2 Consider the following utility function defined over two goods 1 and 2 U x1 x2 x x2 The prices of goods 1 and 2 are p and p2

Question

2 Consider the following utility function defined over two goods 1 and 2 U x1 x2 x x2 The prices of goods 1 and 2 are p and p2 respectively a Does the law of diminishing marginal utility hold for good 2 Find the MRS of good 1 for good 2 15 b Write the equation representing the budget constraint assuming the consumer s income is M 3 c Using the method of Lagrange maximize the utility subject to the budget constraint What are the demand functions for and 2 Assuming p 2 P2 1 and M 100 find the quantities of x and x2 that maximizes utility 25 d Check the SOC for the Lagrangian method 12

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