Question

Find the equilibrium price and quantity for the following related market for two goods.

(a)Qd1=840−5P1−2P2

Qs1=−60+3P1.

and

Qd2=300−P1

−3P2Qs2=−100+3P2.

(b)Qd1=2−3P1+P2

Qs1=−50+15P1.

and

Qd2=220+5P1−4P2

Qs2=−120+32P2.

Answer 1

In general market equilbrium, Quantity demanded equals quantity supplied in each market, and prices equalize in overall (aggregate) economy.

(a)

In market 1, Qd1 = Qs1.

840 - 5P1 - 2P2 = - 60 + 3P1

8P1 + 2P2 = 900

4P1 + P2 = 450 [Dividing both sides by 2]...........(1)

In market 2, Qd2 = Qs.

300 - P1 - 3P2 = - 100 + 3P2

P1 + 6P2 = 400..................................(2)

Multiplying equation (2) by 4,

4P1 + 24P2 = 1600............................(3)

(3) - (1) gives us:

23P2 = 1150

P2 = 50

P1 = 400 - 6P2 [From equation (2)] = 400 - (6 x 50) = 400 - 300 = 100

Q1 = - 60 + (3 x 100) = - 60 + 300 = 240

Q2 = - 100 + (3 x 50) = - 100 + 150 = 50

(b)

In market 1, Qd1 = Qs1.

2 - 3P1 + P2 = - 50 + 15P1

18P1 - P2 = 52.................(1)

In market 2, Qd2 = Qs2.

220 + 5P1 - 4P2 = - 120 + 32P2

- 5P1 + 36P2 = 340..........(2)

Multiplying equation (1) by 36,

648P1 - 36P2 = 1872.......(3)

- 5P1 + 36P2 = 340..........(2)

(2) + (3) gives us: 643P1 = 2212

P1 = 3.44

P2 = 18P1 - 52 [From (1)] = (18 x 3.44) - 52 = 61.92 - 52 = 9.92

Q1 = - 50 + (15 x 3.44) = - 50 + 51.6 = 1.6

Q2 = - 120 + (32 x 9.92) = - 120 + 317.44 = 197.44