In case of two goods, following utility approach, a consumer is in equilibrium when

$$ rac{{M{U_x}}}{{{P_x}}} = rac{{M{U_y}}}{{{P_y}}}$$
$$ rac{{M{U_x}}}{{{P_x}}} > rac{{M{U_y}}}{{{P_y}}}$$
Both B and C

The correct answer is A.

A consumer is in equilibrium when the marginal utility per dollar spent on each good is equal. This is known as the law of diminishing marginal utility. The law of diminishing marginal utility states that as a consumer consumes more of a good, the marginal utility of that good decreases. This means that the consumer will get less satisfaction from each additional unit of the good that they consume.

In order to maximize utility, a consumer will want to allocate their budget in such a way that they are getting the most satisfaction from each dollar that they spend. This means that they will want to consume goods until the marginal utility per dollar spent on each good is equal.

Mathematically, this can be expressed as follows:

$$\frac{{M{U_x}}}{{{P_x}}} = \frac{{M{U_y}}}{{{P_y}}}$$

where $M{U_x}$ is the marginal utility of good $x$, $P_x$ is the price of good $x$, $M{U_y}$ is the marginal utility of good $y$, and $P_y$ is the price of good $y$.

If the consumer is not in equilibrium, they will be able to increase their utility by reallocating their budget. For example, if the consumer is spending more on good $x$ than they are on good $y$, then they can increase their utility by spending less on good $x$ and more on good $y$. This will continue until the consumer reaches equilibrium, at which point they will be getting the most satisfaction from each dollar that they spend.