Final Answer:
The algebraic expression for the individual's budget constraint is 4X + 2Y = 100.
Step-by-step explanation:
To derive the budget constraint equation, we use the formula: Total Expenditure = Price of X * Quantity of X + Price of Y * Quantity of Y. Here, the total expenditure (income) is $100, the price of good X (P_X) is $4, and the price of good Y (P_Y) is $2. Let X represent the quantity of good X consumed and Y represent the quantity of good Y consumed. The equation becomes: 4X + 2Y = 100. This equation signifies the relationship between the quantities of goods X and Y that the individual can purchase while adhering to the budget.
The coefficient of X (4) denotes the price of X, and the coefficient of Y (2) denotes the price of Y. The sum of the products on the left side of the equation represents the total expenditure, which must equal the individual's income. This budget constraint defines the feasible combinations of X and Y that the individual can afford given the specified prices and income. Graphically, it illustrates a straight line in a two-dimensional space, representing the various combinations of goods X and Y that exhaust the individual's budget.
In economic analysis, comprehending and modeling budget constraints is fundamental for studying consumer behavior, market demand, and resource allocation. The equation offers a clear representation of the economic choices available to the individual based on their budget limitations and the prices of the goods in question.