The are 10,000 identical individual buyers in the market for commodity X, each with a demand fucntion given by Qdx=12-2Px and 1,000 indentical producers of commodity X, each with a supply function given by Qsx=20Px.
(i) Find the market demand function and the market supply function for commodity X.
(ii) Obtain the equilibrium price and equilibrium quantity.
(iii) Suppose the government decides to collect a tax of rupee 2 per unit sold from each of the 1,000 sellers of commodity X. What effect will this have on the equilibrium price and quantity of commodity X?

Explanation

(i) Market Demand function: `Q_("Mdx")=10,000(12-2P_("x"))=1,20,000" "P_("x")`
Market Supply function: `Q_("Msx")=1,000 (20 P_("x"))=20,000P_("x")`
(ii) At equilibrium, `O_("Mdx")=Q_("Msx")`
It means, `1,20,000-20,000 P_("x")=20,000P_("x")`
or, `P_(x)= rupee 3`.
Putting the value of equilibrium price `(P_("x"))` in the market demand function, we get:
`Q_("Mdx")=1,20,000-20,000 xx 3=60,000` units.
Equilibrium Price= rupee 3, Equilibrium Quantity= 60,000 units.
(iii) When tax of rupee 2 per unit is imposed and collected from each of the 1,000 sellers of commodity x, then the new equilibrium price becomes: `P_("x")-2`.
New Market Supply function: `Q_("Msx")=20,000(P_("x")-2)=20,000P_("x")-40,000`
For equilibrium, `Q_("Mdx")=Q_("Msx")`
It means, `1,20,000-20,000 P_("x")=20,000P_("x")-40,000`
or, `P_("x")`= rupee 4
Putting the value of equilibrium price `(P_("x"))` in the market demand function we get:
`Q_("Mdx")=1,20,000-20,000xx4=40,000` units.
New Equilibrium Price= rupee 4, New Equilibrium Quantity= 40,000 units.
Thus, the equilibrium price increases and equilibrium quantity falls due to tax of rupee 2 per unit.