Explanation The utility is the satisfaction derived by the consumer by consuming a good or service. The total utility is the summation of all the individual utilities derived from various units of consumption. The marginal utility is the additional utility derived from the consumption of an additional unit of good or service by the consumer. Here, we have two equations for calculating the marginal utility of good A and good B. They are as follows: MU A = 10 − x (1) MU B = 21 − 2 y (2) The x is the amount spent on good A and y is the amount spent on good B. It is also given that the consumer has a total income of $10 to spent on the two goods and we have to calculate the best allocation of $10 between the good A and B. The best allocation will be at the point where the MU A = MU B . The utility derived from the different combinations of the commodity can be calculated using the two equations and substituting various quantities from 0 to 10 to x and y as follows: The utility derived from good A can be calculated by assigning different values to “x” in equation (1) as follows: Utility derived from x 1 = 10 − 1 = 9 Thus, the utility derived from a unit of dollar on A is 9 utils. This can be repeated with the values of x up to 10 because the total units of consumption from the two are 10 ( x + y = 10 ). Similarly, the utility derived from good B can be calculated by assigning different values to y from 10 to 0 because the total units that can be consumed together of A and B is 10; and when x has a value, the y can be calculated by subtracting x from 10, and the utility from consumption of y can be calculated as follows: Utility derived from y 10 = 21 − ( 2 × 10 ) = 21 − 20 = 1 Thus, the utility derived from 10 unit of dollar on B is 1 util

The best allocation of $10 between A and B.

Economics (Irwin Economics)

21st Edition

ISBN: 9781259723223

Author: Campbell R. McConnell, Stanley L. Brue, Sean Masaki Flynn Dr.

Publisher: McGraw-Hill Education

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Chapter 7, Problem 6P

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The best allocation of $10 between A and B.

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The best allocation of $10 between A and B.

Solution Summary: The author explains that the utility is the satisfaction derived by the consumer by consuming a good or service. The marginal utility of good A and good B can be calculated using two equations.

The best allocation of $10 between A and B.

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