Question

1. Consider a pure exchange economy two consumers, Rachel and Lauren, and two commodities, watermelon and tomatoes. Rachel’s initial endowment is 4 units of watermelon and 3 units of tomatoes. Lauren’s initial endowment is 2 units of watermelon and 5 units of tomatoes. Rachel and Lauren have identical utility functions: Rachel’s utility is UR(WR,TR) = WRTR where WR and TR is Rachel’s quantity of watermelon and quantity of tomatoes, respectively; similarly, Lauren’s utility is UL(WL,TL) = WLTL where WL and TL is Lauren’s quantity of watermelon and quantity of tomatoes, respectively. (35 points)
   1. What is the total supply of each good in this economy?
   2. Given the information above, draw the Edgeworth box that depicts this situation. Put watermelon on the horizontal axis and tomatoes on the vertical axis. Measure goods for Rachel from the lower left corner of the box and goods for Lauren from the upper right corner of the box. (Be careful about the length and height of your box!) Label the point of the initial endowment allocation in your box, and label it E1. Make sure to label the quantities of each good for each consumer at the initial endowment on the sides of the box.
   3. Draw an indifference curve for Rachel that shows allocations in which her utility is 4, label it IR1. Draw an indifference curve for Lauren that shows allocations in which her utility is 4, label it IL1.
   4. At any Pareto optimal allocation where both consume some of each good, Rachel’s marginal rate of substitution between watermelon and tomatoes must equal Lauren’s. Write the expression that states this condition in terms of the consumption of each good by each person using the given utility function.
   5. Is Rachel’s bundle WR,TR=(4,1) Pareto efficient? Why or why not? If not, provide a Pareto efficient allocation.
   6. On your Edgeworth box, show the locus of points (connected line through the points) that are Pareto efficient (mark three points on the contract curve).
   7. Suppose the price of watermelon is $2 and the price of tomatoes are $1. Draw the price line on your Edgeworth box. Does this lead to a competitive equilibrium? Why or why not?

Answer 1

Hi,

Please note that for a question with multiple parts to be answered, as per HOMEWORKLIB POLICY first three parts should be answered. Hence, I am answering the first three parts. If you wish any specific part to be answered please let me know by commenting on this question. I'll answer that.

Thank you!

a.) Pure exhange economy with two goods, watermelons and tomatoes.

With two consumers, Rachel and Lauren the total amount of a particular good will be the total with both Rachel and Lauren. Hence, the total amount of watermelon will be (Units of watermelon with Rachel + Units of watermelon with Lauren) = 4+2 =6

Total amount of Tomatoes will be (Units of tomatoes with Rachel + Units of tomatoes with Lauren) = 3+5 =8

b.) Edgeworth box

2. J O 8 2 6 2. 587 O Origin for Lauren 5 3 Tomatoes 4 3 E OR Origin for Rachael 6. 2 7 8 + 4 5 6 OR 2 3 Watermelons Endowment (E) is shown for Rachael (4,3) for Lauren (2.5)

c.) Indifference curve