Ahmad dislikes plain coffee, unless he eats something sweetie with the coffee. In particular, he likes to consume Starbuck's coffee (X₂) only if he is compensated by one caramel doughnut (X₁) while drinking the plain coffee. Otherwise, drinking plain coffee is not desirable for him. Ahmad has budget M, Ahmad's target utility is U = K, the marginal utility of one doughnut is A, and his marginal disutility of one plain coffee without doughnut is " - B". A. Write down Ahmad's consumer optimization (objective and constraints). B. Derive Ahmad's demand functions for plain coffee (X₂) and doughnuts (X₁). C. What is Ahmad's maximum utility?
Ahmad dislikes plain coffee, unless he eats something sweetie with the coffee. In particular, he likes to consume Starbuck's coffee (X₂) only if he is compensated by one caramel doughnut (X₁) while drinking the plain coffee. Otherwise, drinking plain coffee is not desirable for him. Ahmad has budget M, Ahmad's target utility is U = K, the marginal utility of one doughnut is A, and his marginal disutility of one plain coffee without doughnut is " - B". A. Write down Ahmad's consumer optimization (objective and constraints). B. Derive Ahmad's demand functions for plain coffee (X₂) and doughnuts (X₁). C. What is Ahmad's maximum utility?
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.14P
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Transcribed Image Text:Consider the following scenario:
Ahmad dislikes plain coffee, unless he eats something sweetie with the coffee. In particular, he
likes to consume Starbuck's coffee (X2) only if he is compensated by one caramel doughnut (X,)
while drinking the plain coffee. Otherwise, drinking plain coffee is not desirable for him. Ahmad
has budget M, Ahmad's target utility is U = K, the marginal utility of one doughnut is A, and his
marginal disutility of one plain coffee without doughnut is “– B".
A. Write down Ahmaď's consumer optimization (objective and constraints).
B. Derive Ahmad's demand functions for plain coffee (X2) and doughnuts (X,).
C. What is Ahmad's maximum utility?
D. Get the compensation inequality condition.
E. Find the minimum compensation required for Ahmad to consume Starbuck's plain coffee.
F. Show graphically.
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