Howie Consumes Only Beer (B)and Donuts (D)each Week with His

question 34

Essay

Howie consumes only beer (B)and donuts (D)each week with his $100 income.Beer costs $1,while donuts cost only 50¢.Howie has Cobb-Douglas preferences given by:
U(B,D)= B(D-d)
where d is the quantity of donuts that his neighbor Nord consumes.Assume throughout this question that Howie always consumes more donuts than Nord.
a.How does Nord's beer consumption influence Howie's utility function? Specifically,compute and determine the sign of ∂U/∂d.Intuitively,what does this tell you about Howie's happiness and Nord's consumption of donuts?
b.Holding d fixed,compute Howie's optimal consumption bundle of Beer and Donuts as functions of Nord's consumption of donuts,d.
c.How does Nord's consumption of donuts affect Howie's optimal bundle? Specifically calculate and determine the sign of ∂B*/∂d and ∂D*/∂d where (B*,D*)is Howie's optimal consumption bundle.

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Definitions:

Arachnids

A class of joint-legged invertebrate animals that includes spiders, scorpions, ticks, and mites.

Myriapods

A group of arthropods that includes centipedes and millipedes, characterized by having numerous legs.

Deuterostomes

A classification of animals characterized by the development of the anus from the first opening in the embryo, with the mouth forming later.

Echinoderms

A phylum of marine animals known for their radial symmetry and include starfish, sea urchins, and sea cucumbers.