During Droughts,cities Often Impose Water Use Restrictions on Consumers

Essay

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 $50/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 consumer's utility.
c.By how much does the quota harm the representative consumer? Specifically,compute the equivalent variation of the quota.