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 Əx₁' au 2² U Əx₂' dx²¹ 2² U dx²2 (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 = 1/2.

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 Əx₁' au 2² U Əx₂' dx²¹ 2² U dx²2 (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 = 1/2.

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Consumer Choice Theory

Section: Chapter Questions

Problem 3SQP

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Let the following table represents the total utility of a given consumer, in the cardinal utility approach A) Calculate the MUx and MUy and fill the table in the 4th and 5th rows. B) If the two products (X&Y) are free goods how many of X and Y should the cons consumer take to maximize utility? C) What is the maximum utility of X and Y if they are free?. D) Assuming the consumer has any amount of money (enough budget) how many of X and Y should the consumer buy, to maximize utility? E) What is the total utility of X and Y? F) Let now price of X is 4 birr per unit and price of Y is 2 birr per unit and budget of the consumer for consumption of X and Y is 20 birr. Given budget constraint how many of X and Y should the consumer buy to maximize utility? G) What are the total utility of X and Y
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