CUET UG Booster Economics 4 Test (M2)
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QUESTION 1 OF 20
In perfect competition, how do we conceptualize the Total Revenue (TR) earned by a firm?
QUESTION 2 OF 20
If a firm sells 10 units of a good at a market price of Rs 15 per unit, which equation correctly determines the Total Revenue (TR)?
QUESTION 3 OF 20
QUESTION 4 OF 20
QUESTION 5 OF 20
Why does the total revenue curve form an upward rising straight line?
QUESTION 6 OF 20
Assertion (A): The TR curve is a straight line.
Reason (R): The equation TR = p × q operates with a constant market price p.
QUESTION 7 OF 20
Because TR = p × q, when output q is zero, TR is zero. This mathematical rule dictates that the TR curve must physically start exactly from _____.
QUESTION 8 OF 20
Match the graphical characteristics of TR (List I) with their algebraic meaning (List II).
| List I | List II |
|---|---|
| 1. Vertical height (Aq₁) | a. Total revenue |
| 2. Horizontal distance (Oq₁) | b. Output (1 unit) |
| 3. Slope of TR line (Aq₁/Oq₁) | c. Equals market price (p) |
| 4. Curve starting point (0,0) | d. Point O |
QUESTION 9 OF 20
Consider the following statements about Average Revenue (AR):
1. AR is the profit earned per unit of output.
2. AR is defined as total revenue per unit of output.
Which statement is correct?
QUESTION 10 OF 20
Using the formula AR = TR / q, if TR = (p × q), which mathematical simplification correctly proves AR = p?
QUESTION 11 OF 20
For a price-taking firm, why is Average Revenue exactly equal to the market price?
QUESTION 12 OF 20
The AR curve under perfect competition is perfectly horizontal and is interchangeably referred to as the _____.
QUESTION 13 OF 20
Match the curve names (List I) to their shapes (List II) for a perfectly competitive firm.
| List I | List II |
|---|---|
| 1. Total Revenue Curve | a. Upward rising straight line |
| 2. Price Line | b. Horizontal straight line |
| 3. Average Revenue Curve | c. Horizontal straight line |
| 4. Demand Curve facing the firm | d. Horizontal straight line |
QUESTION 14 OF 20
Arrange the sequence connecting the AR curve to the firm's demand:
1. Creating a perfectly elastic demand scenario.
2. Thus, the firm can sell as many units as it wants at price p.
3. The firm faces a horizontal AR curve at market price p.
4. This horizontal price line also represents the firm's demand curve.
QUESTION 15 OF 20
Which of the following accurately defines Marginal Revenue?
I. The decrease in total cost from producing one more unit.
II. The increase in total revenue for a unit increase in the firm's output.
QUESTION 16 OF 20
If Total Revenue changes from Rs 20 to Rs 30 when quantity sold changes from 2 boxes to 3 boxes, what is the MR?
QUESTION 17 OF 20
Setting the algebra aside, when a firm increases its output by one unit, this extra unit is sold at the market price, meaning the ____ is precisely the market price.
QUESTION 18 OF 20
Assertion (A): MR = AR under perfect competition.
Reason (R): Both Marginal Revenue and Average Revenue are strictly equal to the constant market price (p).
QUESTION 19 OF 20
Match the equations (List I) with their corresponding variables for a price-taking firm (List II).
| List I | List II |
|---|---|
| 1. TR equation | a. Zero |
| 2. AR equation | b. p × q |
| 3. MR equation | c. p |
| 4. Demand curve slope | d. p |
QUESTION 20 OF 20
Arrange the algebraic steps used to derive MR = p:
1. MR = [p(q2 - q1)] / (q2 - q1)
2. Given market price p, MR = (pq2 - pq1) / (q2 - q1)
3. MR = p
4. Consider output changes from q1 to q2
Test Complete!
Answer Review
1 In perfect competition, how do we conceptualize the Total Revenue (TR) earned by a firm?
Total Revenue is the firm's total sales income. It depends on market price and quantity sold. Formula: TR = p × q.
In a perfectly competitive market, the firm sells every unit of output at the prevailing market price. Therefore, Total Revenue equals the market price multiplied by the quantity sold. TR = p × q Option D is correct because it gives the NCERT definition of Total Revenue. Option A is incorrect because deducting variable costs relates to profit analysis, not Total Revenue. Option B is incorrect because Total Revenue is calculated before deducting any costs. Option C is incorrect because it defines Marginal Revenue, not Total Revenue.
- Option A → It is the revenue earned after deducting all variable costs.
- Total Revenue is measured before deducting any costs.
- Option B → It is the revenue minus the total fixed cost of production.
- Fixed costs are not deducted when calculating Total Revenue.
- Option C → It is the extra revenue from selling one additional unit.
- This defines Marginal Revenue.
Used: Elimination
Application:
- Eliminate options involving costs or Marginal Revenue, leaving the standard definition of Total Revenue.
Final Logic:
- TR always equals Price × Quantity, making Option D correct.
TR = Price × Quantity
2 If a firm sells 10 units of a good at a market price of Rs 15 per unit, which equation correctly determines the Total Revenue (TR)?
Use TR = p × q. Price = Rs 15. Quantity = 10 units.
The NCERT formula for Total Revenue is: TR = Price × Quantity Substituting the values: TR = 15 × 10 = Rs 150 Option C is correct because it correctly applies the formula. Option A incorrectly divides price by quantity. Option B incorrectly adds price and quantity. Option D incorrectly divides quantity by price.
- Option A → TR = 15 / 10 = Rs 1.5
- Revenue is calculated by multiplication, not division.
- Option B → TR = 15 + 10 = Rs 25
- Addition does not calculate Total Revenue.
- Option D → TR = 10 / 15 = Rs 0.67
- Quantity divided by price has no relevance to Total Revenue.
Used: Substitution
Application:
- Substitute the given values into TR = p × q.
Final Logic:
- 15 × 10 = Rs 150, making Option C correct.
Multiply Price and Quantity
3
TR = p × q. Price = Rs 25. Quantity = 4 units.
The passage states that Total Revenue equals the market price multiplied by the quantity sold. Therefore, TR = 25 × 4 = Rs 100 Option B is correct because it correctly applies the Total Revenue formula. Option A is too low. Option C incorrectly adds the values. Option D is unrelated to the calculation.
- Option A → Rs 50
- This would correspond to only two units sold.
- Option C → Rs 29
- This incorrectly combines the numerical values.
- Option D → Rs 21
- This is not obtained using the Total Revenue formula.
Used: Substitution
Application:
- Insert the given values into TR = p × q.
Final Logic:
- 25 × 4 = Rs 100, making Option B correct.
Price × Quantity = TR
4
Price remains fixed. Output varies. TR changes only because quantity changes.
The passage explains that: TR = p × q When the market price p is constant, the only variable affecting Total Revenue is the quantity sold (q). Therefore, any increase or decrease in output directly changes Total Revenue. Option A is correct because output is the only changing factor. Option B is incorrect because costs do not determine revenue. Option C is incorrect because competitor prices are irrelevant when market price is fixed. Option D is incorrect because Marginal Cost affects production decisions, not the revenue formula.
- Option B → Changes in the average cost.
- Average Cost influences profitability, not Total Revenue.
- Option C → Changes in the competitor's prices.
- The firm's revenue depends on the market price and its own output.
- Option D → Changes in the marginal cost.
- Marginal Cost does not appear in the Total Revenue equation.
Used: Contextual/Tonal Matching
Application:
- Use the relationship explained directly in the passage.
Final Logic:
- With constant price, only output changes Total Revenue.
Constant Price → Output Changes TR
5 Why does the total revenue curve form an upward rising straight line?
TR = p × q. Price remains constant. Revenue increases proportionately with output.
Under perfect competition, the market price remains constant for every unit sold. Since TR = p × q and p is constant, Total Revenue increases by the same amount for every additional unit sold. Therefore, the Total Revenue curve is an upward-sloping straight line. Option D is correct because constant price produces a linear relationship. Option A is incorrect because output does not remain constant. Option B is incorrect because firms are price takers and cannot charge different prices. Option C is incorrect because Total Cost has no effect on the shape of the Total Revenue curve.
- Option A → Because output quantity remains constant.
- The graph shows revenue changing as output changes.
- Option B → Because the firm can charge different prices.
- Firms cannot choose different prices under perfect competition.
- Option C → Because total cost is zero.
- Cost does not determine the shape of the Total Revenue curve.
Used: Contextual/Tonal Matching
Application:
- Relate the equation TR = p × q to its graphical representation.
Final Logic:
- A constant market price produces a straight-line Total Revenue curve, making Option D correct.
Constant Price = Straight TR
6 Assertion (A): The TR curve is a straight line.
Reason (R): The equation TR = p × q operates with a constant market price p.
Total Revenue equals Price × Quantity. Market price remains constant. Therefore, the TR curve is a straight line.
In a perfectly competitive market, the market price (p) remains constant because the firm is a price taker. Since: TR = p × q and p is fixed, Total Revenue changes proportionately with output (q). This produces an upward-sloping straight-line TR curve. Option C is correct because both the Assertion and Reason are true, and the Reason correctly explains why the TR curve is linear. Option A is incorrect because the Reason is true. Option B is incorrect because the Assertion is true. Option D is incorrect because both statements are true.
- Option A → A is true, R is false.
- The Reason is correct because price remains constant.
- Option B → A is false, R is true.
- The TR curve is indeed a straight line.
- Option D → Both A and R are false.
- Both statements correctly describe Total Revenue.
Used: Contextual/Tonal Matching
Application:
- Link the algebraic equation TR = p × q with its graphical representation.
Final Logic:
- Constant price results in a straight-line TR curve, making Option C correct.
Constant Price → Straight TR
7 Because TR = p × q, when output q is zero, TR is zero. This mathematical rule dictates that the TR curve must physically start exactly from _____.
Zero output means zero sales. Zero sales produce zero revenue. The graph begins at the origin.
The Total Revenue equation is: TR = p × q When output (q) is zero, TR = p × 0 = 0 Thus, the Total Revenue curve passes through the origin (0,0) because both output and revenue are zero. Option B is correct because the graph starts at the origin. Option A is incorrect because the price intercept belongs to the AR curve. Option C is unrelated to the graph's starting point. Option D is incorrect because the TR curve has no positive y-intercept.
- Option A → the price intercept
- The price intercept belongs to the Price Line (AR curve), not the TR curve.
- Option C → the highest output level
- The TR curve begins at zero output.
- Option D → a positive y-intercept
- Revenue is zero when output is zero.
Used: Substitution
Application:
- Substitute q = 0 into TR = p × q.
Final Logic:
- Zero output gives zero revenue, so the curve starts at the origin.
0 Output → 0 TR
8 Match the graphical characteristics of TR (List I) with their algebraic meaning (List II).
| List I | List II |
|---|---|
| 1. Vertical height (Aq₁) | a. Total revenue |
| 2. Horizontal distance (Oq₁) | b. Output (1 unit) |
| 3. Slope of TR line (Aq₁/Oq₁) | c. Equals market price (p) |
| 4. Curve starting point (0,0) | d. Point O |
Vertical height represents Total Revenue. Horizontal distance represents output. The slope equals the market price.
From the NCERT graph of the Total Revenue curve: Vertical height (Aq₁) represents Total Revenue. Horizontal distance (Oq₁) measures the firm's output. Slope (Aq₁/Oq₁) equals the market price (p) because TR = p × q. The curve begins at Point O, the origin. Thus, the correct matching is: 1 → a 2 → b 3 → c 4 → d Hence, Option C is correct.
- Option A
- Reverses the meanings of output and Total Revenue.
- Option B
- Incorrectly matches the graphical measurements.
- Option D
- Incorrectly identifies the vertical height and origin.
Used: Option Grouping
Application:
- Match each graph component individually before selecting the complete answer.
Final Logic:
- Only Option A correctly matches every graphical characteristic.
Height = TR | Base = Output | Slope = Price
9 Consider the following statements about Average Revenue (AR):
1. AR is the profit earned per unit of output.
2. AR is defined as total revenue per unit of output.
Which statement is correct?
AR measures revenue per unit sold. Profit and revenue are different concepts. AR = TR ÷ Quantity.
Average Revenue is defined as: AR = TR ÷ q Therefore, Statement 2 is correct. Statement 1 is incorrect because profit is calculated as: Profit = TR − TC Profit per unit is not the definition of Average Revenue. Option D is correct because only Statement 2 is true. Option A incorrectly treats Statement 1 as correct. Option B incorrectly rejects Statement 2. Option C incorrectly rejects both statements.
- Option A → Both 1 and 2
- Statement 1 confuses revenue with profit.
- Option B → Only 1
- Statement 2 gives the correct NCERT definition.
- Option C → Neither 1 nor 2
- Statement 2 is correct.
Used: Option Grouping
Application:
- Evaluate each statement independently before selecting the correct combination.
Final Logic:
- Only Statement 2 correctly defines Average Revenue.
AR = Revenue per Unit
10 Using the formula AR = TR / q, if TR = (p × q), which mathematical simplification correctly proves AR = p?
AR = TR ÷ q. Substitute TR = p × q. Quantity cancels, leaving AR = p.
The NCERT derives Average Revenue (AR) as follows: AR = TR ÷ q Since, TR = p × q Substituting, AR = (p × q) ÷ q AR = p Thus, Average Revenue equals the market price. Option C correctly demonstrates this simplification. Option A incorrectly multiplies by quantity. Option B incorrectly adds price and quantity. Option D uses an incorrect mathematical expression.
- Option A → AR = (p × q) × q = p
- Multiplication by q is mathematically incorrect.
- Option B → AR = (p + q) / q = p
- Addition cannot produce the required derivation.
- Option D → AR = p / (q × TR) = p
- This expression is unrelated to the definition of AR.
Used: Substitution
Application:
- Replace TR with p × q and simplify algebraically.
Final Logic:
- Cancelling q gives AR = p, making Option C correct.
TR/q → p
11 For a price-taking firm, why is Average Revenue exactly equal to the market price?
A price-taking firm sells every unit at the same market price. Average Revenue is revenue per unit sold. Therefore, AR equals the market price.
In perfect competition, a firm has no control over price and must accept the prevailing market price. Since every unit of output is sold at the same price, TR = p × q and AR = TR ÷ q = (p × q) ÷ q = p Thus, Average Revenue is exactly equal to the market price. Option B is correct because it correctly explains why AR equals the market price. Option A is incorrect because firms are price takers, not price makers. Option C is incorrect because Total Revenue is generally positive when output is sold. Option D is incorrect because AR has no direct relationship with Marginal Cost.
- Option A → Because the firm controls the market price.
- Under perfect competition, the market determines price.
- Option C → Because total revenue is equal to zero.
- Total Revenue is zero only when output is zero.
- Option D → Because marginal cost is equal to average cost.
- Marginal Cost and Average Revenue are different concepts.
Used: Contextual/Tonal Matching
Application:
- Apply the price-taking assumption explained in the NCERT.
Final Logic:
- Every unit is sold at the same market price, so AR = Price, making Option B correct.
Same Price → Same Average
12 The AR curve under perfect competition is perfectly horizontal and is interchangeably referred to as the _____.
AR remains constant at every output level. The AR curve is horizontal. This horizontal line is called the Price Line.
Since a perfectly competitive firm sells every unit at the same market price, Average Revenue remains constant regardless of output. When AR is plotted against output, it forms a horizontal straight line known as the Price Line. This line also represents the firm's demand curve. Option A is correct because the horizontal AR curve is called the Price Line. Option B is incorrect because the Variable Cost Line is unrelated to revenue. Option C is incorrect because the supply curve is different from the Price Line. Option D is incorrect because the Total Revenue curve slopes upward.
- Option B → variable cost line
- Variable Cost is a cost concept, not a revenue curve.
- Option C → supply curve
- The supply curve represents output supplied at different prices.
- Option D → total revenue curve
- Total Revenue increases with output and is not horizontal.
Used: Contextual/Tonal Matching
Application:
- Recall the NCERT figure where the horizontal AR curve is labelled as the Price Line.
Final Logic:
- The horizontal AR curve is called the Price Line, making Option A correct.
Horizontal AR = Price Line
13 Match the curve names (List I) to their shapes (List II) for a perfectly competitive firm.
| List I | List II |
|---|---|
| 1. Total Revenue Curve | a. Upward rising straight line |
| 2. Price Line | b. Horizontal straight line |
| 3. Average Revenue Curve | c. Horizontal straight line |
| 4. Demand Curve facing the firm | d. Horizontal straight line |
TR rises with output. Price Line, AR curve and Demand curve are horizontal. The matching follows NCERT graphs.
For a perfectly competitive firm: Total Revenue Curve is an upward-rising straight line. Price Line is a horizontal straight line. Average Revenue Curve is also horizontal. Demand Curve facing the firm is perfectly elastic, represented by a horizontal line. Therefore: 1 → a 2 → b 3 → c 4 → d Hence, Option D is correct.
- Option A
- Incorrectly identifies the Total Revenue curve as horizontal.
- Option B
- Reverses the shapes of the Total Revenue and AR curves.
- Option C
- Incorrectly matches the graphical representations.
Used: Option Grouping
Application:
- Identify each graph independently before matching.
Final Logic:
- Only Option D correctly matches all four curves.
TR Rises | AR Stays Flat
14 Arrange the sequence connecting the AR curve to the firm's demand:
1. Creating a perfectly elastic demand scenario.
2. Thus, the firm can sell as many units as it wants at price p.
3. The firm faces a horizontal AR curve at market price p.
4. This horizontal price line also represents the firm's demand curve.
The AR curve is horizontal. It also represents the demand curve. This leads to perfectly elastic demand.
The logical sequence is: Step 3: The firm faces a horizontal AR curve at market price p. Step 4: This horizontal line also represents the firm's demand curve. Step 2: Therefore, the firm can sell as many units as it wishes at price p. Step 1: This creates a perfectly elastic demand curve. Hence, Option C is correct.
- Option A
- Begins with the demand curve before introducing the AR curve.
- Option B
- Starts with the conclusion instead of the graphical explanation.
- Option D
- Places the selling condition before establishing the demand curve.
Used: Contextual/Tonal Matching
Application:
- Follow the same logical order used in the NCERT explanation.
Final Logic:
- The sequence is 3 → 4 → 2 → 1, making Option C correct.
AR → Demand → Sell → Elastic
15 Which of the following accurately defines Marginal Revenue?
I. The decrease in total cost from producing one more unit.
II. The increase in total revenue for a unit increase in the firm's output.
MR measures additional revenue. It is not related to changes in cost. MR = Change in TR ÷ Change in Output.
Marginal Revenue is defined as the increase in Total Revenue resulting from selling one additional unit of output. Statement II correctly defines Marginal Revenue. Statement I is incorrect because it describes a change in cost, whereas MR is a revenue concept. Therefore, Option A is correct.
- Option B → Only I
- Statement I refers to cost rather than revenue.
- Option C → Both I and II
- Statement I is incorrect.
- Option D → Neither I nor II
- Statement II is the correct NCERT definition.
Used: Option Grouping
Application:
- Evaluate each statement separately before selecting the correct combination.
Final Logic:
- Only Statement II correctly defines Marginal Revenue.
MR = Extra Revenue
16 If Total Revenue changes from Rs 20 to Rs 30 when quantity sold changes from 2 boxes to 3 boxes, what is the MR?
MR measures additional revenue. Formula: MR = ΔTR ÷ ΔQ. Here, MR = (30 − 20) ÷ (3 − 2) = Rs 10.
Marginal Revenue (MR) is defined as the increase in Total Revenue resulting from selling one additional unit of output. The formula is: MR = ΔTR ÷ ΔQ Substituting the given values: MR = (30 − 20) ÷ (3 − 2) MR = 10 ÷ 1 MR = Rs 10 Therefore, Marginal Revenue (MR) = Rs 10. Option A is correct because it correctly applies the NCERT formula. Option B is incorrect because MR is calculated using differences, not sums. Option C is incorrect because it calculates Average Revenue, not Marginal Revenue. Option D is incorrect because it divides the original TR by the original quantity instead of calculating the change.
- Option B → MR = (30 + 20) / (3 + 2) = 10
- Marginal Revenue uses changes (differences), not additions.
- Option C → MR = 30 / 3 = 10
- This calculates Average Revenue, not Marginal Revenue.
- Option D → MR = 20 / 2 = 10
- This also represents Average Revenue for the initial output level.
Used: Substitution
Application:
- Apply the standard formula MR = ΔTR ÷ ΔQ using the given values.
Final Logic:
- The increase in revenue is Rs 10 for one extra unit, making Option A correct.
MR = ΔTR ÷ ΔQ
17 Setting the algebra aside, when a firm increases its output by one unit, this extra unit is sold at the market price, meaning the ____ is precisely the market price.
One extra unit earns one extra price. Additional revenue is Marginal Revenue. Therefore, MR equals the market price.
Under perfect competition, every additional unit produced is sold at the prevailing market price. Hence, the increase in Total Revenue from selling one more unit is exactly equal to the market price. Therefore, MR=PriceMR = PriceMR=Price Option D is correct because Marginal Revenue measures the additional revenue earned from one extra unit. Option A is incorrect because Total Cost is unrelated to revenue. Option B is incorrect because Average Cost is a cost concept. Option C is incorrect because "Variable Revenue" is not an NCERT revenue concept.
- Option A → Total Cost
- Total Cost measures production expenditure, not additional revenue.
- Option B → Average Cost
- Average Cost has no role in defining Marginal Revenue.
- Option C → Variable Revenue
- This is not a recognised revenue concept in the NCERT.
Used: Contextual/Tonal Matching
Application:
- Relate the phrase "extra unit sold" directly to the definition of Marginal Revenue.
Final Logic:
- The extra revenue from one additional unit is Marginal Revenue, making Option D correct.
Extra Unit → Extra Revenue → MR
18 Assertion (A): MR = AR under perfect competition.
Reason (R): Both Marginal Revenue and Average Revenue are strictly equal to the constant market price (p).
Every unit sells at the same market price. AR equals Price. MR also equals Price.
In a perfectly competitive market, the firm is a price taker and sells every unit at the same market price. Therefore, AR = Price MR = Price Hence, MR=AR=pMR = AR = pMR=AR=p The Reason correctly explains why the Assertion is true. Option C is correct. Option A is incorrect because the Reason is true. Option B is incorrect because the Assertion is true. Option D is incorrect because both statements are correct.
- Option A → A is true, R is false.
- The Reason correctly explains the Assertion.
- Option B → A is false, R is true.
- The Assertion is also true.
- Option D → Both A and R are false.
- Both statements are correct.
Used: Contextual/Tonal Matching
Application:
- Recall the NCERT relationship among Price, AR and MR.
Final Logic:
- Since MR = AR = Price, Option C is correct.
Price = AR = MR
19 Match the equations (List I) with their corresponding variables for a price-taking firm (List II).
| List I | List II |
|---|---|
| 1. TR equation | a. Zero |
| 2. AR equation | b. p × q |
| 3. MR equation | c. p |
| 4. Demand curve slope | d. p |
TR = p × q. AR = p. MR = p. Horizontal demand curve has zero slope.
For a perfectly competitive firm: TR = p × q AR = p MR = p The firm's demand curve is horizontal, so its slope is zero. Therefore, 1 → b 2 → c 3 → d 4 → a Thus, Option D is correct.
- Option A
- Total Revenue is not zero.
- Option B
- Reverses the revenue equations.
- Option C
- Incorrectly matches TR and the demand curve slope.
Used: Option Grouping
Application:
- Recall each revenue formula separately before matching.
Final Logic:
- Only Option B correctly matches every equation.
TR = PQ | AR = P | MR = P | Demand Slope = 0
20 Arrange the algebraic steps used to derive MR = p:
1. MR = [p(q2 - q1)] / (q2 - q1)
2. Given market price p, MR = (pq2 - pq1) / (q2 - q1)
3. MR = p
4. Consider output changes from q1 to q2
Begin with a change in output. Substitute the TR expression. Simplify the equation. Obtain MR = p.
The derivation follows this logical sequence: Step 4: Consider output changing from q₁ to q₂. Step 2: Write the marginal revenue expression: MR = (pq₂ − pq₁) / (q₂ − q₁). Step 1: Factor out the common factor p: MR = [p(q₂ − q₁)] / (q₂ − q₁). Step 3: Cancel (q₂ − q₁) from the numerator and denominator to obtain: MR = p. Thus, Option A correctly presents the algebraic derivation used in the NCERT.
- Option B → 1, 2, 3, 4
- Starts with a simplification before introducing the original expression.
- Option C → 4, 3, 2, 1
- Begins with the conclusion before completing the derivation.
- Option D → 2, 1, 4, 3
- Introduces the algebra before defining the change in output.
Used: Contextual/Tonal Matching
Application:
- Arrange the mathematical derivation exactly as presented in the NCERT.
Final Logic:
- The derivation proceeds 4 → 2 → 1 → 3, making Option A correct.
Change → Substitute → Simplify → MR = p
