Define utility using graph or mathimatical expresions

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define the following terms using graphs and mathmatical expressions

1) utility
2)Util
3)Iso cost
4)Indifference curve
5)Budget line
6)Monoplist
7)Kinked demand curve
8)Social exploitation
9) Profit
10) Perfect competation market

please give me above questions solve the answer

utility

Utility can be defined both graphically and mathematically.

Graphically, utility is often represented by a preference or indifference curve diagram. In this diagram, utility is measured on the vertical axis and the consumption of different goods or services is measured on the horizontal axis. The shape of the indifference curves represents the consumer's preferences, where higher curves indicate higher levels of utility. The slope of the indifference curve indicates the consumer's marginal rate of substitution, representing the rate at which the consumer is willing to exchange one good for another while maintaining the same level of utility.

Mathematically, utility is often represented by a utility function. A utility function is a mathematical equation that assigns a numerical value to different combinations of goods and services. The general form of a utility function is U(x1, x2, ..., xn), where x1, x2, ..., xn represent the quantities of different goods or services consumed, and U represents the utility derived from consuming those goods or services. The specific form of the utility function can vary depending on the assumptions made about the consumer's preferences. Examples of commonly used utility functions include:

1. Cobb-Douglas Utility Function: U(x1, x2) = x1^α * x2^β, where α and β are positive constants representing the marginal utility of each good.

2. Perfect Substitutes Utility Function: U(x1, x2) = α * x1 + β * x2, where α and β are positive constants representing the marginal utility of each good, and the consumer is indifferent between consuming more of one good or the other.

3. Perfect Complements Utility Function: U(x1, x2) = min(α * x1, β * x2), where α and β are positive constants representing the marginal utility of each good, and the consumer derives utility only from consuming equal amounts of both goods.

These are just a few examples of utility functions, and there are various other forms depending on different assumptions about consumer preferences.