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 30. If Mr. Rational is a utility maximizer, he should:

In economics, marginal utility refers to the additional pleasure or benefit (utility) a buyer receives by purchasing an additional unit of a good or service.

The general rule in economics is that marginal utility equals total utility change divided by change in quantity of goods.
The equation looks like this Total utility difference divided by amount of commodities difference equals marginal utility.
Find the first event's overall utility.

According to the question:

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.

Now find [tex]$\frac{M U x}{P x}=\frac{30}{3}=10$[/tex]

Now [tex]$\frac{M U y}{P y}=\frac{18}{2}=9$[/tex]

Since the [tex]\frac{M U x}{P x}$ is greater than $\frac{M U y}{P y}$.[/tex]

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

[tex]$\frac{M U x}{P x}=\frac{M U y}{P y}$[/tex]

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