Suppose that Ashley likes 2 goods, good 1 (x_1) and good 2 (x_2). Her utility function is given...


Suppose that Ashley likes 2 goods, good 1 ({eq}x_1 {/eq}) and good 2 ({eq}x_2 {/eq}). Her utility function is given by {eq}U(x_1, x_2) = x_1^2 + x_2 {/eq}. Ashley's income is denoted as {eq}M {/eq} and the cost of good 1 (per unit) is {eq}P_1 {/eq} and the cost of good 2 (per unit) is {eq}P_2 {/eq}.

1. Write down Ashley's utility maximization problem. Remember that she is constrained by her budget.

2. Given the above problem, assume that the budget constraint binds, i.e., set it as equal. Now solve for the optimal {eq}x_1 {/eq} and {eq}x_2 {/eq}. Label them as {eq}x_1^* {/eq} and {eq}x_2^* {/eq}.

3. From your answer in part 2, determine whether good 1 and good 2 are substitutes or complements. Show this mathematically and explain your answer.

4. What type of utility function has been used here? What is so special about this type of function?

Utility Functions

In economics, the happiness or satisfaction a consumer gets from consuming a good or service is called utility, which can be modeled with utility functions. The goal of a consumer is to maximize their utility with respect to their budget constraints.

Answer and Explanation: 1

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1. Ashley's utility maximization problem with her budget constrain can be written down as:

{eq}M = P_{1}x_{1}+P_{2}x_{2} {/eq}

2. The optimal point...

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Learn more about this topic:

Utility Maximization: Budget Constraints & Consumer Choice


Chapter 3 / Lesson 2

Learn about utility maximization. Discover various types of utility, examine utility maximizing rules, and study examples of maximizing utilities in economics.

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