InterviewSolution
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InterviewSolution
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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? |
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Answer» (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. |
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