Joe and Martin, two roommates, have access to music in digital and analog formats. Each are initially endowed with 8 GB of high-resolution digital music and 4 vinyl LP's (analog) per month (there are a total of 16 GB's of music in digital and 8LP's in this case). Joe's preferences for music in digital and analog formats are represented by the utility function up(D, A) = 2D + 2A, where D is the amount of digital music in GB's and A is the numberofLP's. Martin's utility function is um(D,A)=D+4A. 1. If Joe convinces Martin to exchange music at terms which would leave Martin at his initial utility level (i.e., without making him worse-off), what is the set of (D, A) that would make Joe better off. Show this on the Edgeworth box that you drew in part (a). What is the final allocation of music under these terms? What is the exchange rate (LP's per GB of digital music)? 2. On the Edgeworth box, show the set of exchange possibilities for Joe and Martin which would make at least one of them better-off without making the other worse- off. Based on your response, show the contract curve on the Edgeworth box. What is the range of exchange rate?

Joe and Martin, two roommates, have access to music in digital and analog formats. Each are initially endowed with 8 GB of high-resolution digital music and 4 vinyl LP's (analog) per month (there are a total of 16 GB's of music in digital and 8LP's in this case). Joe's preferences for music in digital and analog formats are represented by the utility function up(D, A) = 2D + 2A, where D is the amount of digital music in GB's and A is the numberofLP's. Martin's utility function is um(D,A)=D+4A. 1. If Joe convinces Martin to exchange music at terms which would leave Martin at his initial utility level (i.e., without making him worse-off), what is the set of (D, A) that would make Joe better off. Show this on the Edgeworth box that you drew in part (a). What is the final allocation of music under these terms? What is the exchange rate (LP's per GB of digital music)? 2. On the Edgeworth box, show the set of exchange possibilities for Joe and Martin which would make at least one of them better-off without making the other worse- off. Based on your response, show the contract curve on the Edgeworth box. What is the range of exchange rate?

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter10: Consumer Choice Theory

Section: Chapter Questions

Problem 1P

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Joe and Martin, two roommates, have access to music in digital and analog formats. Each are initially endowed with 8 GB of high-resolution digital music and 4 vinyl LP's (analog) per month (there are a total of 16 GB's of music in digital and 8LP's in this case). Joe's preferences for music in digital and analog formats are represented by the utility function u, (D, A) = 2D + 2A, where D is the amount of digital music in GB's and A is the numberofLP's. Martin's utility function is um(D,A)=D+4A. 1. Draw an Edgeworth box to show the initial endowments and the indifference curves (going through the initial endowments) for Joe and Martin. What are their utility levels from the initial endowments? 2. Calculate the marginal rates of substitution for Joe and Martin. Provide an economic interpretation. 3. Do the initial endowments represent a Pareto efficient allocation? Discuss. 4. If Joe convinces Martin to exchange music at terms which would leave Martin at his initial utility level (i.e.,…
I am unsure the direction the utility functions would go in , with this specific scenario
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