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only solve 7 please Problem 1. Alex has preferences over two goods given by the Cobb-Douglas utility function: u(x1, x2) = Q1 In 21 +

image text in transcribedonly solve 7 please

Problem 1. Alex has preferences over two goods given by the Cobb-Douglas utility function: u(x1, x2) = Q1 In 21 + a2 In 22, where A1, A2 > 0. The prices of the goods are p and P2, and Alex has income y. 1. Suppose ai = 1, Q2 = 3, p1 = 2, P2 = 3 and y = 60. Find the Marshallian demands (21, x*). 2. For generic values of the parameters (Q1, Q2, P1, P2, y), find the Marshallian demand functions xi (p,y) and x*(p, y), and the Lagrange multiplier \* (p,y). 3. Find the budget share of each good. 4. Comment on the functional form of the Marshallian demand functions and budget shares. How are they related to prices, income and the preferences parameters Qi and az? 5. Find the indirect utility function. [For notational convenience, you may denote the constant A = aj In ai + az In Q2 - (a1 + a2) In (a1 + a2)] 6. Evaluate, by direct computation, any and 7. Use the Envelope Theorem to verify your answers to the previous part. Problem 1. Alex has preferences over two goods given by the Cobb-Douglas utility function: u(x1, x2) = Q1 In 21 + a2 In 22, where A1, A2 > 0. The prices of the goods are p and P2, and Alex has income y. 1. Suppose ai = 1, Q2 = 3, p1 = 2, P2 = 3 and y = 60. Find the Marshallian demands (21, x*). 2. For generic values of the parameters (Q1, Q2, P1, P2, y), find the Marshallian demand functions xi (p,y) and x*(p, y), and the Lagrange multiplier \* (p,y). 3. Find the budget share of each good. 4. Comment on the functional form of the Marshallian demand functions and budget shares. How are they related to prices, income and the preferences parameters Qi and az? 5. Find the indirect utility function. [For notational convenience, you may denote the constant A = aj In ai + az In Q2 - (a1 + a2) In (a1 + a2)] 6. Evaluate, by direct computation, any and 7. Use the Envelope Theorem to verify your answers to the previous part

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