● MACROECONOMICS
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MACROECONOMICSβ€ΊREVISIONβ€ΊNUMERICAL LAB

Numerical Lab

The two lecture topics your instruction plan marks APPLY rather than UNDERSTAND are National Income measurement (Lecture 7) and the IS-LM model (Lectures 9–10) β€” so those are where numbers can be asked. Everything below is worked step by step in the textbook's own style.

WHERE EACH PROBLEM COMES FROM

Problems marked TB are reproduced from the textbook's end-of-chapter questions, with the page cited β€” click the citation to read the original. Problems marked Illustrative are written here to drill a formula the textbook explains but does not set an exercise on; their numbers are invented, the method is not.

Cross-check the formulas against Unit 2 β€” National Income Concepts and Consumption Function.

Formula sheet

Memorise these first. Almost every numerical in this portion is one of them, rearranged.

National income
GDPMP = C + I + G + (X βˆ’ M) ← expenditure method GDPMP = Ξ£ Gross Value Added of all firms ← value-added method NDPFC = Compensation of employees + Rent + Interest + Profit + Mixed income ← income method GNPMP = GDPMP + Net Factor Income from Abroad (NFIA) NNPMP = GNPMP βˆ’ Depreciation NNPFC = NNPMP βˆ’ Net Indirect Taxes (= National Income) Net Indirect Taxes = Indirect Taxes βˆ’ Subsidies Gross Value Added = Value of Output βˆ’ Intermediate Consumption Value of Output = Sales + Change in Stock
Down the chain: NI β†’ PI β†’ PDI
Personal Income (PI) = National Income βˆ’ Corporate (undistributed) profits βˆ’ Corporate profit tax βˆ’ Social security contributions + Transfer payments Personal Disposable Income (PDI) = PI βˆ’ Personal (direct) taxes PDI = C + S
Real vs nominal
Nominal GNP GNP Deflator = ───────────────────── Γ— 100 Real GNP Nominal GNP Real GNP = ───────────────────── Γ— 100 GNP Deflator
Consumption, saving, multiplier
C = a + bY a = autonomous consumption, b = MPC S = Y βˆ’ C = βˆ’a + (1 βˆ’ b)Y APC = C / Y MPC = Ξ”C / Ξ”Y APS = S / Y MPS = Ξ”S / Ξ”Y APC + APS = 1 MPC + MPS = 1 Break-even income: Y = C ⟹ Y* = a / (1 βˆ’ b) 1 1 Multiplier k = ───────── = ───── Ξ”Y = k Γ— Ξ”I 1 βˆ’ MPC MPS

Problem 1 β€” Value added method TB

Ahuja, Ch. 2, Questions for Review Q.29 β€” p. 52

Question

An economy consists of only two firms, A and B. From the data below find (a) the value added by Firms A and B, and (b) gross domestic product at market prices.

Itemβ‚Ή crore
(i) Exports by Firm A40
(ii) Imports by Firm A100
(iii) Sales to households by Firm A180
(iv) Sales to Firm B by Firm A80
(v) Sales to Firm A by Firm B60
(vi) Sales to households by Firm B120

Textbook hint: exports by Firm A are part of its value of output; imports by Firm A are part of its intermediate cost of production.

Solution

Step 1 β€” Value of output of each firm. Output is everything the firm sold, to whomever it sold it.

Firm A output = 180 (to households) + 80 (to Firm B) + 40 (exports) = 300 Firm B output = 120 (to households) + 60 (to Firm A) = 180

Step 2 β€” Intermediate consumption of each firm. These are purchases of goods used up in production β€” from the other firm, and from abroad.

Firm A intermediate = 60 (bought from Firm B) + 100 (imports) = 160 Firm B intermediate = 80 (bought from Firm A) = 80

Step 3 β€” Gross value added = output βˆ’ intermediate consumption.

GVA of Firm A = 300 βˆ’ 160 = 140 GVA of Firm B = 180 βˆ’ 80 = 100

Step 4 β€” GDP at market prices = sum of gross value added.

GDPMP = 140 + 100 = β‚Ή 240 crore

This matches the answer printed in the textbook: GDPMP = β‚Ή 240 crore.

⚠ Where marks are lost here
  • Adding all six figures together (180+80+40+120+60 = 480). That is double counting β€” Firm A's sales to Firm B are already inside Firm B's output.
  • Forgetting imports. Imports are not produced domestically, so they must be subtracted as intermediate cost, not added.
  • Forgetting that exports still count as domestic output. Something made in the country counts in GDP no matter who buys it.

Problem 2 β€” Income and expenditure methods TB

Ahuja, Ch. 2, Questions for Review Q.30 β€” p. 52

Question

From the following data calculate Gross National Product and Net National Product at market prices by (i) the income method and (ii) the expenditure method.

Itemβ‚Ή crore
(i) Mixed income of the self-employed400
(ii) Compensation to employees500
(iii) Private final consumption expenditure900
(iv) Net factor income from abroad(βˆ’) 20
(v) Net taxes100
(vi) Consumption of fixed capital (depreciation)120
(vii) Net domestic capital formation280
(viii) Net exports(βˆ’) 30
(ix) Profits350
(x) Rent100
(xi) Government final consumption expenditure300
Solution β€” (ii) Expenditure method (do this one first: it is fully determined)

Step 1 β€” Build gross domestic capital formation. The data gives the net figure, so add back depreciation.

Gross domestic capital formation = Net domestic capital formation + Depreciation = 280 + 120 = 400

Step 2 β€” Add the four expenditure components.

GDPMP = Private final consumption (C) + Government final consumption (G) + Gross domestic capital formation (I) + Net exports (X βˆ’ M) = 900 + 300 + 400 + (βˆ’30) = β‚Ή 1,570 crore

Step 3 β€” Move from domestic to national, then from gross to net.

GNPMP = GDPMP + NFIA = 1570 + (βˆ’20) = β‚Ή 1,550 crore NNPMP = GNPMP βˆ’ Depreciation = 1550 βˆ’ 120 = β‚Ή 1,430 crore
Solution β€” (i) Income method

Step 1 β€” Add the factor incomes. This gives net domestic product at factor cost.

NDPFC = Compensation to employees + Rent + Profits + Mixed income = 500 + 100 + 350 + 400 = β‚Ή 1,350 crore

Step 2 β€” Factor cost β†’ market prices. Add net indirect taxes.

NDPMP = NDPFC + Net indirect taxes = 1350 + 100 = β‚Ή 1,450 crore

Step 3 β€” Net β†’ gross, domestic β†’ national.

GDPMP = NDPMP + Depreciation = 1450 + 120 = β‚Ή 1,570 crore βœ“ matches GNPMP = GDPMP + NFIA = 1570 βˆ’ 20 = β‚Ή 1,550 crore NNPMP = GNPMP βˆ’ Depreciation = 1550 βˆ’ 120 = β‚Ή 1,430 crore

Both methods give the same GNP and NNP β€” which is the whole point of the three-fold identity National Income = National Product = National Expenditure.

⚠ A note on item (v), and on this type of question generally

The printed question labels item (v) as "net direct taxes". Read literally, direct taxes are not added anywhere in the income method β€” direct taxes are paid out of factor incomes that are already counted β€” and the income method would then stop at NNPFC = β‚Ή 1,330 crore, which would not reconcile with the expenditure method's β‚Ή 1,430 crore. The two methods agree only if item (v) is treated as net indirect taxes, which is what the β‚Ή 100 crore is doing arithmetically. The solution above therefore reads it that way; the discrepancy is in the printed wording, not in your method.

Rule to carry into the exam: only net indirect taxes bridge factor cost and market prices. Direct taxes, transfer payments, and receipts from second-hand sales never enter national income at all.

Problem 3 β€” Down the chain: GDPMP to PDI Illustrative

Invented figures; the chain of concepts is the textbook's (Ahuja, Ch. 2, pp. 33–37). This is the single most reliable way to be asked about the whole family of national-income aggregates at once.

Question
Itemβ‚Ή crore
Gross Domestic Product at market prices5,000
Net factor income from abroad(βˆ’) 50
Depreciation400
Indirect taxes600
Subsidies150
Undistributed corporate profits200
Corporate profit tax120
Social security contributions by employees80
Transfer payments to households250
Personal (direct) taxes300

Find GNPMP, NNPMP, National Income (NNPFC), Personal Income and Personal Disposable Income.

Solution β€” work strictly downward, one deduction at a time
GDPMP 5,000 + Net factor income from abroad βˆ’ 50 GNPMP 4,950 βˆ’ Depreciation βˆ’ 400 NNPMP 4,550 βˆ’ Net indirect taxes (600 βˆ’ 150 = 450) βˆ’ 450 NNPFC = NATIONAL INCOME 4,100 βˆ’ Undistributed corporate profits βˆ’ 200 βˆ’ Corporate profit tax βˆ’ 120 βˆ’ Social security contributions βˆ’ 80 + Transfer payments + 250 PERSONAL INCOME 3,950 βˆ’ Personal (direct) taxes βˆ’ 300 PERSONAL DISPOSABLE INCOME 3,650

Whatever is left β€” β‚Ή 3,650 crore β€” is what households can actually do something with, and it splits exactly into consumption and saving: PDI = C + S.

⚠ Where marks are lost here
  • Subtracting indirect taxes instead of net indirect taxes. Subsidies must be netted off first (600 βˆ’ 150 = 450).
  • Getting the sign of NFIA wrong. NFIA is added to GDP to reach GNP, even when it is negative.
  • Adding transfer payments to National Income. Transfers are not payment for any productive service, so they are excluded from NI β€” but they are income to a household, so they come back in at the Personal Income step.
  • Deducting personal taxes before Personal Income. Corporate taxes are deducted at the NI β†’ PI step; personal taxes are deducted at the PI β†’ PDI step.

Problem 4 β€” Nominal GNP, real GNP and the deflator Illustrative

Question

An economy's nominal GNP is β‚Ή 8,400 crore in 2024–25. The GNP deflator for that year, taking 2011–12 as base (= 100), is 175. Find real GNP. If nominal GNP rises by 12% the next year while real GNP rises by 5%, what happens to the deflator?

Solution
Nominal GNP 8,400 Real GNP = ───────────────── Γ— 100 = ─────── Γ— 100 = β‚Ή 4,800 crore Deflator 175

Next year. Scale each series by its own growth rate, then re-take the ratio.

Nominal GNP = 8,400 Γ— 1.12 = 9,408 Real GNP = 4,800 Γ— 1.05 = 5,040 9,408 Deflator = ─────────── Γ— 100 = 186.67 5,040

The deflator rose from 175 to 186.67 β€” an increase of about 6.7%, which is the inflation rate for the year. Note the shortcut: nominal growth (12%) β‰ˆ real growth (5%) + inflation (β‰ˆ7%). Prices, not extra output, account for more than half of the money-value increase.

Problem 5 β€” Completing a consumption–saving schedule TB

Ahuja, Ch. 6, Questions for Review Q.12 β€” p. 169

Question

Given disposable income (Yd) and consumption at the initial level of income (β‚Ή 100), and assuming the marginal propensity to consume is 50 per cent, complete the table and draw the graphs of the consumption and saving functions.

YdCSAPCMPCAPSMPS
100150?????
200??????
300??????
400??????
500??????
600??????
Solution

Step 1 β€” Write the consumption function. MPC = 0.5, so C = a + 0.5Y. Substitute the one point you are given, Y = 100 and C = 150:

150 = a + 0.5(100) ⟹ 150 = a + 50 ⟹ a = 100 C = 100 + 0.5Y and so S = Y βˆ’ C = βˆ’100 + 0.5Y

Step 2 β€” Fill the table. Each row is C from the function, S = Y βˆ’ C, then the four ratios.

YdCSAPC = C/YMPC = Ξ”C/Ξ”YAPS = S/YMPS = Ξ”S/Ξ”Y
100150βˆ’501.50β€”βˆ’0.50β€”
20020001.000.50.000.5
300250500.8330.50.1670.5
4003001000.7500.50.2500.5
5003501500.7000.50.3000.5
6004002000.6670.50.3330.5

Step 3 β€” Read the three things the examiner wants you to notice.

  • APC falls (1.50 β†’ 0.667) while MPC stays constant at 0.5. That is exactly the property the textbook's Fig. 6.3 illustrates.
  • APC + APS = 1 and MPC + MPS = 1 in every single row. Check one: at Y = 300, 0.833 + 0.167 = 1. βœ“
  • At Y = 200, C = Y and S = 0. This is the break-even level of income. Below it the economy dissaves (S is negative); above it, it saves.

Confirm the break-even algebraically: Y* = a / (1 βˆ’ b) = 100 / (1 βˆ’ 0.5) = 200. βœ“

Step 4 β€” The graph (what to draw)

Two panels, stacked, sharing the same income axis β€” exactly the pair of figures on p. 151 and p. 156:

  • Upper panel: the 45Β° line from the origin, and the consumption line C = 100 + 0.5Y starting at an intercept of 100 on the vertical axis. They cross at Y = 200. Label the gap above the 45Β° line (Y < 200) as dissaving and the gap below it (Y > 200) as saving.
  • Lower panel: the saving line S = βˆ’100 + 0.5Y, starting at βˆ’100 and cutting the income axis at Y = 200. The vertical distance of this line from the axis at any income equals the C–45Β° gap directly above it.

Both diagrams are reproduced on Unit 2 β€” Consumption Function and Saving Function.

Problem 6 β€” The textbook's own schedule TB

Ahuja, Ch. 6, p. 152 (Table 6.1, described in the text) and p. 153 (Table 6.2)

Question β€” linear case

The textbook's discussion of Table 6.1 states that at an income of β‚Ή 1,000 crore consumption is β‚Ή 950 crore (APC = 0.95), and that when income rises to β‚Ή 1,200 crore consumption rises to β‚Ή 1,090 crore (APC = 0.908), with MPC constant throughout. Find the consumption function, then tabulate C, S, APC and APS from β‚Ή 1,000 crore to β‚Ή 1,500 crore in steps of β‚Ή 100 crore.

Solution

Step 1 β€” MPC from the two given points.

Ξ”C 1090 βˆ’ 950 140 MPC = ──── = ───────────── = ───── = 0.7 Ξ”Y 1200 βˆ’ 1000 200

Step 2 β€” Autonomous consumption.

950 = a + 0.7(1000) ⟹ a = 950 βˆ’ 700 = 250 C = 250 + 0.7Y S = βˆ’250 + 0.3Y

Step 3 β€” The schedule. (The two anchor rows in bold are the textbook's; the remaining rows follow from the same linear function.)

YCSAPCAPSMPCMPS
1,000950500.9500.050β€”β€”
1,1001,020800.9270.0730.70.3
1,2001,0901100.9080.0920.70.3
1,3001,1601400.8920.1080.70.3
1,4001,2301700.8790.1210.70.3
1,5001,3002000.8670.1330.70.3

APC falls steadily; MPC does not move. The break-even income here is Y* = 250 / 0.3 = β‚Ή 833.3 crore β€” below the whole range shown, which is why every row saves.

Question β€” non-linear case (Table 6.2, p. 153)

The textbook also gives a schedule where MPC itself falls. Reproduced here as printed:

Y (β‚Ή crore)C (β‚Ή crore)APC = C/YMPC = Ξ”C/Ξ”Y
1,0009500.950β€”
1,1001,0400.94590/100 = 0.9
1,2001,1200.93380/100 = 0.8
1,3001,1900.91570/100 = 0.7
1,4001,2500.89360/100 = 0.6
1,5001,3000.86650/100 = 0.5

What to say about it: when both APC and MPC decline, the consumption function is no longer a straight line β€” it is concave to the income axis, as in the textbook's Fig. 6.4. Compare this with the linear case above, where only APC declined.

Problem 7 β€” The investment multiplier Illustrative

The multiplier is the quantity that fixes the slope of the IS curve β€” see Unit 2 β€” IS-LM, textbook Ch. 12 pp. 299–303.

Question

In an economy the consumption function is C = 200 + 0.75Y (β‚Ή crore). Autonomous investment is β‚Ή 400 crore. (a) Find the multiplier. (b) Find equilibrium income. (c) If investment rises by β‚Ή 100 crore, by how much does income rise? (d) What would happen to your answer to (c) if MPC were 0.6 instead?

Solution

(a) Multiplier.

1 1 1 k = ───────── = ───────── = ───── = 4 1 βˆ’ MPC 1 βˆ’ 0.75 0.25

(b) Equilibrium income. Income is at equilibrium where Y = C + I.

Y = 200 + 0.75Y + 400 Y βˆ’ 0.75Y = 600 0.25Y = 600 Y = β‚Ή 2,400 crore

Or, faster, using the multiplier on total autonomous spending: Y = k Γ— (a + I) = 4 Γ— (200 + 400) = 2,400. βœ“

(c) Effect of Ξ”I = 100.

Ξ”Y = k Γ— Ξ”I = 4 Γ— 100 = β‚Ή 400 crore (new equilibrium income = β‚Ή 2,800 crore)

(d) With MPC = 0.6.

k = 1 / (1 βˆ’ 0.6) = 2.5 ⟹ Ξ”Y = 2.5 Γ— 100 = β‚Ή 250 crore

The point of part (d): a lower MPC means a bigger leakage into saving at every round, so the multiplier is smaller and the same injection produces less income. This is precisely why a higher MPC makes the IS curve flatter and fiscal policy more powerful.

⚠ Where marks are lost here
  • Using 1/MPC instead of 1/(1 βˆ’ MPC). The multiplier is the reciprocal of the leakage, not of the spending share.
  • Reporting Ξ”Y as the new income level rather than the change. Read the question: "by how much does income rise" wants 400, not 2,800.
  • Forgetting that autonomous consumption a is also multiplied when you compute the level of Y β€” only the change in I is multiplied when you compute Ξ”Y.

Practice set β€” try these unaided

No solutions given β€” the method for each is worked above
  1. An economy has three firms. Firm X sells β‚Ή 500 to households and β‚Ή 200 to Firm Y; Firm Y sells β‚Ή 400 to households and β‚Ή 100 to Firm Z; Firm Z sells β‚Ή 300 to households. Firm X imports β‚Ή 150. Find each firm's value added and GDPMP. (method: Problem 1)
  2. Given GNPMP = β‚Ή 6,200 crore, depreciation β‚Ή 500 crore, indirect taxes β‚Ή 700 crore, subsidies β‚Ή 200 crore, undistributed profits β‚Ή 150 crore, corporate tax β‚Ή 100 crore, transfer payments β‚Ή 300 crore and personal taxes β‚Ή 400 crore, find National Income, Personal Income and PDI. (method: Problem 3)
  3. Nominal GNP is β‚Ή 12,000 crore and real GNP is β‚Ή 8,000 crore. Find the GNP deflator, and state the inflation since the base year. (method: Problem 4)
  4. C = 60 + 0.8Y. Find (a) the saving function, (b) the break-even income, (c) APC and APS at Y = 500, and (d) verify APC + APS = 1. (method: Problem 5)
  5. At Y = 400, C = 380; at Y = 600, C = 520. Find MPC, MPS, the consumption function, the saving function and the multiplier. (methods: Problems 6 and 7)
  6. An economy with MPC = 0.8 wants to raise national income by β‚Ή 1,000 crore. By how much must autonomous investment increase? (method: Problem 7, rearranged)
Exam habits that save marks in every numerical
  • Write the formula before the numbers. Method marks are usually awarded separately from the final answer.
  • Carry units. "β‚Ή 1,570 crore", not "1570".
  • Cross-check by the second method whenever both are computable β€” as in Problem 2, agreement between income and expenditure methods is itself worth stating.
  • State the identity you used. One line such as "APC + APS = 1, verified at Y = 300" shows the examiner you understood rather than substituted.