Solve part b and c. There two goods, candy and soda, available in arbitrary non-negative quantities (so the consumption set is R2+). A consumer has preferences over consumption bundles that are represented by the following utility function: u(x, y) = −|4 − x| − |4 − y| where x is the quantity of candy (in grams), y is the quantity of soda (in liters), and |.| denotes the absolute value: for any real number r ∈ R, |r| = r if r ≥ 0 −r if r < 0. The consumer has wealth of w > 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 α(4, 5) + (1 − α)(3, 4) for α ∈ [0, 1]. (b) In an appropriate diagram, illustrate the consumer’s map of indifference curves. c) Are the consumer's preferences monotone? Provide an explanation for your answer.
Solve part b and c.
There two goods, candy and soda, available in arbitrary non-negative quantities (so the consumption set is R2+). A consumer has preferences over consumption bundles that are represented by the following utility function:
u(x, y) = −|4 − x| − |4 − y|
where x is the quantity of candy (in grams), y is the quantity of soda (in
liters), and |.| denotes the absolute value: for any real number r ∈ R,
|r| = r if r ≥ 0
−r if r < 0.
The consumer has wealth of w > 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 α(4, 5) + (1 − α)(3, 4) for α ∈ [0, 1].
(b) In an appropriate diagram, illustrate the consumer’s map of indifference
c) Are the consumer's preferences monotone? Provide an explanation for
your answer.
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