The market demand and supply equations for fertilizer in an agricultural district are give… — JAMB UTME

The market demand and supply equations for fertilizer in an agricultural district are given by $Q_d = 1,800 - 40P$ and $Q_s = 200 + 40P$ , where $P$ is the price per bag in Naira ( $\text{N}$ ) and $Q$ is the quantity in bags. The government introduces a price ceiling of $\text{N} 12$ per bag to lower farming input costs. By how many bags does the quantity of fertilizer actually traded in the market decrease as a result of this price control policy?

Answer: 320 bags

Answer

The quantity of fertilizer actually traded in the market decreases by 320 bags.

Prior to government regulation, free market equilibrium is established where quantity demanded equals quantity supplied (

1,800 - 40P = 200 + 40P

), yielding an equilibrium price of

20

Naira and an equilibrium volume of

1,000

bags. When a maximum price ceiling of

12

Naira is imposed, quantity demanded expands to

1,320

bags while quantity supplied shrinks to

680

bags. Because trade is voluntary, the quantity exchanged is constrained by the short side of the market (quantity supplied =

680

bags). Comparing this volume to the initial equilibrium (

1,000 - 680

), the actual quantity of fertilizer traded decreases by

320

bags.

Step-by-Step Solution

Determine the initial free-market equilibrium price and quantity

P_e = 20

Naira and

Q_e = 1,000

bags

Equilibrium occurs where quantity demanded equals quantity supplied (

Q_d = Q_s

Calculate quantity demanded and quantity supplied at the price ceiling of

P = 12

Q_d = 1,320

bags and

Q_s = 680

bags

Lowering the price below equilibrium increases buyer demand but disincentivizes supplier production.

Determine actual traded quantity using the short-side principle and calculate the volume change

Actual quantity traded

= 680

bags; Reduction

= 1,000 - 680 = 320

bags

In a market economy, trade requires voluntary exchange; buyers cannot purchase more than suppliers offer at the regulated price ceiling.

Key Concept

Short-Side Rule and Contraction of Market Traded Volume under Price Ceilings

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