ISC Economics Numericals: An Answer-Writing Workshop

You have revised the formulas. You can usually do the arithmetic. Yet an economics numerical can still go wrong because the answer asks for the new quantity, while your last line gives the original quantity.

That is a frustrating mistake because the difficult part may already be correct.

This workshop is about catching that gap. We will repair five deliberately flawed solutions, then practise writing answers that make the formula, substitution, sign, unit and economic meaning easy to follow. All the numerical data below are invented for practice.

For an ISC Economics numerical, a useful routine is: name the required result, write the relevant relationship, substitute labelled values, calculate with signs and units, and finish with a sentence that answers the exact instruction. This is a study method, not a fixed allocation of marks.

The CISCE Economics performance analysis for 2025 identifies problems including incorrect elasticity signs and stopping before finding the quantity actually requested. Those observations are a good reason to practise the whole answer, rather than only the calculation in the middle.

If you would like a gentler introduction first, our general guide to presenting economics numericals explains the basic routine. Here, you will use it to diagnose mistakes.

Set Up a Small Answer Frame

On a rough sheet, leave room for five things:

1. Target: the quantity or conclusion requested.
2. Relationship: the formula or economic condition you need.
3. Substitution: the given numbers, including their signs.
4. Result: the calculated value with its correct unit or scale.
5. Meaning: one sentence connecting that result to the question.

You do not have to write these headings in every examination answer. They are a rehearsal tool. A short calculation can fit naturally into a few lines; a longer one may need a working note or table.

The most useful habit is to leave the target visible while you work. If the target says “investment required”, an answer ending with “multiplier = 5” is visibly unfinished.

Repair 1: The Correct Calculation Answers the Wrong Question

Question: Price falls from Rs. 50 to Rs. 40 per packet. Weekly quantity demanded increases by 24 packets. Using original values as the percentage base, the signed price elasticity of demand is -0.8. Find weekly quantity demanded at the new price.

A student writes:

-0.8 = (24 / -10) x (50 / Q0)
Q0 = 150 packets
Answer: 150 packets.

The algebra is right. The final answer is not the requested quantity.

Diagnose it before changing the formula

Here, Q0 means the original weekly quantity. The question asks for quantity at Rs. 40, after the increase. The student has reached an intermediate result and stopped.

A repaired answer can be written like this:

Required: new weekly quantity, Q1

Change in price = 40 - 50 = -10
Change in quantity = +24

Ed = (change in Q / change in P)
     x (P0 / Q0)

-0.8 = (24 / -10) x (50 / Q0)
-0.8 = -120 / Q0
Q0 = 150 packets per week

Q1 = Q0 + change in Q
   = 150 + 24
   = 174 packets per week

At the new price of Rs. 40, weekly quantity demanded is 174 packets.

A quick check confirms the setup: quantity increases by 24 / 150 = 16%, while price falls by 10 / 50 = 20%. The signed ratio is 16 / (-20) = -0.8.

The point of the check is not to produce a second full solution. It is to ask whether the result fits the information you began with.

Keep the sign convention visible

For ordinary downward-sloping demand, the signed coefficient is negative; its positive magnitude is used to describe the degree of elasticity. Here, the magnitude is 0.8, so demand is relatively inelastic.

If the question provides a signed coefficient, preserve it during substitution. If your answer uses magnitude, label it clearly. Also keep the specified percentage base: a midpoint calculation uses average values and can give a different coefficient for the same finite movement. OpenStax explains this distinction in its elasticity lesson.

Repair habit: circle the words “original”, “new”, “increase” or “decrease” wherever they describe the required answer.

Repair 2: A Correct Multiplier With the Wrong Unit and Operation

Question: In a simple two-sector economy, MPC is 0.8. Find the additional investment needed to raise equilibrium income by Rs. 450 crore. Assume fixed prices, spare capacity, no government or foreign trade, and a constant MPC.

A student writes:

k = 1 / (1 - 0.8) = Rs. 5 crore
Investment required = 450 x 5
                    = Rs. 2,250 crore

There are two errors. The multiplier has been given a money unit, and the relationship has been used in the wrong direction.

Repair the relationship before touching the numbers

The simple multiplier connects a change in investment to the resulting change in equilibrium income. The model is explained in NCERT’s income-determination chapter.

Use dY for the change in income and dI for the change in investment:

k = 1 / (1 - MPC)
  = 1 / (1 - 0.8)
  = 5

dY = k x dI
Therefore, dI = dY / k
             = 450 / 5
             = Rs. 90 crore

Additional investment of Rs. 90 crore is required to produce an income increase of Rs. 450 crore under these assumptions.

Check: 5 x 90 = 450. That is the direction the model describes.

The multiplier is a ratio, so write 5, or explain it as five times. The change in investment is a monetary amount. Writing units beside the intermediate answer would have exposed the first error immediately.

Do not let a familiar formula choose the operation for you

Students often associate multiplier questions with multiplication. But the unknown decides whether you multiply or divide. Write the relationship with the unknown still present, rearrange it, and only then insert the figures.

Repair habit: whenever you divide or multiply by a ratio, name the quantity you are calculating on the left of the equal sign.

Repair 3: Reversing a National-Income Conversion

Question: Calculate GNP at market prices. Annual figures, all in Rs. crore, are:

Item	Amount
NDP at factor cost	6,800
Depreciation	420
Indirect taxes	560
Subsidies	160
Net factor income from abroad	-90

A student remembers a familiar adjustment pattern and writes:

GNP at market prices
= 6,800 - 420 - 400 - 90
= Rs. 5,890 crore

This applies the wrong directions to two adjustments.

Say the starting and finishing points aloud

We are moving from net to gross, from factor cost to market prices, and from domestic to national. The directions matter. The relevant aggregate relationships are set out in NCERT’s National Income Accounting chapter.

For this textbook conversion:

Net indirect taxes = 560 - 160 = 400

GNP at market prices
= NDP at factor cost
  + depreciation
  + net indirect taxes + NFIA

= 6,800 + 420 + 400 + (-90)
= Rs. 7,530 crore

GNP at market prices is Rs. 7,530 crore for the year.

The formula adds NFIA, but the supplied value is negative. Writing + (-90) makes that distinction explicit.

Use labels to expose the route

For revision, reconstruct the calculation in three small steps:

GDP at factor cost = 6,800 + 420 = 7,220
GDP at market prices = 7,220 + 400 = 7,620
GNP at market prices
= 7,620 + (-90) = 7,530

All figures remain in Rs. crore. You can use either a clear combined expression or labelled stages in your answer; you need not write both unless asked.

The repair is not “always add depreciation”. It is “check the direction of the conversion”. Going from gross to net would require the reverse adjustment.

Repair habit: write the complete names of the starting and required aggregates before remembering any sequence of plus and minus signs.

Repair 4: A Cost Difference Mistaken for Cost Per Unit

Question: Total cost is Rs. 960 at an output of 30 units and Rs. 1,080 at 34 units. Calculate the additional cost per extra unit over this output interval.

A student writes:

Additional cost per unit
= 1,080 - 960 = Rs. 120

Rs. 120 is the additional cost of all four extra units together. The question asks for the amount per extra unit.

Repair the denominator

Additional cost = 1,080 - 960 = Rs. 120
Additional output = 34 - 30 = 4 units

Additional cost per extra unit
= change in total cost / change in output
= 120 / 4
= Rs. 30 per unit

Over the interval from 30 to 34 units, additional cost averages Rs. 30 per extra unit.

This is an interval average. These two observations alone do not tell us the separate cost of the 31st, 32nd, 33rd and 34th units. Their additional costs could differ while still totalling Rs. 120.

In a one-unit output schedule, marginal cost is the change in total cost for that additional unit. The underlying cost concepts are covered in NCERT’s Production and Costs chapter.

Show a method when completing a table

Suppose a different question provides the following one-unit schedule with fixed cost of Rs. 80:

Output	Total cost, Rs.	Variable cost, Rs.	Marginal cost, Rs.
0	80	0	Not applicable
1	110	30	30
2	135	55	25
3	165	85	30

Two short working lines explain the method:

Variable cost = total cost - fixed cost
Marginal cost of the 2nd unit
= 135 - 110 = Rs. 25

Do not write a cost of producing an extra unit at output zero when no extra unit has yet been produced.

Repair habit: look at the change in the output column before subtracting adjacent cost figures.

Repair 5: A Number That Has Been Given Too Much Meaning

Question: A household’s monthly income increases from Rs. 40,000 to Rs. 50,000. Its monthly consumption expenditure rises from Rs. 34,000 to Rs. 41,000. Calculate MPC and explain the result.

A student writes:

MPC = 7,000 / 10,000 = 0.7
The household spends 70%
of its total income.

The calculation is correct. The sentence describes a different ratio.

Repair just the interpretation

Change in consumption
= 41,000 - 34,000 = 7,000
Change in income
= 50,000 - 40,000 = 10,000

MPC = change in consumption
      / change in income
    = 7,000 / 10,000
    = 0.7

Over the observed change, the household spends 70 paise of each additional rupee of income and saves the remaining 30 paise.

The word additional does the important work. For comparison, its new average propensity to consume is 41,000 / 50,000 = 0.82. That is the share of its new total income spent on consumption.

The wrong sentence quietly replaced “change in” with “total”. Clear interpretation depends on reading your own numerator and denominator, not simply attaching a familiar sentence to the result.

Repair habit: turn the fraction into words before writing the conclusion. Ask, “This amount divided by what amount?”

How Much Working Should You Show?

A readable answer gives someone enough information to reconstruct your method. It does not need every mental arithmetic step.

For the investment example, dI = dY / k = 450 / 5 = Rs. 90 crore, after establishing k, is clear. Writing only “90” is not. At the other extreme, a long explanation of every round of spending is unnecessary unless the question asks for the process.

The official 2025 specimen answer key illustrates this connection between working and conclusion: its elasticity item calls for the mathematical expression and the deduction about elasticity. Read that as guidance for that item, not as a universal mark-per-line rule.

Keep the page easy to follow

Use a separate working note when it prevents a crowded substitution, such as calculating net indirect taxes. Put units in table headings when every entry shares the same unit. Keep one calculation per line when a sign could otherwise disappear.

Avoid a false equality such as k = 5 = 450 / 5 = 90. The multiplier and investment requirement are different quantities. Start a new labelled line when you change what you are finding.

Round at the end

If a calculation produces a recurring decimal, retain a fraction or enough decimal places during the working. Follow any precision instruction given in the question. Otherwise, use a sensible final precision and say “approximately” when rounding changes the value.

Do not replace a troublesome decimal with a convenient whole number just because the next step becomes easier.

Practise: Find the Fault, Then Repair the Answer

Try these without looking at the solutions. Your task is to correct both the number and the final sentence where necessary.

1. Wrong destination: Price falls from Rs. 80 to Rs. 72; weekly quantity rises by 15 units. Signed elasticity, using original values, is -0.5. A student calculates original quantity as 300 units and reports it as the new quantity. Repair the answer.
2. Wrong operation: MPS is 0.25 and the required income increase is Rs. 240 crore in the simple two-sector model. A student reports additional investment of Rs. 960 crore. Find the correct amount.
3. Wrong adjustment: NDP at factor cost is Rs. 2,300 crore, depreciation Rs. 180 crore, net indirect taxes Rs. 140 crore and NFIA -20 crore. A student deducts all three adjustments to find GNP at market prices. Repair the calculation.
4. Missing denominator: Total cost rises from Rs. 500 to Rs. 620 as output rises from 10 to 13 units. A student reports Rs. 120 per extra unit. Repair it.
5. Wrong interpretation: Consumption increases by Rs. 4,800 when income increases by Rs. 8,000. A student correctly obtains 0.6 but writes “60% of total income is consumed”. Rewrite the sentence.
6. Missing scale: A table headed “Rs. crore” gives a starting amount of 720 and an increase of 45. A student writes the new amount as Rs. 765. Repair the unit.

Solutions

1. 315 units per week. Original quantity is 300; add the increase of 15. The final answer must refer to the quantity at Rs. 72.
2. Rs. 60 crore. The multiplier is 1 / 0.25 = 4. Required additional investment is 240 / 4 = 60, not 240 x 4.
3. Rs. 2,600 crore. Calculate 2,300 + 180 + 140 + (-20). The conversion moves from net to gross, factor cost to market prices, and domestic to national.
4. Rs. 40 per extra unit over the interval. Divide the additional cost of Rs. 120 by the three extra units.
5. The household consumes 60 paise per additional rupee of income over this change. The observations establish a marginal share, not the share of total income.
6. Rs. 765 crore. Both inputs share the table’s scale, and the sum keeps it.

A Final Check You Can Actually Use

Before leaving an answer, run your finger from the question’s instruction to the last line of your solution. Does it end at the right destination?

Then check the vulnerable parts: the denominator, any negative number, the unit heading, and the words “total”, “additional”, “original” and “new”. These checks are more focused than redoing every sum from the beginning.

For revision, keep a tiny correction log with three columns: my mistaken line, the repaired line, and the check that would have caught it. Revisit it before attempting the next practice set. The aim is to make your own recurring mistakes easier to recognise.

Frequently Asked Questions

1. Must every numerical answer have five headings?

No. Use the five-part frame to organise your thinking. In the answer itself, a few labelled lines are often enough. Add headings only when they make longer working easier to follow.

2. Does a correct final number guarantee full marks?

Do not assume so. A question may require a method, classification, explanation or diagram as well as a number. Follow its instructions and the applicable marking scheme.

3. Should I copy the entire question into my answer?

Usually, no. Write the relevant given values and the required quantity. Copying a long paragraph adds work without necessarily making your solution clearer.

4. Can I drop the minus sign from price elasticity?

Keep signed values consistent during calculation. If reporting elasticity as a positive magnitude, say so clearly and classify that magnitude. Do not silently switch conventions halfway through the algebra.

5. What if my calculation gives the original quantity but the question asks for the new one?

Use the stated change to move from the original quantity to the new quantity. An increase is added and a decrease is subtracted. Label both quantities so the last step is visible.

6. Should the multiplier be written in rupees?

No. It is a ratio. The investment or income change it helps calculate has a monetary unit, but the multiplier itself does not.

7. How do I avoid reversing national-income adjustments?

Identify both aggregates fully before calculating. Decide separately whether you are changing net to gross, domestic to national, and factor cost to market prices, or moving in the reverse direction.

8. Is the difference between two total-cost figures always marginal cost?

Check the output difference. With a one-unit increase, the cost difference gives that extra unit’s marginal cost. Across several units, divide by the output increase to find additional cost per unit over the interval; individual unit costs are not separately identified.

9. What belongs in the interpretation sentence?

State what the result measures in the situation given. Keep changes distinct from levels, and totals distinct from per-unit amounts. Avoid adding claims that the data cannot establish.

10. What should I do when I find an error near the end of the examination?

Correct the first wrong step clearly and carry the correction through the remaining working. Check the final label and unit too. A changed number with an unchanged interpretation can leave the answer inconsistent.