Question:
When MPP (Marginal Physical Product) cuts APP (Average Physical Product) at its highest point then:
When MPP (Marginal Physical Product) cuts APP (Average Physical Product) at its highest point then:
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MPP = APP at APP’s peak; MPP drives APP’s rise or fall.
Updated On: Jul 2, 2026
- MPP \(>\) APP
- MPP \(<\) APP
- MPP \(=\) APP
- MPP is also at its highest level
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The Correct Option is C
Approach Solution - 1
In production theory, Marginal Physical Product (MPP) is the additional output from one more unit of input, and Average Physical Product (APP) is the total output per unit of input. Their relationship follows:
- When MPP $>$ APP, APP is increasing, as each additional input adds more to output than the average.
- When MPP $<$ APP, APP is decreasing, as additional inputs contribute less than the average.
- When MPP = APP, APP is at its maximum, as the marginal contribution equals the average, marking the peak of the APP curve.
Thus, when MPP intersects APP at APP’s highest point, MPP = APP, making option (3) correct.
- Option (1) is incorrect (MPP $>$ APP implies APP is still rising).
- Option (2) is incorrect (MPP $<$ APP implies APP is falling).
- Option (4) is incorrect (MPP peaks before APP, typically when MPP starts declining).
- When MPP $>$ APP, APP is increasing, as each additional input adds more to output than the average.
- When MPP $<$ APP, APP is decreasing, as additional inputs contribute less than the average.
- When MPP = APP, APP is at its maximum, as the marginal contribution equals the average, marking the peak of the APP curve.
Thus, when MPP intersects APP at APP’s highest point, MPP = APP, making option (3) correct.
- Option (1) is incorrect (MPP $>$ APP implies APP is still rising).
- Option (2) is incorrect (MPP $<$ APP implies APP is falling).
- Option (4) is incorrect (MPP peaks before APP, typically when MPP starts declining).
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Approach Solution -2
Calculus derivation:
Let \( TP(L) \) be total product as a function of labour \( L \). Then \( APP = \frac{TP}{L} \) and \( MPP = \frac{d(TP)}{dL} \). APP is maximised where its slope is zero, that is \( \frac{d(APP)}{dL} = 0 \). Differentiating the quotient gives \[ \frac{d(APP)}{dL} = \frac{L \cdot MPP - TP}{L^{2}} = 0 \implies L \cdot MPP = TP \implies MPP = \frac{TP}{L} = APP. \] Thus at the peak of the APP curve, MPP exactly equals APP, confirming option 3.
Let \( TP(L) \) be total product as a function of labour \( L \). Then \( APP = \frac{TP}{L} \) and \( MPP = \frac{d(TP)}{dL} \). APP is maximised where its slope is zero, that is \( \frac{d(APP)}{dL} = 0 \). Differentiating the quotient gives \[ \frac{d(APP)}{dL} = \frac{L \cdot MPP - TP}{L^{2}} = 0 \implies L \cdot MPP = TP \implies MPP = \frac{TP}{L} = APP. \] Thus at the peak of the APP curve, MPP exactly equals APP, confirming option 3.
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