Question

5. (22 pts) Consider the three-commodity market model given by: Qi = 16 – 2p1 + 2p2 + P3 and Qi = 2p1 – 7 Q2 = 8+2p1 – P2 – P3 and Q2 = 4p2 – 4 Q% = 4+421 – P2 – 4p3 and Qs = 2p3 – 3 where Q4, Q and pi denote quantity demanded, quantity supplied and price of good i = 1, 2, 3, respectively. (a) What is the relationship among the three goods? Are the goods substitutes or comple- ments? Give a reason for your answer. (6 pts) (b) Write the equilibrium conditions for the model. (6 pts) (c) Use the substitution and elimination methods to find the equilibrium prices and quan- tities for the three goods. (10 pts)

Answer 1

51 : 16- 2f1 + 2f2 + P3 8° = 2P, - 7 %3D 8+2f, - (2 -P3 9 = %3D 4P2 -4 . 4 + 4P,- Pz -4P3 23 - 3 Relation betwen geed 1 & good 2 Fasom 8," Equation 8,4 So as a P2 ue lan see that is faritively related to ie- jsice j dewanded god jie. sises thee guanditey * good 1 ie- Se, Rises Home, beth goeds are substitute f ene amother Aelation betrmeen good I and goord 8 d Guation me ble that fa ie

Pocitively selated auith lathindy de, one anothes as' f, rises 8 also sises Hemre, lgeod. 1 and Good 3 are substitales, Relation betrueen good 2 and good 3 Faom eguation 8, me see that ils negatively selated to Po Po sises them d Hene as falla o Honce, Good 2 and Gpod 3 Aomflmente. are lonelude Good 1 and Good 2 bubetitules are -> and Good 3 dubstitulis Good I oru -> Ond Good 3 2. -> Good lomplemente are 6) Equilibrium Conditione and B3 = 9% 8o, 16 - 20, + 2f2 + P3 = 28, 2P, -7 .

2p, +2f, - 2f% -P3 16 + 7 こ 4P, -28p - P3 = 23 For こ 8 + 28, - 2 - P3 = 4P2 - 4 8+4 = 4p2 -28, +P2 + P3 こ 5P2 -281 + = 12 92 fog 4 + 46, - (2 - 4P3 2Ps - 3 こ 283 - 4P, + Pz t 4P3 4+3 -4p, + P2 +6P3 こ 222 get 3 Equilibrium :- abone me frem 23 i) 4P. - 212 - P3 こ

"B) - 28, + 5 Pz + P3 w) - 4P, + Pz こ 12、 6/3 ) finding tpuilibrium faices and guantities- Ueing the aboue 3 Conditions by O and O 4P, - 2f2 - - 2P, + 5P, HPa = B12 23 2P1 + 3 Pe 35 by using O and ( (-28, + 5P2 + P3 (-4P1 + P2 + 6P3 = 12) x 6 + ) x %3D - 12P, + 30P2 tbP - 72 + 4Pi |- 8Pi + 292 65 こ

From ® & (b) 35 ) x 4 + 3/% - 8P, + 29P2 65 Hi + 122 - K + 29P2 140 こ 65 こ 41P2 205 こ 205 こ 41 2o, こ 5 28, + 3P2 - 35 >» 2P, +(3x 5) 35 35 - 15 20 2P1 ニ 20 = 10 %3D

f - 10 and :5 In Peguation 1 Gqulbriun cenditien - 4P, -2pz - P3 = 23 ) (4x10) - (2x5) - 23 40 - 10 P3 23 P3 = 30 - 23 ond fs -7 Puthing h -10 i Pr = 5 5 Po =10 ; Pz = * : 28, -7 (2x10) 13 4P2 -4 (4и5) - 4 16 it

->83: 23 - 3 =(2x7) - 3 11 こ As under equilibricum So, 8, = 8,° 13 こ 82 = 8,' - 16 こ 11 こ So finally we couilude undes Equilibrium . P, = 10 81 = l2 = 16 82 P3 1)