(a) Consider Kuhn with the utility function, U= sqrt(xy). Let Px and Py be the prices of goods x and y respectively and M be income. Suppose that Kuhn buys good x from a store that offers him the following deal: buy x units, get x units free, where > 0.

(a) Find an expression for Kuhn's optimal consumption of good X as a function of Px, Py, and M.

(b) Using the function in (a), intuitively explain why a seller of good X will offer the deal above.