4. Janice Doe consumes two goods, X and Y.Janice has a utility function given by the expression:

U = 4X0.5Y0.5.

The current prices of X and Y are 20 and 40, respectively.Janice currently has an income of 800 per time period.

a) Calculate the optimal quantities of X and Y that Janice should choose, given her budget constraint.Graph your answer.

b) Suppose that the government rations purchase 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?

c)Construct a diagram that shows the impact of the limited availability of X on the budget constraint. Is Janice satisfying the usual conditions of consumer equilibrium while the restriction is in effect?