Problem Set #3 NAME:
Micro I – Winter Term 2011
DUE DATE: Friday, November 4 before 1:00 p.m. Drop the problem set off at building J11-C. You may submit problem sets in a group of maximum four students. However, each student in the group must turn in their OWN responses to the problem set (i.e. one assignment with four names on it will not be accepted). The group’s assignments should be turned in stapled together.
NO LATE PROBLEM SETS WILL BE ACCEPTED!!
1. Use a red pen for the initial budget constraint (before the price change), use a blue pen for the intermediate budget constraint (for determining the substitution effect), and use a black pen for the final budget constraint.
Label the initial optimal bundle “A”, the demand due to the substitution effect “B” and the final optimal bundle “C”.
Let good 1 be a normal good. Graph the substitution and income effects of a rise in the price of good 1.
a. Since the price is rising, what is the sign (positive or negative) of the change in demand due to the substitution effect? Indicate >0 or <0 below:
b. Since the price of a good has risen, the level of income for the blue intermediate budget line is temporarily higher than the actual income. Therefore, when we move from the intermediate to the final budget line, income falls. What is the sign (positive or negative) of the change in demand due to the income effect? Indicate >0 or <0 below:
2. Use a red pen for the initial budget constraint (before the price change), use a blue pen for the intermediate budget constraint (for determining the substitution effect), and use a black pen for the final budget constraint.
Label the initial optimal bundle “A”, the demand due to the substitution effect “B” and the final optimal bundle “C”.
Let good 2 be an inferior good. Graph the substitution and income effects of a rise in the price of good 2.
a. Since the price is rising, what is the sign (positive or negative) of the change in demand due to the substitution effect? Indicate >0 or <0 below:
b. Since the price of a good has risen, the level of income for the blue intermediate budget line is temporarily higher than the actual income. Therefore, when we move from the intermediate to the final budget line, income falls. What is the sign (positive or negative) of the change in demand due to the income effect? Indicate >0 or <0 below:
3. Use a red pen for the initial budget constraint (before the price change), use a blue pen for the intermediate budget constraint (for determining the substitution effect), and use a black pen for the final budget constraint.
Label the initial optimal bundle “A”, the demand due to the substitution effect “B” and the final optimal bundle “C”.
Let good 1 be a Giffen good. Graph the substitution and income effects of a fall in the price of good 1.
a. Since the price is falling, what is the sign (positive or negative) of the change in demand due to the substitution effect? Indicate >0 or <0 below:
b. Since the price of a good has fallen, the level of income for the blue intermediate budget line is temporarily lower than the actual income. Therefore, when we move from the intermediate to the final budget line, income rises. What is the sign (positive or negative) of the change in demand due to the income effect? Indicate >0 or <0 below:
4. Use a red pen for the initial budget constraint (before the price change), use a blue pen for the intermediate budget constraint (for determining the substitution effect), and use a black pen for the final budget constraint.
Label the initial optimal bundle “A”, the demand due to the substitution effect “B” and the final optimal bundle “C”.
Let good 2 be a normal good. Graph the substitution and income effects of a fall in the price of good 2.
a. Since the price is falling, what is the sign (positive or negative) of the change in demand due to the substitution effect? Indicate >0 or <0 below:
b. Since the price of a good has fallen, the level of income for the blue intermediate budget line is temporarily lower than the actual income. Therefore, when we move from the intermediate to the final budget line, income rises. What is the sign (positive or negative) of the change in demand due to the income effect? Indicate >0 or <0 below:
5. Suppose in 1995, income is $80, food costs $5/unit and clothing costs $5/unit. In 2005, food costs $6/unit and clothing costs $24/unit. Let preferences be represented by the Cobb-Douglass utility function u(F,C) =F1/2C1/2. Then in 1995, then optimal bundle is F=8 and C=8.
a. Calculate the Laspeyres price index
b. What is the level of utility achieved in 1995?
c. Calculate the new optimal bundle for 2005 that gives the consumer the same utility as in 1995. The formula for the MRS is dC/dF = -C/F, where food is measured on the horizontal axis.
d. Calculate the ideal cost of living index
6. Let Jackie’s utility for CDs (good 1) and DVDs (good 2) be represented as:
U = q10.6q20.4.
- For changes in the price of CDs, draw her price-consumption curve. Explain its shape. How does demand for DVDs depend on the price of CDs?
- Graph Jackie’s income consumption curve.
- Derive an expression (equation) for and graph Jackie’s Engel curve for CDs.
7. Madeline views Coke and Pepsi as one-for-one perfect substitutes. Derive her demand curve for Coke graphically and mathematically.
8. Derive and plot Olivia’s demand curve for pie if she eats pie only with a scoop of ice cream (i.e. they are one-for-one perfect complements).
b. How much does her weekly budget have to rise for her to buy one more piece of pie per week?