Utilities function and equitions with the budget constrains
A utility function is a mathematical representation of a consumer's preferences over a set of goods and services. It is typically represented as a function that takes a set of goods and services and returns a number representing the level of satisfaction or utility that the consumer derives from consuming those goods and services.
The budget constraint equation is a mathematical expression of the consumer's budget. It is typically represented as an equation that takes the prices of the goods and services and the consumer's income and returns the maximum amount of each good or service that the consumer can purchase given their budget.
For example, if a consumer has an income of $100 and the prices of two goods, A and B, are $10 and $20 respectively, then the budget constraint equation would be:
Max(A,B) = 100/(10 + 20)
This equation states that the consumer can purchase a maximum of 5 units of good A and 2.5 units of good B given their budget.