Question

1. The demand and supply functions for two commodities are given by: Qd1 = 410 - 5P1 - 2P2 Qs1 = -60 + 3P Qd2 = 295 – P1 - 3P2 Qs2 = -120 + 2P2 where P = price , Qd = price , Qd = quantity demanded and Qs = quantity supplied. Determine the equilibrium price and quantity for these two commodities. a. Pa = 30; P2 = 75; Q1 = 50; Q2 = 20 b. P1 = 30; P2 = 65; Q1 = 60; Q2 = 20 c. P1 = 40; P2 = 75; Q1 = 50; Q2 = 30 d. P1 = 40; P2 = 75; Q1 = 60; Q2 = 30

Answer 1

- 470 = 285 1. Sole for the equilibrium price and equiti- brium quantity for the 1st Commodity Qdi = QS. 410-5p1-2/2 =-60+3P, 410760 3P,+51, +2P2 8pital2 470 2 (411+P2) ..P2+4P1= 470 P2+4P,=235 Similarly for the second Commodity ada QS2 295-P1-3 P2 = -120+2P2 - Pi-3p2-2p2=-120-295 - - Pi-SP2 70-415 2) (P1+5P2) = +415 - = 11 s 512tP, = 415 -

Now, by solving eq. O, we have P2 +4P,=235 = P2 = 235-491 By putting the value of P2 in eq 5P2+P,=415 =) 5 (235_481) +1,2415 2) 1175-rop, tpi =415 >) -19P, = 415-1175 2) +19P, =+760 . Pi 760 =40 19 Now, putting the value of P, in P2 +421 = 2.35 2) P2 +4440=235 eq.0 2) P2 +160=235 2) P2 =235-160 - 75 ~ P2=

Now, we have Pi= 40 P2=75 - Qd1=410-5pi-2/2 ². Qs = 410-5x40-2x75 2) Qs = 410 - 200 -150 7 Q1 = 410-350 2) Q1 = Go > QS1=-60 +3pi =-60+ 3x40 E-60 +120 = 60 Hence adı = Qs1 = 60 equilibrium price is 40 and equilibrium quanlity is 60 for the Commodity est. a

Similarl erly e we have P1=40 P2= =75 → Qd2=295-P4-312 » Q2 = 295-40-3x75 2) Q2=295-40-225 2) Q2 = 295-265 ~ Q2=30 > QS2=-120+212 Q2=-120+2x75 2) Q2 = -120+150 =3e 2) A2= Hence, Qda = Q52=30 i equilibrium price = P2=75 and eautubx144 qualty-Ф-20

Now, P = 40 P2=75 Qi = 60 Q 2 30 Therefore option @ is the righ answer