Question

Kim recently makes her new favorite snack: 1 dried apricot along with 3 cashews. She insists such combination is the perfect mix, and she wouldn't eat any extra if that doesn't makes her combo. More combos Kim has, the happier Kim is. From the whole bag of dried apricot and the whole jar of cashews, Kim calculated that Price for 1 dried apricot is $0.20 and price for 1 cashew is $0.06. (1) Write a utility function to represent Kim's preference. We use A for Apricot, and C for Cashew. (2) If Kim's daily budget for snack is $m, how many cashews will she consume everyday? Choose one from the following for (1) and (2), and explain your answers.

(1) A. u(A, C)=A+3C

B. u(A, C)=3A+C

C. u(A, C)=3CA

D. u(A, C)=A(C^3)

E. u(A, C)=min{A, 3C}

F. u(A, C)=min{3A, C}

(2)A. 3m/4

B. m/0.38

C. 3m/0.38

D. m/0.66

E. 3m/0.66

F. m/0.06

G. 3m/0.24

Answer 1

(1) This is an example of perfect complements. These goods are consumed in a fixed proportion together. Whatever units of apricots, he must consume thrice of that number of chashews. 1 apricot and 3 cashews, 2 apricots and 6 cashews, 3 apricots and 9 cashews. This way the utility function is

F. u(A,C)= min(3A,C)

(2) As per above utility function, utility is maximum when

3A= C or A= C/3

Given the budget constraint: 0.20A +0.06C= m

Putting the value of A in budget constraint, we get

0.20(C/3) + 0.06 C= m

0.20C + 0.18 C = m

0.38 C= m

C= m/0.38

So the correct answer is

B. m/0.38