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: Recall definitions of Average Product and Marginal Product.
Average product of labour is
\[ AP_L=\frac{Q}{L} \] Marginal product of labour is
\[ MP_L=\frac{dQ}{dL} \]

Step 2: Find the derivative of average product.
Differentiate \(AP_L\) with respect to \(L\):
\[ \frac{dAP_L}{dL} = \frac{L\frac{dQ}{dL}-Q}{L^2} \] Substitute
\[ MP_L=\frac{dQ}{dL} \] and
\[ Q=L\cdot AP_L \] Then,
\[ \frac{dAP_L}{dL} = \frac{LMP_L-LAP_L}{L^2} \] \[ \frac{dAP_L}{dL} = \frac{MP_L-AP_L}{L} \]
Since \(L>0\), the sign of \(\frac{dAP_L}{dL}\) depends on
\[ MP_L-AP_L \]

Step 3: Analyze the cases.
If
\[ MP_L>AP_L, \] then
\[ \frac{dAP_L}{dL}>0 \] Thus, \(AP_L\) rises.
Therefore, option (A) is correct.
If
\[ MP_L<AP_L, \] then
\[ \frac{dAP_L}{dL}<0 \] Thus, \(AP_L\) falls.
Therefore, option (D) is correct.

Step 4: Check remaining options.
Option (B) is incorrect because when \(MP_L<AP_L\), average product decreases rather than increases.
Option (C) is incorrect because when \(MP_L>AP_L\), average product increases rather than decreases.

Step 5: Final conclusion.
Hence, the correct relationships are
\[ \boxed{(A)\text{ and }(D)} \]