Janice Doe Consumes Two Goods, X and Y

Essay

Janice Doe consumes two goods, X and Y. Janice has a utility function given by the expression:
U = 4X^0.5Y^0.5.
So, The current prices of X and Y are 25 and 50, respectively. Janice currently has an income of 750 per time period.
a. Write an expression for Janice's budget constraint.
b. Calculate the optimal quantities of X and Y that Janice should choose, given her budget constraint. Graph your answer.
c. Suppose that the government rations purchases of good X such that Janice is limited to 10 units of X per time period. Assuming that Janice chooses to spend her entire income, how much Y will Janice consume? Construct a diagram that shows the impact of the limited availability of X. Is Janice satisfying the usual conditions of consumer equilibrium while the restriction is in effect?
d. Calculate the impact of the ration restriction on Janice's utility.