Question

Suppose that there are 250 identical individual consumers in the market for commodity X, each with a demand function given by d_x = 6-P_x and 50 identical producers of commodity X, each with a supply function given by s_x =5P_x. (8 Marks)

a)     Derive the market demand function and the market supply function for commodity X.

b)     Compute the market equilibrium price and equilibrium quantity mathematically.

c)     Tabulate the market demand schedule and the market supply schedule for commodity X.

d)    show whether surplus or shortage occurs at 

i)                   P = 2

ii)                 P = 5

Answer 1

a.

$Q_d=(6-P_x)250\\=1500-250P_x$

$Q_s=(5P_x)50\\=250P_x$

b.

$Q_d=Q_s\\1500-250P_x=250P_x\\1500=500P_x\\P_x=\frac{1500}{500}\\P_x=3$

$Q_d=1500-250(3)=750\\Q_s=250(3)=750$

equilibrium quantity is 750

equilibrium price is 3

c.

d.

At P=2

There is shortage since the quantity demanded exceeds the quantity supplied.

$QS=500\\ Qd=100\\ deficit=500-1000\\ =-500$

At P=5

There is surplus because the quantity supplied exceeds the quantity demanded

$Qd=250\\Qs=1250\\surplus=1250-250\\=1000$