There two goods, candy and soda, available in arbitrary non-negative quan- tities (so the consumption set is R). A consumer has preferences over con- sumption bundles that are represented by the following utility function: u(r, u) = -|14 - a| - 14 - vl where r is the quantity of candy (in grams), y is the quantity of soda (in liters), and |.| denotes the absolute value: for any real mumber r ER, if r20 Irl -r ifr 0 Dirhams. The price of candy is p> 0 Dirhams/gram, and the price of soda is q > 0 Dirhams/liter. (a) Calculate the utility of the following consumption bundles: (4, 4). (4,5), (5, 4), (4,3). (3, 4), and a(4,5) +(1-a)(3.4) for a E (0,1]. (b) In an appropriate diagram, illustrate the consumer's map of indiffer- ence curves, (e) Are the consumer's preferences monotone? Provide an explanation for your answer. (d) Find the demand for candy and soda as a function of wealth w> 0 for the following specific prices, explaining how you arrived at your answers: () when p=1 and q = 2, (5) when p = 2 and q = 1, !! (ii) when p =q = 1. For each part (a), (b) and (c), illustrate the demand for candy as a function of wealth in an appropriate diagram. Now consider a different consumer who has preferences represented by the following utility function. S-12 - 1| - 18 u if a Sy 1-18 2| - 12 y if z > y u(x, y) = where r is the quantity of candy (in grams) and y is the quantity of soda (in liters). (e) In an appropriate diagram, illustrate the consumer's map of indiffer- ence curves. (n Are the consumer's preferences monotone? Are the preferences convex? Provide an explanation for each answer.