# Consider the utility function u(x1, x2) = max{x1, x2}. Suppose that the price of good 1 is fixed...

## Question:

Consider the utility function {eq}u(x_{1},x_{2}) = max{(x_{1},x_{2})} {/eq}. Suppose that the price of Good 1 is fixed at 1. The price of Good 2 is given {eq}p_{2}(>0) {/eq} and the income is {eq}m(>0) {/eq}.

(1) Find out the optimal choices at {eq}p_{2}<1 {/eq}, {eq}p_{2}>1 {/eq}, and {eq}p_{2}=1 {/eq}, respectively.

(2) Draw the {eq}p_{2} {/eq}-offer curve in the graph.

(3) Draw the demand curve of Good 2. Can you tell if Good 2 is an ordinary good or a Giffen good?

(4) Draw the Income offer curve in the graph for a fixed price {eq}p_{2} <1 {/eq}.

(5) Draw the Engel curve of Good 2 for a fixed price {eq}p_{2}<1 {/eq}. Draw the Engel curve of Good 1 for a fixed price {eq}p_{2}<1 {/eq}. Can you tell if Good 2 is a normal good or an inferior good when {eq}p_{2}<1 {/eq}?

(6) How is the demand for Good 1 affected when the price of Good 2 changes? Can you tell if Good 1 is a gross substitute or a gross complement of Good 2?

## Utility in Economics:

The utility is the level of satisfaction or enjoyment that a consumer obtains from consuming one or a combination of goods. The higher the consumption, the higher the utility is. However, the consumer's consumption is limited by his budget constraint. That is he cannot consume as much as he wants.

## Answer and Explanation: 1

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View this answerThe consumer's budget constraint is {eq}x_1+p_2x_2=m {/eq}.

(1) Because the margianl utility of both goods is equal, the consumer will choose the...

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Chapter 3 / Lesson 2Learn about utility maximization. Discover various types of utility, examine utility maximizing rules, and study examples of maximizing utilities in economics.

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