# two consumers have the following preferences for goods x and y: u1 =x1^1/3*y1^2/3 u2=x2^2/3*y2^1/3 There are 100 units of x available, and 100 units…

two consumers have the following preferences for goods x and y:

u1=x1^1/3*y1^2/3

u2=x2^2/3*y2^1/3

There are 100 units of x available, and 100 units of y available. Both consumers start with equal quantities of the two goods. Using this information, answer the following questions:

1. Depict the starting point for this exchange using the Edgeworth both. Include as much detail as you can, such as labeling indifference curves, initial endowments, and regions of mutually beneficial trade.

2. Define the contract curve between these two consumers and explain what it means. Accurately graph the contract curve on your graph from question 1.

3. Determine the core[1] for these two consumers given their initial endowment. Mark this area down on your graph.

4. Calculate the price ratio between x and y.

5. Given this ratio of prices, where do you expect the two consumer’s to end up?

[1] You are going to want the help of a machine for this one. Here is a link to WolframAlpha with a query similar to the one you’ll need to type in: https://www.wolframalpha.com/input/?i=solve+1%2Fx+%3D+x%2F%281%2Bx%29+for+x.