Question

Identify the CORRECT relationship(s) between the average product of labour \((AP_L)\) and marginal product of labour \((MP_L)\) in the short-run.

• A. If \(MP_L > AP_L\), then \(\frac{dAP_L}{dL}>0\)
• B. If \(MP_L < AP_L\), then \(\frac{dAP_L}{dL}>0\)
• C. If \(MP_L > AP_L\), then \(\frac{dAP_L}{dL}<0\)
• D. If \(MP_L < AP_L\), then \(\frac{dAP_L}{dL}<0\)

Hint:

The relationship between marginal and average product is similar to marks in exams: if marginal exceeds average, average rises; if marginal is below average, average falls.

Answer 1

The Correct Option is A, D

Step 1: Write the two products.
Average product is $AP_L=\dfrac{Q}{L}$, and marginal product is $MP_L=\dfrac{dQ}{dL}$.

Step 2: Differentiate the average.
Using the quotient rule and $Q=L\cdot AP_L$,
\[ \frac{dAP_L}{dL}=\frac{MP_L-AP_L}{L} \]

Step 3: Read the sign.
Since $L>0$, the sign of the change in $AP_L$ follows the sign of $MP_L-AP_L$.

Step 4: Match the options.
If $MP_L>AP_L$ the average is rising, so $\dfrac{dAP_L}{dL}>0$. That makes option A correct. If $MP_L<AP_L$ the average is falling, so $\dfrac{dAP_L}{dL}<0$, which makes option D correct. The other two reverse these and are wrong.

Step 5: Conclude.
\[ \boxed{(A)\text{ and }(D)} \]