Question

2. (-/2 Points] DETAILS HARMATHAP12 11.5.015. In this problem, p is the price per unit in dollars and is the number of units If the weekly demand function is p 52-9 and the supply function before taxation is p = 16 50, what tax per item will maximize the total revenue? $ Item Need Help? Watch Talk to a Tutor 3. [-/2 Points) DETAILS HARMATHAP12 11.5.019.MI. In this problem, p is the price per unit in dollars and is the number of units. If the weekly demand function is p = 200 - 292 and the supply function before taxation is p = 20 + 34, what tax per item will maximize the total tax revenue? $ item Need Help? Reed Talk to a Tutor

Answer 1

27 Given D: P a 52-q (Demand) Si P = 16+ 59 (supply) ta dax per unit Total Tax Revenue T = p = 16+59 +t At qui librium 52-9 - 16+ 58+t 52-q-16-59 st t = 36-69 Total Tax revenue. Ta ta T= (36-64) 9.

T= 369 - q2 7(a) = (369 - 692) It al T'(a) 36-129 T(") za O = 36-129 3 ho 2 36 qz 3 » T will maximum at ou= 3 t 36 -6(3) t = 36-18 t =$18 A Tax of & 18 per item will maximize the Total tax revenue.

30 Given P= 200 -RUL P= 20+ 39 ta unit tax per Revenue total Tax T = P= 20+ 3qtt At Equilibrium 200 2q² = 20+30 + t t = 200 - 29" - 20-39 ta 200 - 29"-20 - 39 ta -29~_3q + 180, Total Tax revenue TE ta E 29"- q + 180) a

-293_3q² + 1809 T'%)=0 E 29 3_ 39² + 1800 1) a la 20 - 69% -69 + 180 =0 -6(a arta - 3o) so qrt q - 30 zo -30 q?769-59-30 20 6 -5 q (9+6)-5(+6)=0 (-5) (9+6) -0 (91-5)20 or q +620 19=5 or 92-6). 7 will maximum at q=5 t(s) t = -297-39 + 180. -2(5)*- 365) +180 -2 (25) 15t 180 65+180 $115 ... A Tax total dax of $ 115 per item will maximize the revenue.