Microeconomics HW2
Due: 10/20/2008
1. Charlie has a utility function U(A, B) = AB, the price of apples(A) is $1, and the price of bananas(B) is $2. If Charlie’s income were $120, how many units of bananas would he consume if he chose the bundle that maximized his utility subject to his budget constraint?
2. Edmund loves punk rock video tapes. He has no income and therefore has to accept garbage in his backyard in return for money. Each video tape cost $2 and each sack of garbage that he accepts brings him $1. His utility function is given by U(c, g) = min{ 2c, 20 – g}, where c is the number of video tapes and g is the number of sacks of garbage that he gets per month. How many sacks of garbage will he accept each month?
3. Is the following statement true or false? “If consumers spend their entire incomes, it is impossible for the income elasticity of demand for every good to be bigger than 1.” Write a brief but convincing explanation of your answer.
4. Wanda Lott’s utility function is U(x, y) = max{ 2x, y}. Draw some of Wanda’s indifference curves. If the price of x is 1, the price of y is p, and her income is m, how much of y does Wanda demand?
5. Martha has the utility function U = min{ 4x, 2y}. Write down her demand function for x as a function of the variables m, px, and py, where m is income, px is the price of x, and py is the price of y.
6. Briefly explain in a sentence or two how you could tell
a. whether a good is a normal good or an inferior good.
b. whether a good is a luxury or a necessity.
c. whether two goods are complements or substitutes.
7. Define each of the following:
a. Inverse demand function
b. Engel curve