Katniss likes to eat deer (d) and rabbit (r). Her preferences over these game meats are Cobb- Douglas, and can be presented by the utility function u(d,r)= 1/5(d−2)(r+3). These animals must be hunted. Each deer costs 25 units of energy and each rabbit costs 12 units of energy. Katniss has 628 units of energy to exert. Assume that deer and rabbit are both perfectly divisible goods. a. Find Katniss’ optimal bundle. b. Suppose that Katniss is stung by a tracker jacker. This saps her of energy so that she is left only with 50 units of energy. What is her optimal bundle now? c. Now, consider the general case, where Katniss has e units of energy, the energy cost of deer is cd, and the energy cost of rabbits is cr . Find Katniss’s demand for each good in terms of e, cd and cr . d. Find the good on which Katniss will always spend more than half of her energy. e. Find the own-price, cross-price, and income elasticities of rabbit.
Katniss likes to eat deer (d) and rabbit (r). Her preferences over these game meats are Cobb- Douglas, and can be presented by the utility function
u(d,r)= 1/5(d−2)(r+3).
These animals must be hunted. Each deer costs 25 units of energy and each rabbit costs 12 units of energy. Katniss has 628 units of energy to exert. Assume that deer and rabbit are both perfectly divisible goods.
a. Find Katniss’ optimal bundle.
b. Suppose that Katniss is stung by a tracker jacker. This saps her of energy so that she is left only with 50 units of energy. What is her optimal bundle now?
c. Now, consider the general case, where Katniss has e units of energy, the energy cost of deer is cd, and the energy cost of rabbits is cr . Find Katniss’s demand for each good in terms of e, cd and cr .
d. Find the good on which Katniss will always spend more than half of her energy.
e. Find the own-price, cross-price, and income elasticities of rabbit.
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