Reference no: EM13343003

The only two consumers in an exchange economy, consumer A and consumer B, consume the only two goods, X and Y, in the economy. There are 20 units of X available and 20 units of Y.

i). If A and B have identical preferences, mutually beneficial trade cannot occur. True or
false? Explain.

ii). Assume A's preferences are described by UA=XA1/2 YA1/2 and B's preferences are described
by UB=2XBYB, where XA, YA, XB, YB are the consumption of X and Y by consumers A and B,
respectively.
Draw an Edgeworth box describing this scenario. Label the lengths of the sides, draw a few indifference curves for each consumer and (roughly) sketch the contract curve.

*(iii) Now derive an equation for the contract curve. (Hint: the contract curve, MRSA = MRSB. Compute the MRS for consumer A as a function of XA and YA, and for consumer B as a function of XB and YB. Impose the restriction that total consumption of X should equal the total units of X available, and do the same for Y. Rearrange to get an equation of YA as a function of XA (your result should look pretty simple)).
iv). Suppose that consumer A has an initial endowment of 5 units of X and 15 units of Y, and
consumer B has the remainder of what's available. Show, using the concept of MRS and the Edgeworth Box, that a trade could benefit both consumers.

v). Assume the consumers can trade as much as they like at the prices of PX=1 and PY=1. If starting out with the same endowments as in part (iv), how much will each consumer want
to buy/sell of each good? Is the result a competitive equilibrium?

vi). Assume the consumers can trade as much as they like at the prices of PX=2 and PY=1. If starting with equal endowments (each individual has 10 units of both good X and good Y), how much will each consumer want to buy/sell of each good? Is this result a competitive equilibrium?