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6. Let ₁ and 2 be the amounts of two goods whose joint utility function is U (x1, x2) = 9x1 + 3x2 - 4x²-x². (a) Compute the partial derivatives მU მU 8² U 8² U dx₁' дх1 x₂' x²¹ əx² (b) Does the law of diminishing marginal utility hold for this utility function? Justify your answer. (c) Find the marginal rate of commodity substitution (MRCS) when x₁ = = 1 and x₂ = 1/3.

6. Let ₁ and 2 be the amounts of two goods whose joint utility function is U (x1, x2) = 9x1 + 3x2 - 4x²-x². (a) Compute the partial derivatives მU მU 8² U 8² U dx₁' дх1 x₂' x²¹ əx² (b) Does the law of diminishing marginal utility hold for this utility function? Justify your answer. (c) Find the marginal rate of commodity substitution (MRCS) when x₁ = = 1 and x₂ = 1/3.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6. Let ₁ and 2 be the amounts of two goods whose joint utility function is U(x1, x2) = 9x1 + 3x2 - 4x²-x2. (a) Compute the partial derivatives au au 8² U 2² U 7 дх1 əx₂ əx²¹ əx² (b) Does the law of diminishing marginal utility hold for this utility function? Justify your answer. (c) Find the marginal rate of commodity substitution (MRCS) when x₁ = 1 and ₂ = 1/3. 7
Transcribed Image Text:6. Let ₁ and 2 be the amounts of two goods whose joint utility function is U(x1, x2) = 9x1 + 3x2 - 4x²-x2. (a) Compute the partial derivatives au au 8² U 2² U 7 дх1 əx₂ əx²¹ əx² (b) Does the law of diminishing marginal utility hold for this utility function? Justify your answer. (c) Find the marginal rate of commodity substitution (MRCS) when x₁ = 1 and ₂ = 1/3. 7
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