A firm facing a downward-sloping demand curve sells 12 units of an item at a price of \tex… — JAMB UTME

A firm facing a downward-sloping demand curve sells $12$ units of an item at a price of $\text{₦}75$ per unit. In order to sell $13$ units, it must lower the price of all units to $\text{₦}71$ . Calculate the Marginal Revenue of the $13\text{th}$ unit in Naira ( $\text{₦}$ ).

Answer: 23 ₦

Answer

The Marginal Revenue of the 13th unit is ₦23.

Marginal Revenue (MR) measures the change in Total Revenue (TR) when output increases by one unit. Selling 12 units at ₦75 gives TR₁ = ₦900. Selling 13 units at ₦71 gives TR₂ = ₦923. The difference, ₦923 - ₦900 = ₦23, is the additional revenue generated by the 13th unit.

Step-by-Step Solution

Calculate the initial Total Revenue (TR₁) before expanding output

TR₁ = 12 units × ₦75 = ₦900

Total Revenue is calculated as Price multiplied by Quantity (TR = P × Q).

Calculate the new Total Revenue (TR₂) after expanding output to 13 units

TR₂ = 13 units × ₦71 = ₦923

When output increases to 13 units, the lower price of ₦71 applies to all units sold.

Determine the Marginal Revenue (MR) of the 13th unit

MR = TR₂ - TR₁ = ₦923 - ₦900 = ₦23

Marginal Revenue is the change in Total Revenue resulting from selling one additional unit of output (MR = ΔTR / ΔQ).

Key Concept

Marginal Revenue and Total Revenue Relationship in Imperfect Competition

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