Suppose a consumer has just enough money to afford the bundle of 3 apples and 2 oranges, and similarly she also has just enough money to afford the bundle of 2 apples and 4 oranges.

(a) Denoting the number of apples with x and oranges with y, plot the two given bundles on a graph, and calculate the relative price of apples; pX / pY.

(b) If she buys only apples with her budget, how many can she buy? If she buys only oranges, how many can she buy? Write down the budget equation for the consumer. (Notice that knowing two points on the budget line, you can write down the budget equation, even though you weren't given the prices nor the income explicitly!)

(c) Suppose MUx = 20 and MUy = 30 at some point on the budget line. Is she maximizing utility by choosing this bundle? If not, should she buy fewer apples (and more oranges), or more apples (and fewer oranges), to increase her utility?

(d) Forget about (c); instead, you learn that her utility function is u(x,y) = Axy^3 . What is her optimal bundle?

(e) Now, in (d) the price of an orange doubles. What is her optimal bundle in this case? Does she buy fewer apples compared to the case before the price increase? How about oranges; does she buy more or fewer compared to before?