Tutorial Question 4 Consider a consumer with preferences defined over the consumption set B = {(x1.29) 1 21 [D.0c) .23 [0,0)}. In other words, this consumer has preferences defined over the set of all bundles (combinations) of non- negative quantities of each of two commodities. Suppose that these prefer- ences can be represented by a utility function U : B2 R of the form Perfect Substitutes: U(xy, 25) = x4 + 29, 2 Complete the following exercises. 1. Find the equation that defines a representative indifference curve (that is, iso-utility curve) for this consumer, and illustrate that curve. Justify vour answer. 2. In a new diagram, illustrate a representative weak preference set, (that is, weak upper contour set for the utility function) for this consumer. Justify vour answer. 3. The consumer's preferences are said to convex if every weak prefer- ence set (that is, weak upper contour set for the utility function) is a convex set. Are the consumer's preferences convex? Justifv vour answer. 4. The consumer's preferences are said to convex if every weak prefer- ence set (that is, weak upper contour set for the utility function) is a strictly convex set. Are the consumer's preferences strictly convex? Justify vour