BECC 102 key facts: June 2026
- Course code: BECC 102
- Subject: Mathematical Methods in Economics-I (eGyanKosh book title: Mathematical Methods for Economics-I)
- Programme: IGNOU Bachelor of Arts (Honours) Economics (BAECH), Semester I core course
- Credits: 6
- Blocks and units: 6 blocks, 16 units
- Maximum marks: 100 (term-end exam 70% weightage, one TMA 30%)
- Duration: 3 hours
- Questions in the June 2026 paper: 12 questions (24 sub-parts) across Sections A, B and C; printed code B-2468
- Samples shown on this page: 2 (Q1 and Q2, both 20-mark Section A questions); all 12 in the paid file
BECC 102 Solved Question Paper for June 2026 gives you complete, step-by-step answers to the official IGNOU term-end paper of Mathematical Methods in Economics-I. Two answers are open below so you can judge the working; the full file with all 12 questions comes on WhatsApp 9899436384.
1. What the June 2026 Solved Paper Covers
BECC 102 Mathematical Methods in Economics-I is a 6-credit core course of IGNOU's Bachelor of Arts (Honours) Economics (BAECH) that turns sets, calculus, geometry and difference equations into tools for economic analysis.
The June 2026 paper has 12 questions. Section A opens with a monopolist whose average cost falls as output rises, a cobweb model whose supply and demand slopes are both 6, a marginal revenue and elasticity problem, and a difference equation with a 2t5t term on the right side.
Section B moves across the book: phase diagrams, a GP whose terms add up to 315, domain and range, a parabola and a circle, the present value of a ₹700 deposit plus three ₹500 instalments, and total revenue from a given MR function. Section C closes with two limits and short notes on theorem, proof and the point of inflexion.
The solved file answers every one of these in the order printed. Each answer states the formula, shows the working, checks the result and then explains what the number means for a firm or a market, which is the part examiners in this course look for after the arithmetic.
2. Two Answers Solved in Full, Ten Held Back
Questions 1 and 2 of the June 2026 paper are solved in full below; both are 20-mark Section A questions, so together they show 40 marks of working.
The question text is copied exactly as printed in the English version of the paper, including its own numbering and marks.
Monopoly profit maximisation and the cost-minimising output
Question 1 (a): A monopolist has a demand curve x = 106 − 2p and an average cost curve AC = 5 − x/50, where p is the price per unit of output and x is the number of units of output. Determine the most profitable level of output and the maximum profit. (12)
Question 1 (b): For a particular process, the cost function is given by C = 56 − 8x + x2, where C is cost per unit and x is the number of units produced. Find the cost minimising level of output. (8)
(a) Most profitable output and maximum profit
Step 1: revenue. Rewrite the demand curve with price on the left: p = 53 − x/2. Total revenue is TR = p × x = 53x − x2/2.
Step 2: cost. Total cost is average cost multiplied by output: TC = AC × x = 5x − x2/50.
Step 3: profit function. π = TR − TC = 53x − x2/2 − 5x + x2/50 = 48x − (24/50)x2 = 48x − (12/25)x2.
Step 4: first order condition. dπ/dx = 48 − (24/25)x = 0, so x = 48 × 25/24 = 50 units.
Step 5: second order condition. d2π/dx2 = −24/25, which is negative, so x = 50 gives a maximum and not a minimum.
Step 6: price and maximum profit. At x = 50 the price is p = 53 − 25 = ₹28. TR = 28 × 50 = 1,400 and TC = 5(50) − 2,500/50 = 250 − 50 = 200. Maximum profit = 1,400 − 200 = ₹1,200.
Check with MR = MC. MR = d(TR)/dx = 53 − x and MC = d(TC)/dx = 5 − x/25. At x = 50, MR = 3 and MC = 3, so the marginal condition holds. MR falls with slope −1 while MC falls with the gentler slope −1/25, so MC cuts MR from below, which is exactly the second order condition in marginal form.
Economic reading. Average cost falls as output rises (AC is ₹4 at 50 units), yet the firm still stops at 50 because marginal revenue drops faster than marginal cost. The most profitable output is 50 units, sold at ₹28 each, earning a maximum profit of ₹1,200.
(b) Cost-minimising level of output
Step 1: read the function carefully. Here C = 56 − 8x + x2 is cost per unit, so we minimise average cost directly.
Step 2: first order condition. dC/dx = −8 + 2x = 0, which gives x = 4.
Step 3: second order condition. d2C/dx2 = 2, which is positive, so x = 4 is a minimum.
Step 4: minimum cost. C(4) = 56 − 32 + 16 = 40 per unit, so total cost at this output is 4 × 40 = 160. A quick algebraic check: C = (x − 4)2 + 40, which can never fall below 40 and reaches it only at x = 4.
Economic reading. The per unit cost curve is U-shaped: it falls while output rises to 4 units and rises after that. The cost minimising level of output is 4 units, at a minimum cost of 40 per unit.
Cobweb model: intertemporal equilibrium price and stability
Question 2: Consider the demand and supply functions of a cobweb model. (20)
Qd = 19 − 6pt
Qs = −5 + 6pt−1(a) Find the intertemporal equilibrium price. (14)
(b) Determine whether the equilibrium is stable, unstable or regular. (6)
(a) Intertemporal equilibrium price
Set-up. In a cobweb model, producers decide supply on the basis of last period's price (a farmer plants this season using last season's price), while buyers respond to the current price. So demand depends on pt and supply on pt−1.
Note on the paper: the Hindi version prints the supply lag as t + 1; the English version shows the standard lag t − 1, and this solution follows it.
Step 1: market clearing in every period. Qd = Qs gives 19 − 6pt = −5 + 6pt−1.
Step 2: the difference equation. Rearranging, 6pt + 6pt−1 = 24, so pt + pt−1 = 4, or pt = −pt−1 + 4. This is a first order linear non-homogeneous difference equation.
Step 3: intertemporal equilibrium price. In equilibrium the price does not change from period to period, so put pt = pt−1 = p̄. Then 2p̄ = 4 and p̄ = 2. Equilibrium quantity: Qd = 19 − 6(2) = 7 and Qs = −5 + 6(2) = 7, so Q̄ = 7.
Step 4: general formula check. With Qd = α − βpt and Qs = −γ + δpt−1, the equilibrium is p̄ = (α + γ)/(β + δ). Here α = 19, β = 6, γ = 5 and δ = 6, so p̄ = 24/12 = 2, which matches.
Step 5: complete time path. The complementary function is A(−δ/β)t = A(−1)t and the particular solution is p̄ = 2. So pt = A(−1)t + 2. At t = 0, p0 = A + 2, giving A = p0 − 2. The time path is pt = (p0 − 2)(−1)t + 2.
(b) Stability of the equilibrium
Rule. The behaviour of the time path depends on b = −δ/β. A negative b means the price alternates above and below p̄ (oscillation). If |b| < 1 the swings shrink (stable), if |b| > 1 they grow (unstable), and if |b| = 1 they stay the same size.
Applying it. Here b = −6/6 = −1. It is negative, so the path oscillates, and |b| = 1, so the oscillation neither dies out nor explodes. The equilibrium is therefore regular: a uniform oscillation of constant amplitude around p̄ = 2.
Numerical illustration. Suppose p0 = 3. Then p1 = −3 + 4 = 1, p2 = −1 + 4 = 3, p3 = 1, and so on. The price keeps jumping between 3 and 1 and never settles at 2. Check: supply in period 1 is −5 + 6(3) = 13, and demand at p1 = 1 is 19 − 6 = 13, so the market clears each period.
Economic reading. Regular oscillation happens because the supply slope (δ = 6) equals the demand slope in absolute value (β = 6). Producers overreact to last period's price by exactly as much as buyers respond to this period's price, so the cobweb traces the same box forever.
3. Questions Answered Only in the Full File
The 10 questions below are printed exactly as they appear in the June 2026 paper. Their solutions are in the full file only.
Question 3: A monopolist faces a demand function P = 15 − (1/5)q, where P is the price and q is quantity. (20)
(a) Find the expression for marginal revenue. (6)
(b) Calculate the price elasticity of demand. (6)
(c) Does the relationship between Average Revenue (AR), Marginal Revenue (MR) and elasticity hold in this case? Show. (8)
Question 4 (a): Differentiate between homogeneous and non-homogeneous difference equations. (8)
Question 4 (b): Solve the following difference equation: yt+1 + 7yt = 2t5t (12)
Question 5 (a): What are phase diagrams? What are they used for? (6)
Question 5 (b): What are non-linear difference equations? How are they linearised? (6)
Question 6 (a): The sum of some terms of a GP is 315. Its first term is 5 and the common ratio is 2. Find the number of its terms and the last term. (6)
Question 6 (b): Find the tenth term of a GP whose third term is 16 and seventh term is 1. (6)
Question 7 (a): What do you understand by the domain and range of a function? (6)
Question 7 (b): Explain the various properties of relations. (6)
Question 8 (a): Write the equation of a parabola with focus (0, 2) and directrix x = −2. (6)
Question 8 (b): Show that the graph of x2 + y2 − 2x + 6y − 6 = 0 is a circle. Also find its centre and radius. (6)
Question 9 (a): A departmental store advertises a product at a ₹700 deposit and three further equal annual payments of ₹500. If the discount rate is 10%, calculate the present value of the good. (8)
Question 9 (b): How is the concept of present value related to the discounting principle? Explain. (4)
Question 10: Let the Marginal Revenue (MR) function of firm A be 60/(x + 3)2 − 2. Find total revenue. Also derive the demand function. (12)
Question 11: Evaluate the following limits. (6)
(a) the limit as x → ∞ of (1 − x5)/(x5 + x + 1)
(b) the limit as x → 1 of (x4 − 3x3 + 2)/(x3 − 5x2 + 3x + 1)
Question 12: Explain the following. (6)
(a) Theorem and proof
(b) Point of inflexion
4. Blocks and Units
BECC 102 has 6 blocks and 16 units, running from sets and logic in Block 1 to linear and non-linear difference equations in Block 6.
eGyanKosh files the book as Mathematical Methods for Economics-I, while the exam paper prints Mathematical Methods in Economics-I; both names refer to the same course. If you need the unit-wise book first, start with our BECC 102 Study Material page and come back to this paper for exam practice.
| Block | Units | Topics to master | June 2026 questions |
|---|---|---|---|
| Block 1: Preliminaries | Unit 1 Sets and Set Operations; Unit 2 Relations and Functions; Unit 3 Logic | Domain and range of a function, reflexive, symmetric and transitive relations, direct proof and proof by contradiction | Q7, Q12(a) |
| Block 2: Functions of One Independent Variable | Unit 4 Elementary Types of Functions; Unit 5 Analytical Geometry; Unit 6 Sequences and Series | Parabola from focus and directrix, circle centre and radius, geometric progressions and present value | Q6, Q8, Q9 |
| Block 3: Differentiation | Unit 7 Limits; Unit 8 Continuity; Unit 9 First-Order Derivatives; Unit 10 Higher-Order Derivatives | Limits of rational functions, continuity tests, marginal revenue and price elasticity from a demand function | Q3, Q11 |
| Block 4: Single-Variable Optimisation | Unit 11 Concave and Convex Functions; Unit 12 Optimisation Methods | Concavity and point of inflexion, profit maximisation for a monopolist, minimum average cost output | Q1 (Sample 1), Q12(b) |
| Block 5: Integration | Unit 13 Indefinite Integrals; Unit 14 Definite Integrals | Total revenue from a marginal revenue function, total cost from marginal cost, consumer and producer surplus | Q10 |
| Block 6: Difference Equations | Unit 15 Linear Difference Equations; Unit 16 Non-Linear Difference Equations | Cobweb model stability, homogeneous and non-homogeneous equations, phase diagrams and linearisation | Q2 (Sample 2), Q4, Q5 |
Block 3 and Block 6 together supply five of the twelve June 2026 questions, so a student who is weak on derivatives or difference equations loses the widest choice in Sections A and B.
5. Paper Pattern and Marks Split
The BECC 102 question paper carries 100 marks in 3 hours: answer two of four in Section A, four of six in Section B and both questions in Section C.
| Section | Questions offered | You answer | Marks each | Section total | June 2026 sub-part split |
|---|---|---|---|---|---|
| Section A | 4 (Q1 to Q4) | Any 2 | 20 | 40 | Q1: 12 + 8; Q2: 14 + 6; Q3: 6 + 6 + 8; Q4: 8 + 12 |
| Section B | 6 (Q5 to Q10) | Any 4 | 12 | 48 | Q5 to Q8: 6 + 6 each; Q9: 8 + 4; Q10: 12 |
| Section C | 2 (Q11 and Q12) | Both | 6 | 12 | Q11: two limits; Q12: two short explanations |
This 2 × 20, 4 × 12, 2 × 6 layout is identical in every BECC 102 question paper we opened on IGNOU's own servers: December 2021, December 2023, June 2024, June 2025 and June 2026. Only the sub-part split inside each question changes.
Because Section C is compulsory, the two limits in Q11 and the short notes in Q12 are 12 marks nobody can skip. If you are preparing several papers of this programme, our BAECH Question Paper collection follows the same session-wise layout.
6. Topics IGNOU Keeps Repeating
Profit maximisation, conic sections and methods of proof appeared in all five official BECC 102 papers we compared (December 2021, December 2023, June 2024, June 2025 and June 2026).
We counted topics only from papers we could open on ignou.ac.in and webservices.ignou.ac.in. The June 2022, December 2022, June 2023, December 2024 and December 2025 papers could not be retrieved from those servers, so they are not counted and we do not claim a five-year run.
| Topic (unit) | Where it appeared | Count (of 5) | In June 2026 |
|---|---|---|---|
| Profit-maximising output and maximum profit (Unit 12) | Dec 2021 Q1(b); Dec 2023 Q4; Jun 2024 Q4 and Q9; Jun 2025 Q4; Jun 2026 Q1(a) | 5 | Q1(a) (Sample 1) |
| Theorems and methods of proof (Unit 3) | Dec 2021 Q9; Dec 2023 Q5 and Q11(b); Jun 2024 Q5 and Q11(a); Jun 2025 Q9; Jun 2026 Q12(a) | 5 | Q12(a) |
| Lines, circles and parabolas (Unit 5) | Dec 2021 Q3; Dec 2023 Q6; Jun 2024 Q6; Jun 2025 Q8; Jun 2026 Q8 | 5 | Q8 |
| Cobweb model (Unit 15) | Dec 2021 Q2 and Q7; Jun 2024 Q2(a); Jun 2025 Q2; Jun 2026 Q2 | 4 | Q2 (Sample 2) |
| Geometric progression terms and sums (Unit 6) | Dec 2023 Q7(b); Jun 2024 Q7(b); Jun 2025 Q5; Jun 2026 Q6 | 4 | Q6 |
| Evaluating limits (Unit 7) | Dec 2021 Q11; Jun 2024 Q8(a); Jun 2025 Q10; Jun 2026 Q11 | 4 | Q11 |
| Total revenue or total cost from a marginal function (Unit 13) | Dec 2021 Q6; Dec 2023 Q1(b); Jun 2024 Q1(b); Jun 2026 Q10 | 4 | Q10 |
| Order, homogeneity and linearisation of difference equations (Units 15 and 16) | Dec 2021 Q12(b); Dec 2023 Q2; Jun 2024 Q2(b); Jun 2026 Q4(a) and Q5(b) | 4 | Q4(a), Q5(b) |
| Maxima, minima and point of inflexion (Unit 11) | Dec 2021 Q12(a); Dec 2023 Q9; Jun 2025 Q11(a); Jun 2026 Q12(b) | 4 | Q12(b) |
| Continuity of a function (Unit 8) | Dec 2021 Q10; Dec 2023 Q8(b); Jun 2024 Q8(b); Jun 2025 Q12 | 4 | — |
| Market equilibrium, supply shifts and per unit tax (Unit 4) | Dec 2021 Q4(a); Dec 2023 Q3; Jun 2024 Q3; Jun 2025 Q3(b) | 4 | — |
| MR, AR and elasticity for a monopolist (Unit 9) | Dec 2021 Q1(a); Jun 2025 Q1; Jun 2026 Q3 | 3 | Q3 |
| Output with minimum average cost (Unit 12) | Dec 2023 Q10; Jun 2024 Q10; Jun 2026 Q1(b) | 3 | Q1(b) (Sample 1) |
| Interest, sinking funds and present value (Unit 6) | Dec 2023 Q7(a); Jun 2024 Q7(a); Jun 2026 Q9 | 3 | Q9 |
| Sets, relations and types of function (Units 1 and 2) | Dec 2021 Q8; Dec 2023 Q11(a); Jun 2026 Q7 | 3 | Q7 |
| Consumer and producer surplus (Unit 14) | Dec 2023 Q1(a); Jun 2024 Q1(a); Jun 2025 Q6 | 3 | — |
| Phase diagrams (Unit 16) | Jun 2026 Q5(a) only | 1 | Q5(a) |
Some June 2026 questions are straight reprints. Q6(a) and Q6(b) repeat June 2025 Q5 word for word, Q11(b) repeats June 2025 Q10(a), and the MR function in Q10 is the same one set in June 2024 Q1(b). For a wider list of likely questions across courses, see our IGNOU Solved Guess Paper page.
7. How the Answers Were Worked and Checked
Every BECC 102 answer in the file is solved by hand and then checked by substituting the result back into the original functions.
Before writing, the team worked through older BECC 102 papers from our IGNOU Previous Year Question Paper collection, so the file uses the method and notation the course book uses, such as α, β, γ and δ for cobweb slopes.
Three checks run on every numerical answer. Optimisation answers must pass both the first and second order conditions and an MR = MC cross-check. Difference equation answers are tested by putting the first few periods into the original demand and supply functions. Geometry answers are checked by expanding the final equation back to the printed form.
Where the Hindi and English versions of the paper differ, as with the supply lag in Q2, the answer says so and follows the English version. Theory answers are kept to the length the marks deserve: short and definition-led for 6 marks, fuller with an example for 12.
8. Solved File Index for All 12 Questions
The full BECC 102 file answers all 12 June 2026 questions; Q1 and Q2 are open on this page and Q3 to Q12 are in the WhatsApp file only.
BECC 102 has no practical or record work, since assessment is one tutor marked assignment plus the term-end exam. So instead of a practical file index, the table below maps every question in the solved file to its unit and marks.
| Question | What it asks | Course unit | Marks | Where to find the answer |
|---|---|---|---|---|
| Q1 | Monopoly profit maximisation; minimum cost per unit | Unit 12 | 20 | Sample 1 above |
| Q2 | Cobweb model: intertemporal equilibrium and stability | Unit 15 | 20 | Sample 2 above |
| Q3 | Marginal revenue, price elasticity, AR and MR relationship | Unit 9 | 20 | Full file |
| Q4 | Homogeneous versus non-homogeneous equations; solving a first order equation | Unit 15 | 20 | Full file |
| Q5 | Phase diagrams; linearising non-linear difference equations | Unit 16 | 12 | Full file |
| Q6 | Number of terms of a GP; tenth term of a GP | Unit 6 | 12 | Full file |
| Q7 | Domain and range; properties of relations | Unit 2 | 12 | Full file |
| Q8 | Parabola from focus and directrix; circle centre and radius | Unit 5 | 12 | Full file |
| Q9 | Present value of instalment payments; discounting principle | Unit 6 | 12 | Full file |
| Q10 | Total revenue and demand function from marginal revenue | Unit 13 | 12 | Full file |
| Q11 | Limit as x tends to infinity; limit as x tends to 1 | Unit 7 | 6 | Full file |
| Q12 | Theorem and proof; point of inflexion | Units 3 and 11 | 6 | Full file |
9. Programmes That Include BECC 102
BECC 102 is a compulsory Semester I core course of IGNOU's BA (Honours) Economics and the base for BECC 104 Mathematical Methods in Economics-II.
Students of the IGNOU Bachelor of Arts (Honours) Economics programme (BAECH) take BECC 102 alongside BECC 101 Introductory Microeconomics in the first semester. The optimisation and elasticity tools practised here come back in microeconomics papers such as BECC 105 and BECC 108.
BAECH is a 148-credit programme with 14 core courses of 6 credits each, and it can be completed in three to six years. IGNOU lists the full course structure and admission details on its official BAECH programme page.
10. How to Get the Full Solved Question Paper
Message WhatsApp 9899436384 with the words BECC 102 June 2026 to get the complete solved paper with answers to all 12 questions.
- Open WhatsApp and send "BECC 102 June 2026" to 9899436384.
- Our team replies with the file details and confirms your course code.
- You receive the complete solved PDF with all 12 answers, including the 10 not shown here.
The file is a digital PDF, so it reaches your phone the same day and you can revise it anywhere before the exam.
11. BECC 102 FAQs
These answers cover the June 2026 BECC 102 paper, the full file and how to use it for the next exam.
Is this solved paper based on the official June 2026 IGNOU paper?
Yes. The file follows the official IGNOU June 2026 term-end paper of BECC 102 Mathematical Methods in Economics-I, question by question and with the same numbering. Nothing is paraphrased or reordered, so you can keep the printed paper beside the file while revising. Two of its twelve answers, Q1 and Q2, are shown in full on this page so you can judge the standard of working first.
How do I get the full solved paper on WhatsApp, and how many answers does it contain?
Send a message to WhatsApp 9899436384 with the words BECC 102 June 2026. Our team replies with the details and shares the complete file as a PDF. It contains solutions to all 12 questions in the paper: the 2 shown on this page plus the 10 questions from Q3 to Q12 that are answered only in the full file.
Which questions are solved on this page?
Question 1 and Question 2 from Section A are solved in full. Q1 finds a monopolist's most profitable output and maximum profit, then the output that minimises cost per unit. Q2 works through a cobweb model, finds the intertemporal equilibrium price and classifies its stability. Both are 20-mark questions, so the two samples show 40 marks of complete working.
How many questions do I answer in the BECC 102 exam?
You answer eight questions in three hours for 100 marks. Section A offers four 20-mark questions and you pick two. Section B offers six 12-mark questions and you pick four. Section C has two 6-mark questions and both are compulsory. The same split appeared in every official BECC 102 paper we compared, from December 2021 to June 2026.
Which BECC 102 topics repeat most often in IGNOU papers?
In the five official papers we compared, profit maximisation, conic sections and methods of proof appeared every time. Cobweb models, geometric progressions, limits and integrating a marginal function to get total revenue or cost appeared in four of the five. June 2026 also reused some June 2025 and June 2024 questions word for word, which the repeat table on this page lists.
Does the file show every step of the calculations?
Yes. Each numerical answer starts from the given functions, writes the formula being used, shows every substitution and ends with a clearly stated result. Optimisation answers include both the first order and second order conditions, and difference equation answers show the complete time path before the stability verdict. Theory answers, such as phase diagrams, use definitions and a worked economic example.
Will the June 2026 solved paper help for the December 2026 exam?
It should help, because BECC 102 papers draw on a stable set of topics. Monopoly optimisation, the cobweb model, geometric progressions, conics, limits and proof methods have come up again and again in recent official papers. Practising the June 2026 solutions trains the exact methods examiners reward. It is not a prediction of the December 2026 paper, so study the full syllabus as well.
How many credits and units does BECC 102 have?
BECC 102 is a 6-credit core course in the BAECH programme, which means around 180 hours of study at IGNOU's 30 hours per credit. The course book has 6 blocks and 16 units, from sets and logic up to linear and non-linear difference equations. Assessment is one tutor marked assignment worth 30 per cent and the term-end exam worth 70 per cent.
12. Who Wrote and Checked the BECC 102 Answers
The BECC 102 answers were written by Prateek Talwar and reviewed by Sheetal Kirola at Unnati Educations.
Prateek Talwar prepares IGNOU economics and mathematics solved papers from the course blocks and the official term-end paper. Sheetal Kirola, Academic Head (M.Ed.), re-works every numerical by hand and substitutes each result back into the original functions before the file is released.