Define the following terms using graths&mathmaticals experessions of budget line:utility &util ?

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To define the terms "budget line," "utility," and "util" using graphs and mathematical expressions:

1. Budget Line:
- Graphically: The budget line represents the different combinations of two goods that a consumer can afford to purchase within a given budget constraint. It is typically drawn as a straight line connecting the intercepts on the axes, where one axis represents the quantity of one good and the other axis represents the quantity of the second good.
- Mathematically: The equation of a budget line can be expressed as:
P₁Q₁ + P₂Q₂ = M,
where P₁ and P₂ are the prices of the two goods, Q₁ and Q₂ are the quantities of the two goods consumed, and M is the consumer's income or budget.

2. Utility:
- Graphically: Utility refers to the satisfaction or happiness a consumer derives from consuming a particular good or service. In graphical terms, utility is represented by an upward-sloping curve known as the indifference curve. Higher indifference curves indicate higher levels of utility, representing higher levels of satisfaction.
- Mathematically: Utility cannot be measured directly, but it can be represented mathematically through an individual's utility function. A standard utility function is U(Q₁, Q₂), where Q₁ and Q₂ are the quantities of the two goods consumed. The utility function assigns a level of satisfaction or utility to each combination of goods consumed.

3. Util:
- Util, short for utility unit, is a hypothetical measurement unit used to represent the degree of utility or satisfaction derived from consuming a specific product or service. It helps economists quantify the changes in utility when analyzing consumer preferences.
- Mathematically, utils are typically measured along an indifference curve, where each point represents a particular level of utility. However, the specific numerical value of utils does not hold any universal standard or meaning, as it is unique to each individual's preferences and utility function.

Note: While the above explanations outline the general concepts, it's important to note that the applications of budget lines, utility, and utils can vary depending on the specific economic theory or model being used.