Marginal Cost and Marginal Revenue

Differentiation's most direct use in commerce is measuring how cost and revenue change as the level of output changes — a topic that is a recurring feature of Gujarat board class 12 commerce statistics question papers.

Marginal Cost (MC)

If $TC(Q)$ is the Total Cost of producing $Q$ units, the Marginal Cost is the rate of change of total cost with respect to output — approximately, the extra cost of producing one more unit:

Example: if $TC = Q^2 + 8Q + 40$ (₹), then $MC = \dfrac{d(TC)}{dQ} = 2Q + 8$. At $Q = 10$: $MC = 2(10)+8 = 28$, meaning the 11th unit costs approximately ₹28 more to produce than the 10th.

Marginal Revenue (MR)

If $TR(Q)$ is the Total Revenue from selling $Q$ units, the Marginal Revenue is the rate of change of total revenue with respect to output:

Total Revenue is generally $TR = P \times Q$, where $P$ is price. If the (linear) demand function is $P = a - bQ$, then:

Notice that $MR$ falls twice as fast as $P$ as $Q$ rises (the coefficient of $Q$ doubles from $-b$ in the demand function to $-2b$ in $MR$) — a standard result worth remembering directly for GSEB Std 12 Statistics exam questions on marginal revenue from a linear demand function.

Relating Marginal and Average Values …