During droughts, cities often impose water use restrictions on consumers. Suppose Rusalka 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 25¢. Rusalka has a budget of $50/week.
a. How much water will Rusalka purchase each week? Show how you determined your answer. Note: you do not need to use the Lagrangian method unless you want to.
b. Suppose the government imposes a quota limiting water use to a maximum of 40 units/week. Calculate the effect the quota has on Rusalka's utility. If you are unable to determine this numerically, show it graphically for partial credit.
c. What is the dollar equivalent value of the quota’s impact on Rusalka? If you are unable to determine this numerically, show it graphically for partial credit.