Applied calculation and case workbook
All rupee amounts, populations, rates and output figures in this workbook are hypothetical teaching inputs. They are not estimates for India or Andhra Pradesh. Read the assumptions in each problem before applying a formula.
Case 01 — Compare the next-best use
Households, firms, banks, government and trade respond to shared shocks. | Original explanatory diagram; schematic, not a measured data chart.
A town has ₹12 lakh available for one small public facility. A bus shelter costs ₹10 lakh and is expected to serve 400 daily users. A market shed costs ₹12 lakh and could serve 200 traders; a repair to a water point costs ₹7 lakh and could protect access for 600 households. Assume the town can choose exactly one project this year and has no carry-forward funds. What is the opportunity cost of selecting the bus shelter?
Worked answer. The opportunity cost is the value of the best feasible alternative forgone: either the market shed or water-point repair, depending on the town's stated objective and valuation of benefits. We cannot choose by comparing users alone because 400 daily commuters, 200 traders and 600 households are different units and benefit types. The foregone alternative is not both rejected projects added together. Nor is the opportunity cost simply the ₹10 lakh price of the shelter. The problem needs a criterion—such as access, economic return, equity, urgency or cost-benefit—before ranking. The question teaches the definition, not a definitive allocation recommendation.
Case 02 — Avoid double counting
A farm sells vegetables to a processor for ₹80,000. The processor spends ₹50,000 on purchased inputs and sells packaged produce for ₹1,40,000. A retailer buys it and sells to households for ₹2,00,000. Calculate value added at the farm, processor and retail stage if the retailer's purchase price is ₹1,40,000 and other costs are ignored.
Worked answer. Farm output contributes ₹80,000, assuming no intermediate purchases are listed. The processor's value added is ₹1,40,000 − ₹80,000 − ₹50,000 = ₹10,000 if the ₹50,000 input is additional to the purchased vegetables. Retail value added is ₹2,00,000 − ₹1,40,000 = ₹60,000. The total represented in this simplified chain is ₹1,50,000, matching final sales minus the processor's other intermediate inputs. The numbers demonstrate why we cannot add each sale (₹80,000 + ₹1,40,000 + ₹2,00,000) as new output: that would count the produce at every resale stage. Actual accounts require more detail about inputs, taxes, inventory and service charges.
Case 03 — Growth and population
An imaginary region's constant-price output is ₹20,000 crore in Year A and ₹21,000 crore in Year B. Population grows from 20 lakh to 21 lakh. Find total real-output growth and the per-capita output for both years.
Worked answer. Total real output rises by ₹1,000 crore on a base of ₹20,000 crore, or 5%. Year A per-capita output is ₹20,000 crore divided by 20 lakh, equal to ₹1 lakh per person. Year B is ₹21,000 crore divided by 21 lakh, also ₹1 lakh per person. The average is unchanged because output and population grew at the same proportional rate. It remains an average; the exercise says nothing about distribution, household earnings or public services. Check unit conversion before a live calculation: one crore is ten million and one lakh is one hundred thousand.
Case 04 — Index level versus rate
The price index is 100 in the base period, 105 in the next period and 110.25 in the third. Calculate the inflation rate in each period and the total price-level change from the base.
Worked answer. First-period inflation is `(105−100)/100 ×100 = 5%`. Second-period inflation is `(110.25−105)/105 ×100 = 5%`. The cumulative price-level increase is 10.25%, not 10%, because the second 5% is applied to 105. The index level 110.25 does not mean inflation is 110.25%. In an official CPI question, identify the series and base; the invented calculation is not a reported CPI value.
Case 05 — Interest and contract timing
A hypothetical firm borrows ₹2,00,000 at 9% annual simple interest for one year. A separate loan is floating-rate and reprices after three months. Calculate simple interest on the first loan and state whether the second loan's instalment changes immediately when a policy rate is announced.
Worked answer. Simple annual interest is principal × rate × time: ₹2,00,000 × 0.09 × 1 = ₹18,000. This assumes the full principal is outstanding for a full year and no compounding or repayments occur. The second loan cannot be answered from the policy announcement alone: the contract benchmark, reset date, spread and bank pass-through determine the change. The exercise separates arithmetic from transmission. The simple-interest calculation is not a substitute for an amortisation or EMI schedule.
Case 06 — Bank asset and liability totals
A small bank has customer deposits of ₹9 crore, other borrowing of ₹1 crore and equity of ₹1 crore. Its assets are loans of ₹7 crore, investments of ₹2 crore and cash/reserves of ₹2 crore. Check the accounting identity and identify the bank's liability to depositors.
Worked answer. Assets total ₹11 crore. Liabilities other than equity total ₹10 crore (₹9 crore deposits plus ₹1 crore borrowing); equity is ₹1 crore. Liabilities plus equity equal ₹11 crore, so the simplified balance sheet balances. The bank owes customers the ₹9 crore in deposits, subject to account terms and applicable law. Loans and investments are assets because they represent claims or holdings. This balance sheet is only a teaching example; regulatory statements classify items in more detail. Deposit protection is not calculated by applying a blanket amount to the whole bank balance sheet.
Case 07 — Deficit calculation with missing data
Total expenditure is ₹5,000 crore, revenue receipts are ₹3,800 crore, non-debt capital receipts are ₹200 crore and interest payments are ₹350 crore. Calculate fiscal deficit and primary deficit. Can revenue deficit be calculated?
Worked answer. Simplified fiscal deficit = total expenditure − revenue receipts − non-debt capital receipts = ₹5,000 − ₹3,800 − ₹200 = ₹1,000 crore. Primary deficit = fiscal deficit − interest payments = ₹1,000 − ₹350 = ₹650 crore. Revenue deficit cannot be calculated because revenue expenditure is missing. Do not subtract interest from total expenditure to calculate revenue deficit; the formulas are different. For official documents, use the exact account scope and published definition.
Case 08 — Tax amount and incidence
A hypothetical invoice has a taxable value of ₹10,000 and a supplied GST rate of 12%. The seller has ₹600 of eligible input tax credit. Find output tax and the net tax after credit, ignoring other rules. Who bears the economic burden?
Worked answer. Output tax = ₹10,000 × 12% = ₹1,200. Net amount after the stated eligible credit = ₹1,200 − ₹600 = ₹600. The problem explicitly supplies the rate and credit eligibility; do not infer a live product rate. The legal remitter is governed by tax rules. The ultimate economic burden cannot be calculated from the invoice alone; it depends on whether prices, margins, wages or supplier terms adjust. This distinction separates mechanical tax arithmetic from incidence analysis.
Case 09 — State grant stages
A state agency receives approval for a ₹50 crore grant to local bodies. ₹35 crore is released during the year, and local bodies record ₹28 crore of eligible expenditure by year-end. Calculate the release-to-approval ratio and expenditure-to-release ratio. What do these ratios not show?
Worked answer. Release-to-approval is 35/50 = 70%. Expenditure-to-release is 28/35 = 80%. They describe stages of the flow using the stated denominator. They do not alone explain why the remaining amount was unreleased or unspent, whether commitments exist, or whether service outcomes were achieved. Check conditions, matching requirements, timing, project readiness and accounts. Approval, release, cash receipt, expenditure and outcomes are related but distinct.
Case 10 — Labour-force denominator
In a hypothetical group, 8,000 people are in the relevant population. Of them, 5,000 are in the labour force and 250 are unemployed under the supplied definition. Calculate the unemployment rate. If 250 people stop seeking and leave the labour force, with all other statuses unchanged, what is the new rate?
Worked answer. Initial unemployment rate = 250/5,000 ×100 = 5%. After the 250 stop seeking, the labour force is 4,750 and unemployed are zero for this stylised calculation, so the measured rate becomes 0%. This does not mean all 250 found work; the problem says they left the labour force. Real survey classification requires the official availability and reference-period rules. The example shows why participation and employment measures should accompany unemployment.
Case 11 — Farm margin and loss
A farmer harvests 12 tonnes of produce. At ₹25,000 per tonne, gross sale value before loss is ₹3 lakh. Storage loss is 1.2 tonnes; transport and input costs are ₹1.5 lakh in total. Find sale value after loss and a simple net return before any other costs.
Worked answer. Marketable volume is 12 − 1.2 = 10.8 tonnes. At the stated price, sales are 10.8 × ₹25,000 = ₹2,70,000. Simple net return is ₹2,70,000 − ₹1,50,000 = ₹1,20,000. This simplified figure excludes family labour valuation, land rent, interest, taxes and any quality premium. It shows that reducing loss can increase saleable output without increasing harvest quantity; the actual benefit depends on storage costs and whether buyers accept the quality.
Case 12 — Productivity and capacity use
A workshop produces 800 units in 400 worker-hours. After training and maintenance, it produces 900 units in the same hours. Calculate output per worker-hour before and after and the percentage change. What is the limitation of the result?
Worked answer. Before: 800/400 = 2 units per hour. After: 900/400 = 2.25 units per hour. Increase is 0.25/2 ×100 = 12.5%. The measure does not show product quality, safety, input use, unpaid overtime or whether demand supports the additional output. To conclude that welfare improved, examine wages, hours, job security and other outcomes. Productivity is useful but not a complete social measure.
Case 13 — Digital-service completion rate
A public portal receives 1,000 applications. 800 are submitted successfully, and 720 are resolved within the stated service period. Calculate submission success as a share of all applications and timely resolution as a share of submitted cases. What further data would help?
Worked answer. Submission success is 800/1,000 = 80%. Timely resolution is 720/800 = 90% of successfully submitted cases. If the denominator is all applications, timely resolutions are 72%. Both ratios are valid but answer different questions. To assess access, also inspect abandonment, authentication failures, assisted/offline completion, language accessibility, complaints, fraud and repeat submissions. A transaction count alone is not a complete service-quality measure.
Case 14 — Exchange conversion and trade account
An importer owes US$2,500. The exchange quote is ₹82 per US dollar. The rupee weakens to ₹84 before settlement. Calculate the rupee cost at each rate and the increase, ignoring fees. Classify the purchase of imported machinery conceptually.
Worked answer. At ₹82, cost is ₹2,500 ×82 = ₹2,05,000. At ₹84, cost is ₹2,10,000. The increase is ₹5,000, about 2.44% of the original rupee cost. The actual invoice could be hedged, fixed, or include other charges. Imported machinery is a goods import in the current account; when acquired for productive use it may also be recorded in domestic investment under national accounts, with imports subtracted in the expenditure identity to retain domestic production. Do not confuse the two accounting views.
Case 15 — Cost per sustained outcome
A training programme costs ₹1.2 crore and enrolls 600 people. 480 complete the course; 180 remain in a relevant job six months later. Calculate cost per enrollee, completer and sustained placement. What should the reader avoid concluding?
Worked answer. Cost per enrollee is ₹1.2 crore/600 = ₹20,000. Cost per completer is ₹1.2 crore/480 = ₹25,000. Cost per sustained placement is ₹1.2 crore/180 ≈ ₹66,667. The ratios use different outcomes and denominators. They do not show causal impact without a counterfactual, job quality, baseline or programme selection information. A programme may still be worthwhile for non-employment benefits; evaluation should state the objective and compare alternatives.
Case 16 — Unit conversion and state comparison
State A reports GSDP of ₹8 lakh crore and State B ₹75,000 crore. Convert State A to crore and State B to lakh crore. Can these totals establish which state grew faster?
Worked answer. One lakh crore equals 100,000 crore. State A is ₹8,00,000 crore; State B is ₹0.75 lakh crore. The levels show State A's stated aggregate is larger, assuming the same year and series. They do not establish growth rates, price basis, per-capita output or welfare. For a growth comparison, obtain the same indicator at two periods, under compatible series and price basis, and calculate the percentage change. Convert all units before comparing.
Case 17 — Check a headline rise
A report says collections rose 20%, from ₹500 crore to ₹610 crore. Recalculate the percentage. If the comparison is RE for one year and actual for another, what label should accompany it?
Worked answer. Increase = ₹610 − ₹500 = ₹110 crore. Percentage = 110/500 ×100 = 22%, not 20%, before considering rounding. If the amounts are RE and actual, say exactly which estimate stage and financial year each represents. The comparison may be informative but should not be labelled as actual year-on-year growth if one amount is an estimate. Also check that both values refer to the same receipt category and accounting scope.
Case 18 — Combine the channels
A food processor borrows ₹10 lakh at a stated annual simple rate of 10%, buys local produce worth ₹6 lakh and imported packaging worth ₹2 lakh at ₹80 per foreign-currency unit per assumed unit of import cost, then sells final output for ₹12 lakh. Calculate annual simple interest and the rupee change in packaging if the exchange rate becomes ₹84, holding its foreign price constant. Which measures are still missing for profit?
Worked answer. Annual simple interest is ₹1 lakh, assuming the full loan remains outstanding for one year. The imported packaging's rupee cost rises by 5% because 84/80 = 1.05; if its original rupee value was ₹2 lakh, the new value is ₹2.1 lakh, an increase of ₹10,000. A simple residual of sales minus listed produce, packaging and interest would be ₹12 lakh − ₹6 lakh − ₹2 lakh − ₹1 lakh = ₹3 lakh before the exchange change and before other costs. Under the changed exchange rate it becomes ₹2.9 lakh on the same assumptions. Wages, electricity, transport, depreciation, taxes, other inputs, inventory and sales timing are still missing; therefore this is not net profit. It demonstrates how one external-price change can flow into firm cost without proving its final outcome.
Case 19 — Separate nominal growth from volume growth
An imaginary producer sells 1,000 units for ₹100 each in Year 1 and 1,050 units for ₹110 each in Year 2. Calculate nominal sales in each year, nominal growth and real volume growth at the Year 1 price. What conclusion can the numbers support?
Worked answer. Year 1 nominal sales are 1,000 × ₹100 = ₹1,00,000. Year 2 sales are 1,050 × ₹110 = ₹1,15,500. Nominal sales rise by ₹15,500, or 15.5% of ₹1,00,000. At the Year 1 price, Year 2 volume is worth 1,050 × ₹100 = ₹1,05,000, a 5% real volume increase in this one-product example. The remaining nominal rise reflects the price change and its interaction with quantity. The result is not an official GDP estimate and does not describe quality, costs or profit. It supports the limited statement that nominal receipts rose 15.5% while units sold rose 5% under the stated price basis.
Case 20 — Use compatible denominators
Two hypothetical districts report 300 unemployed people each. District X has a labour force of 6,000 and District Y has a labour force of 10,000. Calculate each unemployment rate. A headline says the districts have the same unemployment problem because their unemployed counts are equal. Assess it.
Worked answer. District X's rate is 300/6,000 ×100 = 5%. District Y's rate is 300/10,000 ×100 = 3%. The equal counts do not imply equal rates because the denominators differ. Even the rates alone do not reveal job quality, duration, participation, age structure or survey uncertainty. A fair comparison also checks that both use the same definition, reference period and survey method. The headline is correct only about counts; it is not sufficient evidence that labour-market conditions are otherwise identical.
Case 21 — Separate price and volume change
A local food processor's sales rise from ₹20 lakh to ₹23.1 lakh. Over the same comparison, the price index for its product rises from 100 to 110. Assume the index captures the full price change and the product mix is unchanged. Estimate the real sales change at the earlier price level. What limitation remains?
Worked answer. Deflate later sales by the price relative: ₹23.1 lakh ÷ 1.10 = ₹21 lakh at the earlier price level. Real sales therefore rise from ₹20 lakh to ₹21 lakh, or 5%. Nominal sales rose by 15.5%; the difference reflects the assumed price change and its interaction with quantity. This is a teaching calculation, not an official GDP estimate. The result depends on the price index, unchanged product mix and quality; it says nothing by itself about costs, profit or welfare.