Examkin

Question

Difficulty: MediumMarket Equilibrium Price and Quantity

A competitive market for yam tubers consists of 40 identical buyers and 10 identical sellers. The demand function for each individual buyer is given by qd=15−0.5Pq_d = 15 - 0.5P, and the supply function for each individual seller is given by qs=−4+2Pq_s = -4 + 2P, where PP represents the price per tuber in Naira (N\text{N}). What is the market equilibrium quantity of yam tubers (in units)?

Answer: 280 units

Answer

The market equilibrium quantity is 280 units.
To find the market equilibrium quantity, first aggregate individual demand and supply: total market demand is Qd=40(15−0.5P)=600−20PQ_d = 40(15 - 0.5P) = 600 - 20P and total market supply is Qs=10(−4+2P)=−40+20PQ_s = 10(-4 + 2P) = -40 + 20P. Equating Qd=QsQ_d = Q_s gives 600−20P=−40+20P600 - 20P = -40 + 20P, which simplifies to 640=40P640 = 40P and yields an equilibrium price P∗=16P^* = 16. Substituting P∗=16P^* = 16 into the market demand equation yields Q∗=600−20(16)=280Q^* = 600 - 20(16) = 280 units.

Step-by-Step Solution

1
Calculate market demand function (QdQ_d)
Qd=40×(15−0.5P)=600−20PQ_d = 40 \times (15 - 0.5P) = 600 - 20P
Market demand is obtained by multiplying the individual demand function by the total number of buyers.
2
Calculate market supply function (QsQ_s)
Qs=10×(−4+2P)=−40+20PQ_s = 10 \times (-4 + 2P) = -40 + 20P
Market supply is obtained by multiplying the individual supply function by the total number of sellers.
3
Set market demand equal to market supply to solve for equilibrium price (P∗P^*)
600−20P=−40+20P  ⟹  640=40P  ⟹  P∗=16600 - 20P = -40 + 20P \implies 640 = 40P \implies P^* = 16
Market equilibrium occurs at the price level where quantity demanded equals quantity supplied.
4
Substitute equilibrium price into the market demand function to find equilibrium quantity (Q∗Q^*)
Q∗=600−20(16)=280Q^* = 600 - 20(16) = 280 units
Evaluating market demand at the equilibrium price determines the total equilibrium quantity traded.

Key Concept

Market Equilibrium Price and Quantity via Aggregated Demand and Supply Functions
Rate this question

Topics

Market Equilibrium Price and Quantity

More questions from this topic