Q.Explain the law of variable proportion.

Showing the 12 most recent of 16 on this concept.

1. CA Foundation 2026Set jan-20261 markMCQ
   Q.Which of the following is not true with regard to stage of diminishing returns? (A) Total product continues to decrease (B) Both marginal product and average product of the variable factor are diminishing but are positive (C) A rational producer will seek to produce within the range of this stage (D) By the end of this stage, total product reaches its maximum

   ›Reveal solutionSolution

   During diminishing returns (Stage II) total product still increases at a diminishing rate; it does not decrease, so statement (A) is not true.

   The three stages of the Law of Variable Proportions

   • Stage I (increasing returns): MP rises then AP rises; TP increases at an increasing rate.
   • Stage II (diminishing returns): both MP and AP are falling but remain positive; TP continues to increase but at a diminishing rate, and by the end of this stage TP reaches its maximum (where MP = 0). A rational producer operates in this stage.
   • Stage III (negative returns): MP becomes negative and TP actually falls.

   Applying it

   • (B), (C) and (D) are all correct features of Stage II.
   • (A) — 'Total product continues to decrease' — describes Stage III, not the diminishing-returns stage, and is therefore the untrue statement. …

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2. CA Foundation 2026Set may-20261 markMCQ
   Q.The three stages of the law of variable proportion can be referred to as the stages of __________. (A) Increasing returns, optimum returns & nil returns (B) Positive returns, diminishing returns & nil returns (C) Increasing returns, diminishing returns & negative returns (D) Negative returns, nil returns & positive returns

   ›Reveal solutionSolution

   The three stages of the law of variable proportions are increasing returns, diminishing returns and negative returns.

   Step 1 — The law

   As successive units of a variable input are added to fixed inputs, the marginal product first rises, then falls, and finally becomes negative. This gives three stages:

   Step 2 — The three stages

   1. Stage I — Increasing returns: total product increases at an increasing rate; marginal product rises.
   2. Stage II — Diminishing returns: total product increases at a decreasing rate; marginal product falls but stays positive. (A rational producer operates here.)
   3. Stage III — Negative returns: additional input reduces total product; marginal product becomes negative.

   Step 3 — Why the other options are wrong …

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3. CA Foundation 2025Set jan-20251 markMCQ
   Q.What will be the average product when quantity of labour is 6 ? (A) 9 (B) 10 (C) 11 (D) 12

   ›Reveal solutionSolution

   Reconstruct the schedule: at L = 6, TP = 60, so AP = 60/6 = 10.

   Step 1 — Rules linking TP, AP and MP

   $AP = \frac{TP}{L}, \qquad MP_n = TP_n - TP_{n-1}$

   Step 2 — Fill the product schedule step by step

   Starting from the given entries (TP₁ = 10, MP₂ = 11, AP₃ = 11, MP₄ = 11, TP₅ = 52, MP₆ = 8):

   Labour (L)	Total Product (TP)	Average Product (AP)	Marginal Product (MP)
   1	10	10	–
   2	21	10.5	11
   3	33	11	12
   4	44	11	11
   5	52	10.4	8
   6	60	10	8

   • TP₂ = 10 + 11 = 21; TP₃ = AP₃ × 3 = 33; TP₄ = 33 + 11 = 44; TP₅ = 52 (given); TP₆ = 52 + 8 = 60.

   Step 3 — Read off AP at L = 6

   $AP_6 = \frac{TP_6}{6} = \frac{60}{6} = 10$ …

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4. CA Foundation 2025Set jan-20251 markMCQ
   Q.What will be the total product when quantity of labour is 4 ? (A) 38 (B) 40 (C) 42 (D) 44

   ›Reveal solutionSolution

   Cumulate the schedule: TP₄ = TP₃ (33) + MP₄ (11) = 44.

   Step 1 — Relationship used

   $TP_n = TP_{n-1} + MP_n, \qquad AP = \frac{TP}{L}$

   Step 2 — Reconstruct up to L = 4

   Labour (L)	Total Product (TP)	How obtained
   1	10	given
   2	21	10 + MP₂(11)
   3	33	AP₃(11) × 3
   4	44	33 + MP₄(11)

   Step 3 — State the answer

   $TP_4 = 33 + 11 = 44$

   We can cross-check: AP₄ = 44/4 = 11, consistent with the schedule's pattern. …

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5. CA Foundation 2025Set jan-20251 markMCQ
   Q.What will be the marginal product when quantity of labour is 5 ? (A) 8 (B) 9 (C) 10 (D) 11

   ›Reveal solutionSolution

   $MP_5 = TP_5 - TP_4 = 52 - 44 = \mathbf{8}$.

   Step 1 — Definition of marginal product

   $MP_n = TP_n - TP_{n-1}$

   MP is the extra output produced by employing one additional unit of labour.

   Step 2 — Get the two TP values

   From the reconstructed schedule (see Q18/Q19):

   Labour (L)	Total Product (TP)
   4	44
   5	52 (given)

   Step 3 — Compute MP at L = 5

   $MP_5 = 52 - 44 = 8$

   So the marginal product when the quantity of labour is 5 equals 8. …

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6. CA Foundation 2025Set may-20251 markMCQ
   Q.Which of the following is not true about relationship between average product and marginal product ? (A) When average product rises as a result of an increase in the quantity of variable input marginal product is more than the average product. (B) When average product is maximum, marginal product is equal to average product. (C) When average product falls, marginal product is less than the average product. (D) When average product is negative, marginal product becomes zero.

   ›Reveal solutionSolution

   Average product can never be negative, so statement (D) is the one that is not true.

   Step 1 — AP–MP relationships that ARE true

   • (A) When AP is rising (as variable input increases), MP > AP — true (MP pulls AP up).
   • (B) When AP is at its maximum, MP = AP — true (MP cuts AP at AP's peak).
   • (C) When AP is falling, MP < AP — true (MP pulls AP down).

   Step 2 — Why (D) is false

   $AP = \frac{TP}{L}$

   As long as total product (TP) is positive and the number of units of the variable input (L) is positive, AP is always positive — it cannot become negative. Marginal product can become negative (when TP falls), but average product cannot. So a statement premised on "average product is negative" is impossible, making (D) not true. …

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7. CA Foundation 2025Set may-20251 markMCQ
   Q.Total product starts declining in which stage of production ? (A) Stage 1 : The stage of increasing returns (B) Stage 2 : The stage of diminishing returns (C) Stage 3 : The stage of negative returns (D) It may decline in any stage of production

   ›Reveal solutionSolution

   Total product actually declines only in Stage 3 (negative returns), where marginal product is negative → (C).

   Step 1 — The three stages (law of variable proportions)

   • Stage 1 — increasing returns: TP rises at an increasing rate; MP rising.
   • Stage 2 — diminishing returns: TP rises at a decreasing rate and reaches its maximum at the end of this stage; MP positive but falling to zero.
   • Stage 3 — negative returns: MP becomes negative, so TP actually falls.

   Step 2 — Locate where TP declines

   TP is still increasing (or at its peak) through Stages 1 and 2. It starts declining only when MP turns negative — that is Stage 3.

   Step 3 — Reject the others

   • (A) Stage 1 — TP rising fast.
   • (B) Stage 2 — TP still rising, then at maximum. …

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8. CA Foundation 2025Set may-20251 markMCQ
   Q.Use the following data to answer question 24-25 :

   Output (Q)	0	1	2	3	4	5
   Total cost (TC)	₹ 200	₹ 310	₹ 410	₹ 500	₹ 604	₹ 710

   Diminishing marginal returns start to occur between units : (A) 1 and 2 (B) 2 and 3 (C) 3 and 4 (D) 4 and 5

   ›Reveal solutionSolution

   Diminishing marginal returns begin where marginal cost stops falling and starts rising — here between the 3rd and 4th units.

   Step 1 — Compute marginal cost for each unit

   $MC$ = change in TC per extra unit:

   Unit	TC	MC (ΔTC)
   1	310	110
   2	410	100
   3	500	90
   4	604	104
   5	710	106

   Step 2 — Link MC to marginal returns

   Falling MC ⇔ rising marginal product (increasing marginal returns); rising MC ⇔ falling marginal product (diminishing marginal returns). MC declines 110 → 100 → 90 through the 3rd unit, then RISES to 104 at the 4th unit.

   Step 3 — Locate the turning point

   The reversal — MC's minimum at unit 3, then upward — occurs between units 3 and 4, so diminishing marginal returns start there.

   Why the other options are wrong …

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9. CA Foundation 2025Set sep-20251 markMCQ
   Q.When average product rises as a result of an increase in the quantity of variable input, marginal product is : (A) less than the average product (B) minimum (C) equal to the average product (D) more than the average product

   ›Reveal solutionSolution

   AP rises only when MP is above AP; so a rising AP ⇒ MP > AP.

   Step 1 — Recall the MP–AP relationship

   Marginal product pulls the average up or down like a running average:

   • When $MP > AP$, AP is rising.
   • When $MP = AP$, AP is at its maximum.
   • When $MP < AP$, AP is falling.

   Step 2 — Apply to the stated case

   We are told AP rises as the variable input increases. From the relationship above, AP can only rise while marginal product exceeds average product. Hence MP is more than AP. …

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10. CA Foundation 2025Set sep-20251 markMCQ
    Q.Based on the information given in the following table, answer the Questions Nos. 18 to 20 : Product Schedule

    Quantity of labour	Total Product (TP)	Average Product (AP)	Marginal Product (MP)
    0	0	–	–
    1	–	–	20
    2	–	–	26
    3	66	–	–
    4	–	19	–
    5	–	–	4

    What will be the average product when the quantity of labour is 3 ? (A) 22 (B) 24 (C) 20 (D) 18

    ›Reveal solutionSolution

    AP at L = 3 is TP ÷ L = 66 ÷ 3 = 22.

    Step 1 — Read the total product at L = 3

    The schedule directly gives $TP = 66$ when the quantity of labour is 3.

    Step 2 — Apply the average product formula

    $AP = \frac{TP}{L} = \frac{66}{3} = 22$

    For completeness, filling the whole schedule: TP is 0, 20, 46, 66, 76, 80 for L = 0…5 (using the given MP and AP values), which confirms $AP_3 = 22$. …

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11. CA Foundation 2025Set sep-20251 markMCQ
    Q.Based on the information given in the following table, answer the Questions Nos. 18 to 20 : Product Schedule

    Quantity of labour	Total Product (TP)	Average Product (AP)	Marginal Product (MP)
    0	0	–	–
    1	–	–	20
    2	–	–	26
    3	66	–	–
    4	–	19	–
    5	–	–	4

    What will be the total product when the quantity of labour is 5 ? (A) 86 (B) 84 (C) 80 (D) 92

    ›Reveal solutionSolution

    TP₄ = AP₄ × 4 = 76; add MP₅ = 4 ⇒ TP₅ = 76 + 4 = 80.

    Step 1 — Find TP at L = 4

    Average product at L = 4 is given as 19, so

    $TP_4 = AP_4 \times L = 19 \times 4 = 76$

    Step 2 — Add the marginal product of the 5th unit

    Marginal product at L = 5 is given as 4, so

    $TP_5 = TP_4 + MP_5 = 76 + 4 = 80$

    The completed TP column (0, 20, 46, 66, 76, 80) confirms this. …

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12. CA Foundation 2025Set sep-20251 markMCQ
    Q.Based on the information given in the following table, answer the Questions Nos. 18 to 20 : Product Schedule

    Quantity of labour	Total Product (TP)	Average Product (AP)	Marginal Product (MP)
    0	0	–	–
    1	–	–	20
    2	–	–	26
    3	66	–	–
    4	–	19	–
    5	–	–	4

    What will be the marginal product when the quantity of labour is 4 ? (A) 26 (B) 20 (C) 10 (D) 19

    ›Reveal solutionSolution

    MP₄ = TP₄ − TP₃ = 76 − 66 = 10.

    Step 1 — Get the two total products

    • At L = 3: $TP_3 = 66$ (given).
    • At L = 4: $AP_4 = 19$, so $TP_4 = 19 \times 4 = 76$.

    Step 2 — Compute the marginal product

    $MP_4 = TP_4 - TP_3 = 76 - 66 = 10$

    Marginal product is the extra output from the 4th unit of labour, which is 10. …

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