Question

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 .a.Find the market demand function and the market supply function for commodity X. b.Find the market demand schedule and the market supply schedule of commodity X and from them find the equilibrium price and the equilibrium quantity. c.Plot, on one set of axes, the market demand curve and the market supply curve for commodity X and show the equilibrium point. d.Obtain the equilibrium price and the equilibrium quantity mathematically, assume Px 6 5 4 3 2 1 0

Answer 1

Demand And Supply

a. Since, no. of consumers=10000

and individual demand function QDx=12-2Px

therefore, market demand function:

MQDx= nQDx

=10000*(12-2Px)

=120000-20000Px(eq.1)

In the same way, no. of producers= 1000

and individual supply function QSx=20Px

therefore, market supply function:

MQSx=nQSx

=1000*20Px

=20000Px (Eq. 2)

b. In equilibrium,

MQDx=MQSx

120000-20000Px=20000Px

solving the equation we get,

Px=$3

Putting it into eq.2,

MQSx=20000*3

=60000 units

Therefore, our equilibrium price=$3 and equilibrium quantity= 60000 units.

c. shown in the diagram attached.

d. Px($)      MQSx(units)      MQDx(units)

    6            120000              0

    5             100000          20000

    4              80000          40000

    3               60000         60000

    2              40000          80000

     1               20000         100000

    0                  0                120000

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