Answers to problem set 3 - California State University ...
Economics 310
Problem Set 2
1. Draw Joe’s indifference curves for each of the following cases.
a. Joe says, "Coke and Pepsi are both the same to me."
b. Right shoes and left shoes.
c. Joe considers his own income to be a good. When his income is greater than Oscar's, he also considers Oscar’s income to be a good. When Oscar's income is larger than Joe’s income, Joe thinks of it as a neutral good. (Plot Joe's income on the y-axis and Oscar's on the x-axis.)
2. The price of a textbook is $50. The price of pizza is $25. Jane spends her entire $250 income on these two goods. Jane purchases 2 textbooks and 6 pizzas. If her satisfaction is at a maximum, draw Jane's budget line and her indifference curves. (Graph pizza on the y-axis and textbooks on the x-axis.) What is her marginal rate of substitution? How do you know?
3. The price of a textbook is $100. The price of pizza is $50. Tarzan spends his entire $500 income on these two goods. If Tarzan purchases 2 textbooks and 6 pizzas, he is willing to give up 3 pizzas to get one more textbook. If he purchases 2 textbooks and 6 pizzas will his satisfaction be maximized? Explain your answer.
4. The price of a textbook is $100. The price of pizza is $50. Jane's income goes up to $800. Tarzan's income goes down to $400. Jane purchases 4 textbooks and 8 pizzas and her satisfaction is at a maximum. Tarzan purchases 3 textbooks and 2 pizzas and his satisfaction is at a maximum. Is it possible that Jane and Tarzan have the same marginal rate of substitution?
5. Joe’s income is $50. He spends all of it on two goods, bread and water. The price of water is $5 a gallon. The price of bread is $10 a loaf.
a. Draw Joe’s budget line. (Graph bread on the y-axis and water on the x-axis)
b. Now there is a drought and the price of water increases to $10. Draw Joe’s new budget line. Will Joe be worse off now than he was in part a? How do you know? (Hint: Your answer must discuss his indifference curves.)
c. The government decides to freeze the price of water at $5 and place a limit of 2 gallons of water on each consumer’s purchase of water. Draw Joe’s new budget line assuming the law is perfectly enforced. (i.e. He can buy no more than 2 gallons of water.) Will the rationing plan always make him better off compared to his level of satisfaction in part b? Explain using indifference curves and the budget lines.
Answers to problem set 3
1. a
b.
Right shoes and left shoes perfect complements.
c.
Above the dotted line Joe’s income is greater than Oscar’s and Oscar’s income is a good for Joe. Below the dotted line the opposite is true and Oscar’s income is neutral to Joe.
2. The marginal rate of substitution is 2. When Jane’s satisfaction is maximized her MRS is equal to the slope of the budget line which is 2.
3. No his satisfaction will not be maximized if purchases 2 textbooks and 6 pizzas. The relative price of a textbook is 2 pizzas, but he is willing to give up 3 pizzas to get one more textbook (his marginal rate of substitution). He will be better off giving up the pizzas and buying more textbooks.
4. Yes Tarzan and Jane have the same MRS. If a consumer is maximizing his level of satisfaction, his/her marginal rate of substitution is equal to the relative price. Since Tarzan and Jane face the same prices, their MRSs will be equal when they are they are consuming the combination of text books and pizza that maximize there satisfaction.
5. a.
b. Joe will be worse off. He will be forced to move to a lower indifference curve.
c.
Which he will prefer depends on his preferences. If his indifference curves are relatively flat (graph 1) he will better off with the lower price even though the amount he can purchase is limited. (B is preferred to A) If his curves are steep (graph 2), he is willing to give up a lot of bread to get one more gallon of water. He is better off with the higher price because he can buy all he wants. Point A is on a higher indifference curve than B.
-----------------------
P
TB
10
5
6
2
oscar's income
Joe’s income
LS
1
1
RS
4
2
P
2
C
4
B
W
5
10
B
W
10
5
5
2
2 5
B
W
B
W
A
B
A
B
Ji=Oi
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