Question

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. Due to droughts, the government imposes a quota on water use of 50 units/week. By how much does the quota harm the representative consumer?

Answer 1

Pw = 50 cents = $0.5
Px = $1
Income, M = 100

We have to find equivalent variation here.

Utility is maximized where MRS = Pw/Px
MRS = MUw/MUx =

So, X/W = 0.5/1 = 0.5
So, X = 0.5W

After quota, W = 50
Cost of water = .5*(50) = 25
Amount left for other goods = M - 25 = 75
So, X = Amount left for other goods/Px = 75/1 = 75
U(W,X) = 50*75 = 3750

We find the income which will give U = 3750 without quota.
We know, X = 0.5W
So, U = WX = W(0.5W) = 3750
So, W2 = 3750/0.5 = 7500
So, W = 75001/2
So, W = 86.6
So, X = 0.5W = 0.5(86.6) = 43.3
M' = Px*X + Pw*W = (1*43.3) + (.5*86.6) = 43.3 + 43.3 = 86.6

So, EV = M' - M = 86.6 - 100 = -13.4

The quota harm the representative consumer by $-13.4