A. Suppose first that 2 cannot pay the firm not to store waste, and the competitive price for storage is 1. Compute the Walrasian equilibrium and show that it is not Parteo efficient.

a) according to the question, the market price of waste storage is 1, and the market level of w is decided by person 1 only, as 2 cannot pay for prevention of waste.
First, let's try to draw the two person's indifference curves:
For person 1, U1 = log w + m1
Then the marginal utility is:
U1w = dU1 / dw = 1/w
U1m1 = dU1 / dm1 = 1
Then the slope of i.c. is (U1w / U1m1) = 1/w

M1

10

w
10
his budget constraint is pW + m1 = 10
or w + m1 = 10
as we know that the first order condition for utility maximization is
U1w / p = U1m1 / 1
(1/w) /1 = 1 /1
we can solve for w = 1
then M1 = 10-w = 9
Then the utility maximization level of w is 1, and person 1's bundle is
(w, m1) = (1, 9)

For person 2, her utility is
U2 = 2log(6-w)+m2
U2w = dU2 / dw = - 2/(6-w)
U2m2 = dU2/ dm2= 1
Then the slope of i.c. is (U2w / U2m2) =- 2/(6-w)

M2

10

w
10
his budget constraint is m2 = 10 (because she consumes no w)
as we know that the marginal utility of w is always negative, there's no tangency condition for utility maximization, and we have to find the corner solution:
for person2, she wants w as low as possible. However, since the waste stored is already decided by person 1 and the firm, her bundle will be:
(w, m2) = (1, 10)

now, let's combine both person's ...

Solution Summary

The expert computes the Walrasian equilibrium and show that it is not Parteo efficient.

The attached question is about 2 consumers with 3 goods in an exchange economy. The consumer's utility functions are given. The question asks to find demand functions for each consumer as well as finding Walrasianequilibrium under certain assumptions.
Thanks
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