In a regional commodity market, the monthly demand function for cocoa beans is given by Q_… — JAMB UTME

In a regional commodity market, the monthly demand function for cocoa beans is given by $Q_d = 250 - 4P$ and the supply function is given by $Q_s = -50 + 6P$ , where $P$ represents the price per bag in thousands of Naira (₦), $Q_d$ is the quantity demanded in bags, and $Q_s$ is the quantity supplied in bags. What is the equilibrium quantity of cocoa beans traded in this market?

Answer: 130 bags

Answer

The equilibrium quantity of cocoa beans is 130 bags.

Market equilibrium occurs at the price where quantity demanded equals quantity supplied (

Q_d = Q_s

). Setting

250 - 4P = -50 + 6P

yields

10P = 300

, so the equilibrium price

P^* = 30

. Substituting

P^* = 30

into the demand function gives

Q^* = 250 - 4(30) = 130

bags.

Step-by-Step Solution

Equate the demand function and supply function

250 - 4P = -50 + 6P

Market equilibrium occurs at the price level where quantity demanded equals quantity supplied.

Solve for equilibrium price (

P^*

)

P^* = 30

Rearranging

300 = 10P

yields the equilibrium price of ₦30 thousand per bag.

Calculate equilibrium quantity (

Q^*

)

Q^* = 130

Substituting

P = 30

into

Q_d = 250 - 4(30)

gives 130 bags.

Key Concept

Market Equilibrium Price and Quantity

Question

Answer

Step-by-Step Solution

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