Problem 2: Satiation point(s) There two goods, candy and soda, available in arbitrary non-negative quan- tities (so the consumption set is R1). A consumer has preferences over con- sumption bundles that are represented by the following utility function: \"(5679) = -|4 - wl - l4 yl where a: is the quantity of candy (in grams), y is the quantity of soda (in liters), and M denotes the absolute value: for any real number r E R, r if 'r 2 0 |r|= , - r 1fr 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 044,5) + (1 01)(3,4) for 0! 6 [0,1]- (b) In an appropriate diagram, illustrate the consumer's map of indiffer- ence CUI'VBS . (o) 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 to > O for the following specic prices, explaining how you arrived at your answers Z (i) when p = 1 and q = 2, (ii) when p = 2 and q = 1, (iii) when p = q = 1.For each part (a), (b) and (0), 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. where :c 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 CHI'VGS . (f) Are the consumer's preferences monotone? Are the preferences convex? Provide an explanation for each