Consider a two-person, two-good economy exchange economy in which person 1 is endowed with (e11,e12) and person
2 is endowed with (e21,e22) of the goods x1 and x2. Suppose that tastes are homothetic and assume throughout that
that preferences are also identical. (Homothetic preferences: Preferences whose map of indifference curves has the
property that the marginal rate of substitution depends only on the ratio of goods (and is thus the same along any
ray from the origin).)
a) Draw the Edgeworth Box and place the endowment points to one side of the line connecting the lower left and
the upper right corners of the box.
b) Illustrate the contract curve (i.e., the set of efficient allocations). Then illustrate the set of mutually beneficial
trades as well as the set of core allocations.
c) Why would we expect these two individuals to arrive at an allocation in the core by trading with one another?
d) Where does the competitive equilibrium lie in this case? Illustrate this by drawing the budget line that arises
from the equilibrium prices.
e) Does the equilibrium lie in the core?
f) Why would your prediction when the two individuals have different bargaining skills differ from this?

Q: Consider a two-good exchange economy with two individuals, A andB. A's preference is represented by uA(xA1, xA2) = 0.3ln(xA1) +0.7ln(xA2), and B's is represented by uB(xB1, xB2) = 0.8ln(xB1) +0.2ln(xB2). A's initial holding is (wA1, wA2) = (10,4) and B's is(wB1, wB2) = (8,12).

a) Calculate the demand function for each of A and B.

b) Find the competitive equilibrium relative price p1/p2, by equating the demand for good 1 (or good 2) to the supply of it.

c) Derive the equation which describes the set of efficient allocations (ie, contract curve).

Humphrey and Lauren are splitting 10 gallons of soda and six pounds of popcorn. Let's represent Humphrey's preference with the utility function UH = 3SH + PH and Lauren's preferences with UL = 2SL + 4PL, where SH and SL indicate their soda consumption, while PH and PL indicate their popcorn consumption. Consider the social welfare function W(UH,UL) = UH + UL. According to this social welfare function, which of the following two allocations is better: (1) SH = 1, SL = 9, PH = 2, and PL = 4, or (2) SH = 5, SL = 5, PH = 3, and PL = 3? Which allocation does each consumer prefer? Considering all possible allocations, which is the most socially desirable? [HINT: How is social welfare affected by shifting a gallon of soda between Humphrey and Lauren? What about a pound of popcorn?]

Suppose Humphrey starts out with four pounds of food and seven gallons of water, while Lauren starts out with eight pounds of food and five gallons of water. Draw an Edgeworth box that shows all possible allocations of these goods, and plot the endowment points. Now suppose that both Lauren and Humphrey's preferences correspond to the utility function U(F, W) = min{F, W} (where F refers to pounds of food and W refers to gallons of water). This is a case of perfect complements. Add Humphrey and Lauren's indifference curves to the Edgeworth box. Then draw the contract curve. To which points on the contract curve is each consumer willing to trade?

Explain why an economy in which airlines charge different passengers different prices for the same flight will not have exchange efficiency. b. Going back to our two good (Apples, Oranges), two-person (Ed, Mary) economy, suppose that at a given allocation, Ed's MRSAO is 3 and Mary's MRSAO is 1. Use proof by contradiction to show that this allocation is not exchanged efficiently. Identify a trade that will increase the utility of Ed and Mary. Explain. Show this graphically (with indifference curves).

Going back to our two good (Apples, Oranges), two-person (Ed, Mary) economy, suppose that at a given allocation, Ed's MRSAO is 3 and Mary's MRSAO is 1. Use proof by contradiction to show that this allocation is not exchanged efficiently. Identify a trade that will increase the utility of Ed and Mary. Explain. Show this graphically (with indifference curves).