Question

Two people, Aaron and Brenda, live next door to each other. Aaron enjoys playing loud music, but Brenda does not enjoy hearing Aaron's loud music. Let Aaron's utility for hours of music, h, and money, m be given by Waſh,m) = 24h - 2 + m. Let Brenda's utility be given by U,(h,m) = m -2h. Suppose that it is costless to play music, and that Aaron is able to choose h. How many hours of music will Aaron choose to play? 3b. How many hours of music maximize the sum of Aaron and Brenda's utilities. That is what is the Pareto Optimal number of hours of music? 3c. Suppose government has assigned Aaron the property right to produce loud music. Describe a bargaining solution between Aaron and Brenda that restores the Pareto Optimal number of hours of music you found in (3b).

Please answer with explanation

Answer 1

a UA = 24h - h²rm Up = m-2h. a) Now. QUA 24-2h=0 (ort) ah h * = 12 hours Ans. Aaron will Maximize his utility : 6.) Now Joint utility U= UATUB 2 u= 24 h h2 tm +m-ah u=22h - h²ram au 22-2h =o. h=11 hours property right to Aaron, to produce load music, Now Brenda will compensate Aaron , since Aaron will be playing for Do II hours, instead of his private optimal Number of houss = 12

a UA = 24h - h²rm Up = m-2h. a) Now. QUA 24-2h=0 (ort) ah h * = 12 hours Ans. Aaron will Maximize his utility : 6.) Now Joint utility U= UATUB 2 u= 24 h h2 tm +m-ah u=22h - h²ram au 22-2h =o. h=11 hours property right to Aaron, to produce load music, Now Brenda will compensate Aaron , since Aaron will be playing for Do II hours, instead of his private optimal Number of houss = 12

80. UA (h=12) = (24x12) - (( 2)2 +m - 144+m Page No : New UA Chall) = (24X11) - (11)² +m= 143tm 80 DUA=L. Now UB (h=12)=m-2812 = m-24 UB' (h=11) = m-axl1 = m-22. .80 DUB= m-22-m+ 24 = +2 80 with socially efficient 8011, utility of A falls by 1 & I utility of B rises by 2 80 of Brenda could compensate Aaron for loss un utility then optimal No. of hours of loud music could be restored. 80 Brenda 8 hould pay at least & 1$. to Aaron