The same consumer wants to choose an optimal consumption bundle of books and pens. The

optimal bundle is denoted by (x^, y^).

a.) What two mathematical conditions should be satisfied at this optimal bundle? (20%)

b.) Find the optimal bundle (x^, y^) when I = 20, Px= 10, Py = 2, MUx = 1/x, and M U y = 1/y. (40%)

c.) Find the optimal bundle (x^, y^) when I= 20, MUx = 1/x, MUy = 1/y, Py = 4, and where Px is a parameter that has not been assigned a numerical value. Notice that here, your solution will not be numerical.(40%)

d.) (Extra credit 2 points) From part c., what does x represent? Explain in words, and draw a carefully-labeled graph to support your explanation.