Suppose that a consumer has preferences dened over the consumption set R3 = {[I],$2} :cl E [0, so} ,cg E [0, {33)}. In other words, this consumer has preferences dened over the set of all bundles {combinations} of non- negative quantities of each of two commodities. Suppose that these pref- erences can be represented by a utility function of the form U : R1 :~ 13.. Consider the following example of such a utility function. Perfect Substitutes: U{$1,I2) = 1:1 + .132. Complete the following exercises for this utility function. 1. 2. 3- Find the equation of a representative indifference curve. [The equa- Eon should express 1:2 as a function of 1:1 and the xed utility level U). Draw the representative indifference curve. Are the preferences rational {that is, are they both strongly complete and transitive}? Justify your answer. . Are the preferences locally non-satiated? What about monotone? What about strongly monotone? Justify your answers. . Are the preferences convex? What about strictly convex? Justify $01.1]