Question

In: Economics

During droughts, cities often impose water use restrictions on consumers. Suppose a representative consumer has preferences...

During droughts, cities often impose water use restrictions on consumers. Suppose a representative consumer has preferences for Water (W) and other goods (X) given by the utility function: U(W,X) = WX. Suppose the price of other goods is $1 and the price of water is initially 50¢. The consumer has a budget of $100/week. a. How much water will the consumer purchase each week? b. Suppose the government imposes a quota on water use of 50 units/week. Show that the quota reduces the representative consumerʹs utility. c. By how much does the quota harm the representative consumer? Specifically, compute the equivalent variation of the quota.

Expert Solution

a)

U(W,X)=WX

Marginal Utility from water=MUw=dU/dW=X

Marginal Utility from other goods=MUx=dU/dX=W

Px=$1, Pw=$0.50

In utility maximization,

MUx/MUw=Px/Pw

W/X=(1/0.50)

W=2X

We know that

XPx+WPw=$100 or

X+0.5W=100

Put W=2X in budget constraint

X+0.5*(2X)=100

2X=100

X=50

W=2X=2*50=100

Consumer will purchase 100 units of water and 50 units of other goods to maximize utility.

Utility=WX=100*50=5000 utils

b)

Given W=50

We have derived in part a that

X+0.5W=100

X+0.5*50=100

X=75

So, new consumption level is W=50 and X=75

Utility=WX=50*75=$3750

We have calculate the utility at earlier consumption level in part (a)

Earlier utility=5000

We can see that utility has decreased due to quota.

c)

Let us calculate the X for which consumer gets the total utility equal to earlier utility i.e. 50000

U(X,W)=WX

5000=50*X

X=100

So, total budget required to meet this condition.

Required budget=WPw+XPx=50*0.50+100*1 =$125

Equivalent variation=New budget required-Earlier consumption=125-100=$25

Rahul Sunny answered 1 year ago

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