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

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.