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

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.