Question

Suppose that a fast-food junkie derives utility from three goods-soft drinks (x), hamburgers (y), and ice cream sundaes (z)-according to the Cobb- Douglas utility function: Suppose also that the prices for these goods are given by Px-1,py-4, and pz-8 and this consumer's income is given by 1-8 If z-0, then the combination of x and y that optimize utility involve x*- utility U and y*- , These values of x* and y result in a level of If z- 1, then U of utility than the bundle of (4,1,0) . Further, if z 0.1, U is approximately Both of these consumption bundles leads to a evel MU Using the utility function, at the pointz MU MU P. 0 and x- x* as well as y - y*, it can be shown that1 ,and 1/ MU MU MUz After evaluating M0-,--, and-: at the point (x*.y*,0), it is clear that MU, p, . In other words, this consumer would p, receive a lower marginal utility per dollar for good than either of the other two goods Hint: Think of U as a cobb-douglas utility function in which this consumer spends an equal amount of his income on z + 1, x, and y Which of the following conditions ensures that some positive level of z will be purchased by the consumer?

Answer 1