The correct answer is $\boxed{\frac{{M{U_x}}}{{{P_x}}} = \frac{{M{U_y}}}{{{P_y}}} = \frac{{M{U_z}}}{{{P_z}}}}$.
This is the condition for consumer equilibrium, which states that a consumer will maximize their satisfaction when they allocate their income in such a way that the marginal utility per dollar spent on each good is equal.
In other words, the consumer will buy more of the goods that give them the most satisfaction per dollar, and less of the goods that give them less satisfaction per dollar. This will continue until the marginal utility per dollar spent on each good is equal.
The marginal utility of a good is the additional satisfaction that a consumer gets from consuming one more unit of that good. The price of a good is the amount of money that a consumer has to give up in order to consume one more unit of that good.
The marginal utility per dollar spent on a good is the marginal utility of that good divided by the price of that good.
The consumer equilibrium condition states that the marginal utility per dollar spent on each good is equal. This means that the consumer is getting the same amount of satisfaction per dollar from each good that they are consuming.
If the marginal utility per dollar spent on one good is higher than the marginal utility per dollar spent on another good, then the consumer can increase their satisfaction by buying more of the good with the higher marginal utility per dollar and less of the good with the lower marginal utility per dollar.
This process will continue until the marginal utility per dollar spent on each good is equal.
The consumer equilibrium condition is a fundamental concept in economics. It is used to explain how consumers make decisions about what to buy. It is also used to analyze the effects of changes in prices, income, and preferences on consumer demand.