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# Walrasian equilibrium

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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.

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#### Solution Preview

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.

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