A consumer has Cobb-Douglas preferences over two goods: good 1 and good 2. The consumer's preference...

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A consumer has Cobb-Douglas preferences over two goods: good 1 and good 2. The consumer's preference can be represented by the utility function u(x₁, x₂) = x²x₂ where x₁ is the amount of good 1 and x₂ is the amount of good 2 that the consumer consumes respectively. The price of good 1 is p₁ and the price of good 2 is p2. The consumer has a money income of m that she intends on spending on both goods. a) State the consumer's constrained maximization problem. [2 points] b) Find the demand functions for good 1 and good 2. [6 points] c) Is good 1 a normal good or an inferior good? Prove your answer. [2 points] A consumer has Cobb-Douglas preferences over two goods: good 1 and good 2. The consumer's preference can be represented by the utility function u(x₁, x₂) = x²x₂ where x₁ is the amount of good 1 and x₂ is the amount of good 2 that the consumer consumes respectively. The price of good 1 is p₁ and the price of good 2 is p2. The consumer has a money income of m that she intends on spending on both goods. a) State the consumer's constrained maximization problem. [2 points] b) Find the demand functions for good 1 and good 2. [6 points] c) Is good 1 a normal good or an inferior good? Prove your answer. [2 points]

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