Utility maximization was first developed by utilitarian philosophers Jeremy Bentham and John Stuart Mill. In microeconomics, the utility maximization problem is the problem consumers face: "How should I spend my money in order to maximize my utility?" It is a type of optimal decision problem. It consists of choosing how much of each available good or service to consume, taking into account a constraint on total spending (income), the prices of the goods and their preferences. Utility maximization is an important concept in consumer theory as it shows how consumers decide to allocate their income. Because consumers are rational, they seek to extract the most benefit for themselves. However, due to bounded rationality and other biases, consumers sometimes pick bundles that do not necessarily maximize their utility. The utility maximization bundle of the consumer is also not set and can change over time depending on their individual preferences of goods, price changes and increases or decreases in income. Basic setup For utility maximization there are four basic steps process to derive consumer demand and find the utility maximizing bundle of the consumer given prices, income, and preferences. 1) Check if Walras's law is satisfied 2) 'Bang for buck' 3) the budget constraint 4) Check for negativity 1) Walras's Law Walras's law states that if a consumers preferences are complete, monotone and transitive then the optimal demand will lie on the budget line. Preferences of the consumer For a utility representation to exist the preferences of the consumer must be complete and transitive (necessary conditions). Complete Completeness of preferences indicates that all bundles in the consumption set can be compared by the consumer. For example, if the consumer has 3 bundles A,B and C then; A B, A C, B A, B C, C B, C A, A A, B B, C C. Therefore, the consumer has complete preferences as they can compare every bundle. Transitive Transitivity states that individuals preferences are consistent across the bundles. therefore, if the consumer weakly prefers A over B (A B) and B C this means that A C (A is weakly preferred to C) Monotone For a preference relation to be monotone increasing the quantity of both goods should make the consumer strictly better off (increase their utility), and increasing the quantity of one good holding the other quantity constant should not make the consumer worse off (same utility). The preference is monotone if