Budget Equation:

The budget equation is a mathematical representation of the relationship between the income of a consumer and the prices of the goods he or she intends to consume. In this case, the consumer has a fixed money income, M, and intends to spend it on two commodities, X and Y, with prices Px and Py respectively. The budget equation is given by:

M = PxX + PyY

where M is the total money income, Px and Py are the prices of the two commodities, and X and Y are the quantities of the two commodities consumed.

Explanation:

The budget equation represents the idea that the total money income of a consumer is equal to the total expenditure on the two commodities. The left-hand side of the equation represents the total money income of the consumer, which is fixed. The right-hand side of the equation represents the total expenditure on the two commodities, which is determined by the prices of the commodities and the quantities consumed.

The budget equation can also be used to determine the maximum amount of one commodity that a consumer can buy given the prices of the two commodities and the fixed income. For example, if a consumer has a fixed income of M and intends to consume X and Y with prices Px and Py respectively, then the maximum quantity of X that the consumer can buy is given by:

X = (M - PyY) / Px

Similarly, the maximum quantity of Y that the consumer can buy is given by:

Y = (M - PxX) / Py

These equations represent the consumer's budget constraint, which shows the combinations of X and Y that the consumer can afford given the fixed income and the prices of the two commodities.

In conclusion, the budget equation is an important tool for analyzing the consumption behavior of consumers. It represents the relationship between the income of a consumer and the prices of the goods he or she intends to consume, and can be used to determine the maximum amount of one commodity that a consumer can buy given the prices of the two commodities and the fixed income.