## Understanding Joan's Utility FunctionJoan has the following utility function: $ U = 4x + 4y $, where $ x $ and $ y $ represent two goods.### a. Preferences for GoodsJoan's utility function $ U = 4x + 4y $ indicates that she derives utility from consuming goods $ x $ and $ y $. The equal coefficients (4) for both $ x $ and $ y $ suggest that Joan views these goods as perfect substitutes. This means Joan is willing to replace one good with the other at a constant rate without any loss in utility.### b. Consumer Choice Graph**Scenario:** - Income: $120- Price of $ x $: $5- Price of $ y $: $4To draw Joan's indifference curve, one can start by calculating the budget constraint. The budget constraint equation is:\[ 5x + 4y = 120. \]Solving for $ y $ in terms of $ x $:\[ y = \frac{120 - 5x}{4}. \]**Steps to draw the graph:**1. **Draw the budget line:** - When $ x = 0 $, $ y = 30 $ (intercept on the y-axis). - When $ y = 0 $, $ x = 24 $ (intercept on the x-axis).2. **Plot the indifference curve:** - Because Joan's utility function represents perfect substitutes, the indifference curves are straight lines with a constant slope. - The slope of the indifference curve can be derived from the utility function $ U = 4x + 4y $. It suggests a 1:1 substitution rate, i.e., the slope is -1.3. **Graph the intersections and slopes:** - Draw the budget line using intercepts (30 on y-axis and 24 on x-axis). - Overlap the indifference curve to show all combinations of $ x $ and $ y $ providing the same utility.### c. Demand for $ x $ and Effects of Price Change**Scenario:** Prices of $ x $ falling successively to $4.01, then to $3.99, and finally to $3.**Steps to analyze:**1. **Calculate the new

Utility function : U = 4x + 4y Utility function describes the level of satisfaction derived by a…

Joan has the following utility function U = 4x + 4y. a. Describe her preferences for these two goods. b. Draw a consumer choice graph describing her indifference curve when income $120, the price of x is $5 and the price of y is $4. C. Draw the demand for x as the price falls to $4.01, and then to $3.99, and then $3. Describe or illustrate in a graph the income and substitution effects as the price of x falls.

Joan has the following utility function U = 4x + 4y. a. Describe her preferences for these two goods. b. Draw a consumer choice graph describing her indifference curve when income $120, the price of x is $5 and the price of y is $4. C. Draw the demand for x as the price falls to $4.01, and then to $3.99, and then $3. Describe or illustrate in a graph the income and substitution effects as the price of x falls.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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