Question 3 A certain household comprises of a couple, Adam (A) and Betty (B). They have exicographic preferences over two goods G1 and G2 - A wants to consume as much of G1 as possible, before moving on to G2 whereas, for B, it is the opposite, she wants to consume as much of G2 as possible before moving on to G1.¹ Given their varying preferences, they decide to shop separately, after dividing the household income equally. The household income is $8. One difference to the usual setting - there are government restrictions in place so that no individual s allowed to buy more than two units of either good. Hint: Do not use mathematical brute force (like Calculus) to solve this problem. A simple diagram with appropriate budget lines, etc. should suffice. 1) Suppose prices are p= (p₁, p2) = (1, 2). Denote the optimal choice of A and B as a = (a₁, a2) and b= (b₁,b₂) respectively. Solve for a and b.

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Question 3 A certain household comprises of a couple, Adam (A) and Betty (B). They have
lexicographic preferences over two goods G1 and G2 - A wants to consume as much of G1 as possible,
before moving on to G2 whereas, for B, it is the opposite, she wants to consume as much of G2 as
possible before moving on to G1.¹ Given their varying preferences, they decide to shop separately,
after dividing the household income equally. The household income is $8.
One difference to the usual setting - there are government restrictions in place so that no individual
is allowed to buy more than two units of either good.
Hint: Do not use mathematical brute force (like Calculus) to solve this problem. A simple diagram
with appropriate budget lines, etc. should suffice.
1) Suppose prices are p= (P₁, P2) = (1,2). Denote the optimal choice of A and B as a=
b= (b₁,b₂) respectively. Solve for a and b.
(a1, a2) and
Transcribed Image Text:Question 3 A certain household comprises of a couple, Adam (A) and Betty (B). They have lexicographic preferences over two goods G1 and G2 - A wants to consume as much of G1 as possible, before moving on to G2 whereas, for B, it is the opposite, she wants to consume as much of G2 as possible before moving on to G1.¹ Given their varying preferences, they decide to shop separately, after dividing the household income equally. The household income is $8. One difference to the usual setting - there are government restrictions in place so that no individual is allowed to buy more than two units of either good. Hint: Do not use mathematical brute force (like Calculus) to solve this problem. A simple diagram with appropriate budget lines, etc. should suffice. 1) Suppose prices are p= (P₁, P2) = (1,2). Denote the optimal choice of A and B as a= b= (b₁,b₂) respectively. Solve for a and b. (a1, a2) and
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2) Now suppose the prices change to q = (91, 92) = (2,1). Again, obtain the optimal choices for A
d= (d₁, d2). Solve for c and d.
and B, denote them by c =
= (C₁,
(C₁, C2)
C₂) and
and d
Transcribed Image Text:2) Now suppose the prices change to q = (91, 92) = (2,1). Again, obtain the optimal choices for A d= (d₁, d2). Solve for c and d. and B, denote them by c = = (C₁, (C₁, C2) C₂) and and d
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