# Walrasian equilibrium

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

Please refer to the attachment.

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.