Question

Derive mathematically the optimal choice that maximizes a consumer's utility subject to their budget constraint. Use the utility function U(x, y) = x + y and explain how this mathematical model helps in consumer decision-making.

Answer 1

To maximize a consumer's utility subject to their budget constraint, we can use mathematical models. By comparing the ratio of the marginal utility to price of goods, consumers can determine their optimal choice. This helps in consumer decision-making by allowing consumers to find the combination of goods that provides the most utility within their budget constraint.

Step-by-step explanation:

To maximize a consumer's utility subject to their budget constraint, we can use mathematical models. If we have a utility function like U(x, y) = x + y, we can find the optimal choice by comparing the ratio of the marginal utility to price of good 1 with the marginal utility to price of good 2. At the optimal choice, these two ratios should be equal. This helps in consumer decision-making by allowing consumers to determine the combination of goods that will provide the most utility within their budget constraint.