4.2 Suppose that a fast-food junkie derives utility from three goods soft drinks (x), hamburgers (y), and ice cream sundaes (2)-according to the Cobb-Douglas utility function U(x,y,z) 505(1+2) 05 Suppose also that the prices for these goods are given by p, 0.25, py-1, and p. 2 and that this consumer's income is given by I = 2.

a. Show that, for 0, maximization of utility results in the same optimal choices as in Example 4.1. Show also that any choice that results in z > 0 (even for a fractional 2) reduces utility from this optimum.

b. How do you explain the fact that z 0 is optimal here?

c. How high would this individual's income have to be in order for any z to be purchased?