Three Stark kids, named Sansa, Arya, and Rickon, like to collect interesting items, especially dolls (D),...

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Three Stark kids, named Sansa, Arya, and Rickon, like to collect interesting items, especially dolls (D), needles (N), and sticks (S). Let D, N, and S designate the number of pieces in each collection, respectively. Each of them has $100 to spend on their collection. The dolls cost $5 each, needles $10 each, and sticks cost $1 each. 1. Sansa's utility function is U (D, N, S) = max {4D, N} ("max {...}" refers to "taking the maximal number amongst the parameters." For example, max {2,4} = 4). Find Sansa's optimal bundle, indicating the number of dolls (D), the number of needles (N), and the number of sticks (S) in her optimal bundle. [4 marks] 2. Arya's utility function is U (D, N, S) = ln (N) + In (S). Find Arya's optimal bundle, indicating the number of dolls (D), the number of needles (N), and the number of sticks (S) in her optimal bundle. [4 marks] 3. Rickon's utility function is U (D, N, S) = D + N + S. Find Rickon's optimal bundle, indicating the number of dolls (D), the number of needles (N), and the number of sticks (S) in his optimal bundle. [4 marks] Three Stark kids, named Sansa, Arya, and Rickon, like to collect interesting items, especially dolls (D), needles (N), and sticks (S). Let D, N, and S designate the number of pieces in each collection, respectively. Each of them has $100 to spend on their collection. The dolls cost $5 each, needles $10 each, and sticks cost $1 each. 1. Sansa's utility function is U (D, N, S) = max {4D, N} ("max {...}" refers to "taking the maximal number amongst the parameters." For example, max {2,4} = 4). Find Sansa's optimal bundle, indicating the number of dolls (D), the number of needles (N), and the number of sticks (S) in her optimal bundle. [4 marks] 2. Arya's utility function is U (D, N, S) = ln (N) + In (S). Find Arya's optimal bundle, indicating the number of dolls (D), the number of needles (N), and the number of sticks (S) in her optimal bundle. [4 marks] 3. Rickon's utility function is U (D, N, S) = D + N + S. Find Rickon's optimal bundle, indicating the number of dolls (D), the number of needles (N), and the number of sticks (S) in his optimal bundle. [4 marks]

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1 Sansas utility function is UD N S max4D N To find Sansas optimal bundle we need to maximize her utility function given the budget constraint Budget ... View the full answer