Question

Instructions: Answer the following questions as completely as possible. Write your answer neatly and legibly. When drawing a graph, make sure that you label axes and curves, and include appropriate coordinates. Always show your work.

1. Suppose that Bridget and Erin spend their incomes on two goods, food (F) and clothing (C). Bridget’s preferences are represented by the utility function U(F,C) = 10FC, while Erin’s preferences are represented by the utility function

   U ( F , C ) = 0.20 F^2 C^2.

   1. With food on the horizontal axis and clothing on the vertical axis, identify on a graph the set of points that give Bridget the same level of utility as the bundle (10, 5). Do the same for Erin on a separate graph.

   2. On the same two graphs in (a), identify the set of bundles that give Bridget and Erin the same level of utility as the bundle (15, 8).

   3. Do you think Bridget and Erin have the same preferences or different preferences? Explain.

2. Jane receives utility from days spent traveling on vacation domestically (D) and days spent traveling on vacation in a foreign country (F), as given by the utility function: U(D, F) = 10DF. In addition, the price of a day spent traveling
   domestically is $100, the price of a day spent traveling in a foreign country is $400, and Jane's annual travel budget is $4000.

   1. With D on the horizontal axis and F on the vertical axis, draw the indifference curve associated with a utility of 800 and the indifference curve associated with a utility of 1200. Use an appropriate scale. Label axes and curves.

   2. Write Jane’s budget line and draw it on the same graph as in (a). What is the marginal rate of transformation of D for F (MRTDF)?

   3. Can Jane afford any market basket that gives her utility of 800? What about a utility of 1200? Explain.

   4. Find Jane’s utility-maximizing choice of days spent travelling domestically and days spent in a foreign country, i.e. her best affordable choice mathematically.

3. Consumers in Georgia pay twice as much for avocados (Y) as they do for peaches (X). However, avocados and peaches are the same price in California. If consumers in both states maximize utility, will the marginal rate of substitution of peaches for avocados (MRSXY) be the same for consumers in both states? If not, which will be higher? Explain. Be as specific as possible.

PS#1, Winter 2020 Page 1

4. Picabo, an aggressive skier, spends her entire income on bindings (X) and skis (Y). She wears out one pair of skis for every pair of bindings she wears out.

   1. Graph Picabo’s indifference curves for skis and bindings.

   2. Now draw her indifference curves on the assumption that she is such an

      aggressive skiers that she wears out two pairs of skis for every pair of bindings

      she wears out.

   3. Suppose that Picabo has $3,600 to spend on skis and bindings each year. Find

      her optimal choice for skis and bindings under both of the preferences

      described in (a) and (b). Skis are $480/pair and bindings are $240/pair.

   4. Find Picabo’s optimal choice given the information in (b) and (c) mathematically.

5. Your local phone company has offered you a choice between the following billing plans:

   Plan A: Pay $0.05 per call.
   Plan B: Pay an initial $2/week, which allows you up to 30 calls per week at no

   charge. Any calls over 30 per week cost $0.05 per call.
   If your income is $12 per week and the composite good costs $1 per unit, graph your budget constraints for the composite good (Y) and calls (X) under the two plans.

6. Connie has a monthly income of $200 that she allocates between two goods: potatoes (P) and meat (M).

   1. Suppose meat costs $4 per pound and potatoes $2 per pound. Draw her budget constraint. Put potatoes on the horizontal axis and meat on the vertical axis.

   2. Suppose also that her utility function is given by the equation

      U(P,M) = P + 2M. If she maximizes her utility, how many pounds of meat and

      of potatoes should she buy?

   3. Connie’s supermarket has a special promotion. If she buys 20 pounds of

      potatoes at $2 per pound, she gets the next 10 pounds for free. This offer applies only to the first 20 pounds she buys. All potatoes in excess of the first 20 pounds (excluding bonus potatoes) are still $2 per pound. The meat cost remains at $4 per pound. Draw her budget constraint and find her optimal combination of meat and potatoes. Will she be better off with this promotion? Explain.

Answer 1

Answering only first Question

For bridget

1) U(F,C) = 10FC

Bundle :(10,5)

Indifference Curve IC: U(10,5) = 10*10*5 = 500

So, IC : 10FC = 500

.

For Erin:

U(F,C) = .2F^2 C^2

U(10,5) = .2*100*25 = 500

So, IC : .2F^2 C^2 = 500

.

Now (F,C) = (15,8)

Then for Bridget :

10FC = 10*15*8 = 1200

For Erin:

.2F^2 C^2 = .2*(15)^2 (8)^2 = 2880

Bridget IC -40 -20- (15,8) (10,5) on 5 F10

Erin IC -60- -40- 20 (15,8) (10,5) 5 10 F 15

.

MRS for bridget : MUF/MUC

= C/F

For Erin: MRS = .2*2F*C^2/ .2*2C*F^2

= C/F

as two have same MRS, so two have same Preferences

.

Q2)