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Question 4: Rose's preferences over food (x) and tobacco (y) are given by U=f(x)+by. The prices and income are Px-2, Py=4 and m=20. Tobacco

Question 4: Rose's preferences over food (x) and tobacco (y) are given by U=f(x)+by. The prices and income are Px-2, Py=4 and m=20. Tobacco

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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### Question 4: Understanding Budget Constraints and Preferences #### Context Rose's preferences over food (x) and tobacco (y) are described by the utility function \( U=f(x)+by \). Here, the prices of the goods are given as \( P_x=2 \) for food and \( P_y=4 \) for tobacco, with her income \( m=20 \). #### Graph Explanation The graph shows: - **Axes:** The horizontal axis represents the quantity of Food, and the vertical axis represents the quantity of Tobacco. - **Budget Line:** This is a straight line that depicts all combinations of Food and Tobacco that Rose can buy with her entire income. The slope of the budget line is determined by the relative prices of the two goods. - **Indifference Curve:** This curve shows combinations of Food and Tobacco that give Rose the same level of satisfaction. The point where the indifference curve is tangent to the budget line indicates the optimal consumption bundle. #### Questions and Instructions a. **Consumption Levels** - Rose consumes ______ food and ______ tobacco. b. **Budget Line with Assistance** - Draw her new budget line considering she receives a $4 food voucher, effectively increasing her budget for food. c. **Consumption with Assistance** - Determine her consumption of each good after receiving the assistance. Explain your reasoning based on the new budget line. d. **Evaluation of Claim** - Comment on Rose’s claim that she would like to buy more food but cannot afford it, considering her utility and budget line. e. **Policy Consideration** - Assuming all households have the same preferences as Rose, determine the income threshold for food assistance eligibility and justify your answer. This exercise demonstrates the impact of budget constraints on consumer choice, highlighting how external assistance can alter consumption patterns.
Transcribed Image Text:### Question 4: Understanding Budget Constraints and Preferences #### Context Rose's preferences over food (x) and tobacco (y) are described by the utility function \( U=f(x)+by \). Here, the prices of the goods are given as \( P_x=2 \) for food and \( P_y=4 \) for tobacco, with her income \( m=20 \). #### Graph Explanation The graph shows: - **Axes:** The horizontal axis represents the quantity of Food, and the vertical axis represents the quantity of Tobacco. - **Budget Line:** This is a straight line that depicts all combinations of Food and Tobacco that Rose can buy with her entire income. The slope of the budget line is determined by the relative prices of the two goods. - **Indifference Curve:** This curve shows combinations of Food and Tobacco that give Rose the same level of satisfaction. The point where the indifference curve is tangent to the budget line indicates the optimal consumption bundle. #### Questions and Instructions a. **Consumption Levels** - Rose consumes ______ food and ______ tobacco. b. **Budget Line with Assistance** - Draw her new budget line considering she receives a $4 food voucher, effectively increasing her budget for food. c. **Consumption with Assistance** - Determine her consumption of each good after receiving the assistance. Explain your reasoning based on the new budget line. d. **Evaluation of Claim** - Comment on Rose’s claim that she would like to buy more food but cannot afford it, considering her utility and budget line. e. **Policy Consideration** - Assuming all households have the same preferences as Rose, determine the income threshold for food assistance eligibility and justify your answer. This exercise demonstrates the impact of budget constraints on consumer choice, highlighting how external assistance can alter consumption patterns.
Expert Solution
Step 1

Given information

U=f(X)+bY

Price of X (Px)=2

Price of Y (Py)=4

M=20

Given graph

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