Econ 100A Problem Set #5: Income and Price Changes Spring 2022
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
Econ 100A
Problem Set #5: Income and Price Changes
Spring 2022
1. A consumer gets utility from two goods, x1 and x2 . Suppose the consumer’s income increases and that, in this income range, x1 is a normal good and x2 is an inferior good. Using budget lines and indifference curves, explain and illustrate this consumer’s response to the change in income.
2. Bart consumes 5 goods. What’s the greatest number ofthem that could be inferior? What’s the greatest number ofthem that could be normal?
3. Consider the following constant elasticity of substitution utility maximization problem:
max U x1 , x2 2x 2x subject top1x1 p2x2 Y x1 ,x2
a. Use the Lagrangian technique to find the utility maximizing bundle, x1*, x2* as functions ofp1, p2 and Y. (You did this on Problem Set 4, #5.)
b. Calculate the income elasticities for x1 and x2 .
c. Prove that x1 and x2 are normal goods.
4. Sarah regards pizza slices (S) and whole pizzas (W) as perfect substitutes. A pizza has eight slices and Sarah is only concerned with the total number of slices she can consume. Originally the price of a slice is $1, the price of a whole pizza is $20 and her income is $20.
a. How many slices does she consume?
b. Ifthe price of a slice increases to $2 how many slices will she consume?
c. What is her total change in the number of slices? What is the change caused by the substitution effect? What is the change caused by the income effect? Illustrate graphically.
d. Repeat parts (b) and (c) ifthe price of a slice increases to $3. (Still starting from the original price of $1.)
5. Consider the following Cobb-Douglas utility maximization problem:
max U x1 , x2 3xx subject to 3x1 4x2 72
a. Find the optimum values ofx1* and x2*.
b. Ifp1 increases to $4, find the new optimum values ofx1* and x2*.
c. What is the total change in x1*? What is the change caused by the substitution effect? What is the change caused by the income effect?
2022-05-11