4. A consumer decides to choose an optimal consumption bundle of hot dogs (x) and buns (y).

a.) What can the two mathematical conditions that should satisfied at this optimal bundle?

b.) Find the optimal bundle (x^,y^) when Income = 100, Px = 2, Py = 2, MUx = 1/x, and MUy = 1/y.

c.) Suppose Income increases to 120. What happens to the budget set? Write both equations and

draw both budget sets, before and after the income change.

d.) Find the optimal bundle (x^,y^) when Income = 120, Px= 2, Py= 2, MUx=1/x, and MUy = 1/y.

e.) What is the property of good x that you can confirm based on your solutions from a.) and c.) that is true?

(note: Many properties may be true about good x , but only one in particular is related to your solutions above.)