Question

Problem1

1. There are 10,000 identical individuals in the market for commodity “X”, each with a demand function given by

     Qdx = 12 – 2Px ,   and 1000 identical producers of commodity “X”, each with a function given by Qsx = 20Px

Problem5:

•Suppose that from the condition of equilibrium in problem #1, there is an increase in consumers’ incomes so that the market demand curve becomes

           QD”x = 140,000 – 20,000Px ,

   and at the same time there is an improvement in technology of producing commodity “X” so that the new market

•supply curve becomes

           QS”x = 40,000 + 20,000Px .

Everything else remains the same.

1.Show the new market demand curve   D”x , and the new market supply curve S”x.

2.What are the new equilibrium price and equilibrium quantity for commodity “X”?

Answer 1

(1)

Since there are 10,000 buyers,

Market demand (QDM) = 10,000 x QDx = 10,000 x (140,000 - 20,000Px)

When QDM = 0, Px = 140,000/20,000 = 7 (vertical intercept)

When Px = 0, QDM = 10,000 x 140,000 = 1,400 million (horizontal intercept)

Since there are 1,000 buyers,

Market supply (QSM) = 1,000 x QSx = 1,000 x (40,000 + 20,000Px)

When QSM = 0, Px = - 40,000/20,000 = - 2 (vertical intercept)

When Px = 0, QSM = 1,000 x 40,000 = 40 million (horizontal intercept)

(b)

In equilibrium, QDM = QSM.

10,000 x (140,000 - 20,000Px) = 1,000 x (40,000 + 20,000Px)

10 x (140,000 - 20,000Px) = (40,000 + 20,000Px)

1,400,000 - 200,000Px = 40,000 + 20,000Px

220,000Px = 1,360,000

Px = 6.18

Q = 1,000 x (40,000 + 20,000 x 6.18) = 1,000 x (40,000 + 123,600) = 1,000 x 163,600 = 163,600,000 = 163.6 million