He spends all of it on concert tickets and paintball. His preferences over the two goods are u(c, p) = 2c + p where c is the number of concerts he attends and p is the number of paintball sessions in which he participates. Currently concert tickets and paintball sessions both cost $25 each. a) What is José's Marginal Rate of Substitution as a function of c and p? b) It turns out we can't solve for José's demand functions using calculus. Why? (Try setting Marginal Rate of Substitution equal to relative price.) c) Draw José's budget set in (c, p) space. Indicate the horizontal and vertical intercepts of the budget line and sketch the u = 4,6,8, and 10 indifference curves. d) What is José's optimal bundle at these prices? e) Next week, José's favorite paintball location is offering a special where members can purchase sessions for $10 each. If Jose is already a member, how many sessions will he buy? f) If the paintball location charges a fee to become a member, what is the maximum fee José is willing to pay? (Assume the special in part e) is for one week only.)
Chapter10: Consumer Choice Theory
Section: Chapter Questions
Problem 8P
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Transcribed Image Text:Problem 3.
José gets earns $100 per week from his YouTube videos. He spends all of it on concert tickets and
paintball. His preferences over the two goods are
u(c,p) = 2c + p
where c is the number of concerts he attends and p is the number of paintball sessions in which he
participates. Currently concert tickets and paintball sessions both cost $25 each.
a) What is José's Marginal Rate of Substitution as a function of c and p?
b)
It turns out we can't solve for José's demand functions using calculus. Why? (Try setting
Marginal Rate of Substitution equal to relative price.)
c)
Draw José's budget set in (c, p) space. Indicate the horizontal and vertical intercepts of the
budget line and sketch the u = 4,6,8, and 10 indifference curves.
d)
e)
What is José's optimal bundle at these prices?
Next week, José's favorite paintball location is offering a special where members can purchase
sessions for $10 each. If Jose is already a member, how many sessions will he buy?
f)
If the paintball location charges a fee to become a member, what is the maximum fee José is
willing to pay? (Assume the special in part e) is for one week only.)
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