The utility a consumer derives from the consumption of two goods x, and y is given...

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The utility a consumer derives from the consumption of two goods x, and y is given by U (x, y) = xa y The consumer has an income of I and the prices of the two goods x and y are px and py respectively. a) Set up the Lagrangian for the consumer's utility maximization problem, derive the first order conditions, and solve for the utility maximizing levels of x and y as a function of the consumer's income and the prices of the two goods. b) Derive the indirect utility function and the expenditure function. Find the expenditure necessary to achieve a utility level of 100, when the prices are px = 2 and py = 8 and when a = 0.25 B = 0.75 c) What is the reduction in the price of good Y necessary to double the consumer's utility level d) Calculate and illustrate the approximate dollar equivalent of this utility increase under the Marshallian demand function. The utility a consumer derives from the consumption of two goods x, and y is given by U (x, y) = xa y The consumer has an income of I and the prices of the two goods x and y are px and py respectively. a) Set up the Lagrangian for the consumer's utility maximization problem, derive the first order conditions, and solve for the utility maximizing levels of x and y as a function of the consumer's income and the prices of the two goods. b) Derive the indirect utility function and the expenditure function. Find the expenditure necessary to achieve a utility level of 100, when the prices are px = 2 and py = 8 and when a = 0.25 B = 0.75 c) What is the reduction in the price of good Y necessary to double the consumer's utility level d) Calculate and illustrate the approximate dollar equivalent of this utility increase under the Marshallian demand function.

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