Question

Demand for apartments in a certain town is D(x) = 1460 - 3x, and the supply is S(x) = 500 + 9x, where x is the number of apartments, in hundreds, and D(x) and S(x) are the rent in dollars per month, per apartment a) Find the equilibrium point. b) Find the consumer surplus and producer surplus. c) Suppose a maximum rent of $716 per month is imposed by the town council. Find the point (*c. PC) d) Find the new consumer surplus and new producer surplus e) Find the deadweight loss.

Answer 1

7 Demand Dix) = 1460-34 Supply Sw= 500 +93 ca) Equiliboium point! Cequate Demand = Supply). 1460 - 3* = 500+95 960 12x = 1460-500 960 180 12 2 = 80; equilibrium point CBO, 1220) = (te, PC) 62 Consumer Sup plus - Cs. = 19 S 2000 - feln S (1460 - 32 -p220) dx = soo 80 Esgo ( 240-3x) dx 80 240(X) 36180 240 (80)-3 809) ros = 9600 de Scce)) dax See (Pet PS- NO Pelodecars surplus a Bo ps = 6 ( 1220-(500 +9x) dx = S80 (720-9a) de 72062780 - 96472180 = 720(80) - kost ( 803)- PS = 18,800 CS Scanned with CamScanner

Maximum rent of 716 per month is imposed by the the town Council point (Pc, Pc) Sca=716 716 = 500 + 92. 9x=716-500 216 x = 216 ma 24 16:24 (ac, Pc) = (24, 716) Consumers Susplay.- (Cs) a Xc Sa CD (2) -pe) da 24 24 ((146 460-3x) — 7267) de S (744 - 3x) dx 24 = yuu (a) (1), 3(71)29 744 ( 24) -1,5 (242) ics 16,992 PS a 24 See ( 716 – SCx) dx = s 24 (416-500-9x) die 216 - 92 ) -ax) dx 216 (0)24 9672229 = 216 (24) - 405 (24*24) PS = 2,592 CS Scanned with CamScanner

* Dead weight Loss D.wike (P-P) Co-Q1) P2 =D (QI) = D. (24) 1460 - 3(24) = 1388 Pie SCQ,) s (24) 500+ 9 (24) = 716 Po = the = Donnafon) 80. ) Q. xc= 144 B-N.L= 12 (1388 - 716) (80-14) T D.W.L 22176 CS Scanned with CamScanner