1). A consumer considers the choice of consumption bundles ( x, y ) which are made up of two goods: books (x) and pens (y).

a.) Write the general definition of the consumer's budget constraint.

b.) Write the budget constraint when Px= 20, Py= 4, and I = 80.

c.) Draw the budget constraint when Px = 20, Py= 4, and I= 80 in a clearly labeled (axes, intercepts) graph.

d.) Label at least 3 affordable bundles on your graph. Label at least 3 unaffordable bundles on your graph.

e.) What happens to the collection of affordable bundles if Py increases from 4 to 8? Draw this change, and give a new equation for the budget constraint.

2). 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.