Utility maximization problem

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. 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.

Check if Walras's law is satisfied
'Bang for buck'
the budget constraint
Check for negativity Walras's law states that if a consumers preferences are complete, monotone and transitive then the optimal demand will lie on the budget line. For a utility representation to exist the preferences of the consumer must be complete and transitive (necessary conditions). 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. Transitivity states that individuals preferences are consistent across the bundles.

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Information Theoretic Characterization of Uncertainty Distinguishes Surprise From Accuracy Signals in the Brain

Kerstin Preuschoff, Leyla Loued-Khenissi

Uncertainty presents a problem for both human and machine decision-making. While utility maximization has traditionally been viewed as the motive force behind choice behavior, it has been theorized that uncertainty minimization may supersede reward motivation. Beyond reward, decisions are guided by belief, i.e., confidence-weighted expectations. Evidence challenging a belief evokes surprise, which signals a deviation from expectation (stimulus-bound surprise) but also provides an information gain. To support the theory that uncertainty minimization is an essential drive for the brain, we probe the neural trace of uncertainty-related decision variables, namely confidence, surprise, and information gain, in a discrete decision with a deterministic outcome. Confidence and surprise were elicited with a gambling task administered in a functional magnetic resonance imaging experiment, where agents start with a uniform probability distribution, transition to a non-uniform probabilistic state, and end in a fully certain state. After controlling for reward expectation, we find confidence, taken as the negative entropy of a trial, correlates with a response in the hippocampus and temporal lobe. Stimulus-bound surprise, taken as Shannon information, correlates with responses in the insula and striatum. In addition, we also find a neural response to a measure of information gain captured by a confidence error, a quantity we dub accuracy. BOLD responses to accuracy were found in the cerebellum and precuneus, after controlling for reward prediction errors and stimulus-bound surprise at the same time point. Our results suggest that, even absent an overt need for learning, the human brain expends energy on information gain and uncertainty minimization.

2020

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