Mr. Rational has $27 that he plans to spend purchasing 5 units of good X (priced at $3 per unit) and 6 units of good Y (priced at $2 per unit). The marginal utility of the fifth unit of X is 30, and the marginal utility of the sixth unit of Y is 18. If Mr. Rational is a utility maximizer, he should: a. buy less of X and more of Y. b. buy more of X and less of Y. c. buy X and Y in the quantities indicated. d. buy less of X and even lesser than that of Y. e. not buy anything.

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Priatouri Priatouri · Answer 1 · 2020-05-26T04:45:47+02:00

Answer:

Option A, buy less of X and more of Y is correct.

Explanation:

The amount that Mr. Rational is going to spend = $27

Quantity of good X = 5 units

Price of good X (Px) = $3 per unit

Marginal utility of 5th unit of X (MUx) = 30

Quantity of good Y = 6 units

Price of good Y (Py) = $2 per unit

Marginal utility of 6th unit of Y (MUy) = 18

[tex]Now \ find \ \frac{MUx}{Px} = \frac{30}{3} = 10 \\[/tex]

[tex]Now \ \frac{MUy}{Py} = \frac{18}{2} = 9[/tex]

[tex]Since \ the \ \frac{MUx}{Px} is \ greater \ than \ \frac{MUy}{Py}.[/tex]

So good x will be substituted for y in order to reach the consumer equilibrium.

[tex]\frac{MUx}{Px} = \frac{MUy}{Py}[/tex]

Thus, Option a. buy less of X and more of Y is correct.