Assignment 3 : Accounts | Economics | Business Mathematics

Assignment 2: Business Studies

Focus Edge Education Network (FEEN)

Section 1: Business Mathematics

Instructions: Solve the following questions based on the concepts of Calculus and Linear Algebra. Show all calculation steps clearly.

Question 1: Profit Maximization

The demand function of a firm is given by P = 150 - 0.5Q and the total cost function is TC = 0.25Q² + 30Q + 100. Find the level of output (Q) that maximizes the total profit.

Hint: Profit (π) = Total Revenue (TR) - Total Cost (TC). First find TR = P × Q. Profit is maximum when the first derivative dπ/dQ = 0 and the second derivative is negative.

Question 2: Elasticity of Demand (Ed)

Find the Price Elasticity of Demand (Ed) for the demand function Q = 100 - 2P - 0.1P² when the price P = 10. State whether the demand is elastic or inelastic.

Hint: Use the formula Ed = |(dQ/dP) × (P/Q)|. Differentiate the function with respect to P first.

Figure 1: Visualizing Elasticity Points on a Demand Curve

Question 3: Revenue & Marginal Analysis

If the average revenue function is AR = 60 - 3Q, find the Marginal Revenue (MR) function. At what level of output is the Total Revenue (TR) at its maximum?

Hint: TR = AR × Q. Marginal Revenue is the derivative of TR. TR is maximum when MR = 0.

Question 4: Cost Function & Optimization

A manufacturer's total cost function is C = Q³ - 5Q² + 12Q + 20. Find the Marginal Cost (MC) and Average Cost (AC) when Q = 5.

Hint: MC = dC/dQ and AC = C / Q. Plug in the value of Q after differentiating.

Figure 2: The intersection of MC and AC curves at the minimum point

Question 5: Break-Even Analysis

A company sells its product at Rs. 20 per unit. The variable cost is Rs. 12 per unit and the fixed cost is Rs. 4,000. Calculate the Break-Even Point in units.

Hint: Break-Even Quantity = Fixed Cost / (Selling Price - Variable Cost).

Question 6: Matrix Application in Business

Two types of products A and B are produced using two machines M1 and M2. Product A requires 2 hours on M1 and 3 hours on M2. Product B requires 4 hours on M1 and 1 hour on M2. If the total available hours are 40 for M1 and 30 for M2, set up the system of equations and solve for units of A and B using the **Matrix Inversion Method**.

Hint: Create the equation AX = B. Solve for X = A⁻¹B.

--- End of Section 1. Please await further instructions for Section 2. ---

Section 2: Financial Accounting (Long-Form Problems)

Instructions: Prepare the necessary financial statements with full working notes. Ensure all adjustments are clearly shown in the final accounts.

Question 7: Comprehensive Final Accounts & Balance Sheet

The Trial Balance of Focus Edge Education Network (FEEN) as of 31st Ashadh, 2081 is given below:

Particulars	Debit (Rs.)	Credit (Rs.)
Opening Stock	1,50,000	-
Purchases & Sales	9,00,000	18,50,000
Wages and Productive Salaries	2,50,000	-
Plant and Machinery	8,00,000	-
Land and Buildings	12,00,000	-
Debtors and Creditors	2,00,000	1,20,000
Share Capital (Rs. 100 each)	-	15,00,000
12% Debentures	-	3,00,000
Office Rent (paid for 15 months)	75,000	-
Cash and Bank Balance	1,45,000	-
General Reserve	-	50,000

Additional Adjustments:

• Closing stock was valued at Rs. 1,80,000.
• Depreciate Machinery by 15% and Land & Buildings by 5%.
• Create a 5% Provision for Bad Debts on Debtors after writing off Rs. 5,000 as further bad debts.
• Outstanding Wages amounted to Rs. 20,000.
• The Board of Directors proposed a 10% dividend on Share Capital and a transfer of Rs. 30,000 to General Reserve.
• Interest on Debentures is outstanding for the full year.

Required: (a) Trading Account (b) Profit & Loss Account (c) P/L Appropriation Account (d) Balance Sheet.

Hint: Calculate the Net Profit first before moving to the Appropriation account. Remember, "Proposed Dividend" is shown in the P/L Appropriation (Debit) and as a Current Liability in the Balance Sheet.

Figure 3: Format for Corporate Balance Sheet (Vertical Presentation)

Question 8: Detailed Cost Sheet & Tender Price

A manufacturing company provides the following information for the production of 2,000 units of a product:

• Cost of Raw Materials: Rs. 4,00,000
• Direct Wages: Rs. 2,50,000
• Direct Expenses: Rs. 50,000
• Factory Overheads: 60% of Direct Labor
• Office & Administrative Overheads: 20% of Works Cost
• Selling & Distribution Overheads: Rs. 20 per unit sold
• Profit Margin: 25% on Selling Price

During the period, 1,800 units were sold. You are required to prepare a Cost Sheet showing:

1. Prime Cost
2. Works/Factory Cost
3. Cost of Production
4. Total Cost & Profit

Hint: Factory overhead is calculated on wages. Works Cost = Prime Cost + Factory Overhead. Cost of Production is used to value the closing stock of finished goods.

Figure 4: Components and flow of a Manufacturing Cost Sheet

Question 9: 10-Column Work Sheet Preparation

From the following Unadjusted Trial Balance, prepare a 10-Column Work Sheet for the year ended Dec 31:

(Assume the following Adjusted Balances for the exercise): Cash Rs. 50k, Supplies Rs. 10k, Equipment Rs. 200k, Acc. Depreciation Rs. 40k, Capital Rs. 150k, Revenue Rs. 300k, Salaries Expense Rs. 120k, Rent Expense Rs. 10k.

Adjustments: (1) Supplies on hand Rs. 2,000 (2) Accrued Salaries Rs. 5,000 (3) Depreciation on Equipment Rs. 20,000.

Hint: The Work Sheet must include columns for Trial Balance, Adjustments, Adjusted Trial Balance, Income Statement, and Balance Sheet. Ensure the Net Income is added to the Balance Sheet Credit side.

--- End of Section 2. Please await further instructions for Section 3 (25 Economics MCQs). ---

Section 3: Economics - 25 Comprehensive MCQs

Instructions: Select the most appropriate option. Use the hints provided to understand the underlying economic principles.

1. Which cost curve is known as the "Planning Curve" or "Envelope Curve"?

A) Short-run Average Cost (SAC)

B) Long-run Average Cost (LAC)

C) Average Variable Cost (AVC)

D) Marginal Cost (MC)

Hint: It wraps around all SAC curves and helps a firm plan its scale of production.

Figure 5: The Long-run Average Cost (LAC) Envelope Curve

2. When Marginal Revenue (MR) is zero, Total Revenue (TR) is:

A) Zero

B) Falling

C) At its Maximum

D) Negative

Hint: MR represents the addition to TR. If no more is added, TR has reached its peak.

3. The shape of the Average Fixed Cost (AFC) curve is:

A) U-shaped

B) Horizontal line

C) Rectangular Hyperbola

D) Upward sloping

Hint: TFC is constant; as output (Q) increases, AFC (TFC/Q) falls continuously but never touches the axes.

4. Under Perfect Competition, the relationship between Price (P), AR, and MR is:

A) P > AR > MR

B) P = AR = MR

C) P < AR < MR

D) AR = MR / P

Hint: Since price is constant for all units in perfect competition, every extra unit sold adds the same amount to TR.

5. Marginal Cost (MC) is calculated as:

A) ΔTC / ΔQ

B) TC / Q

C) TR - TC

D) TFC + TVC

Hint: Marginal always refers to the change in total cost resulting from one extra unit of output.

6. The U-shape of the Short-run Average Cost (SAC) curve is explained by:

A) Law of Demand

B) Law of Variable Proportions

C) Returns to Scale

D) Economies of Scale

Hint: It relates to the stages of production where efficiency first increases and then decreases due to fixed factors.

7. Which of the following is an Implicit Cost?

A) Wages paid to laborers

B) Rent paid for a rented building

C) Salary of the owner's own labor

D) Interest on bank loan

Hint: Implicit costs are the opportunity costs of using self-owned resources.

8. Marginal Revenue is the slope of the:

A) Total Cost Curve

B) Average Revenue Curve

C) Total Revenue Curve

D) Demand Curve

Hint: Slope represents change; MR is the change in Total Revenue.

9. Normal Profit is achieved when:

A) TR > TC

B) AR = AC

C) AR > AC

D) MR = MC = 0

Hint: Normal profit is the minimum return required to keep a firm in business, occurring where total revenue equals total cost.

10. Total Cost (TC) is equal to:

A) TFC - TVC

B) TFC + TVC

C) AFC + AVC

D) MC × Q

Hint: Total cost is the sum of costs that do not change with output and costs that do.

11. At the point of intersection of MC and AC:

A) AC is maximum

B) AC is minimum

C) MC is minimum

D) TC is minimum

Hint: The Marginal Cost curve always cuts the Average Cost curve from below at its lowest point.

Figure 6: The relationship between AC, AVC, and MC curves

12. In a Monopoly, the AR curve is:

A) Horizontal

B) Upward sloping

C) Downward sloping

D) Vertical

Hint: To sell more units, a monopolist must lower the price, causing the demand (AR) curve to slope down.

13. Real Cost refers to:

A) Money expenses

B) Efforts and sacrifices of factors

C) Opportunity cost

D) Fixed cost

Hint: It is a psychological concept introduced by Marshall regarding the pain/boredom of work.

14. If TC = 100 + 5Q, what is the Marginal Cost?

A) 100

B) 5Q

C) 5

D) 105

Hint: Differentiate the TC function with respect to Q.

15. Total Variable Cost (TVC) is zero when:

A) Output is zero

B) Output is maximum

C) TFC is zero

D) AC is minimum

Hint: Variable costs are only incurred when production takes place.

16. The vertical distance between TC and TVC curves:

A) Decreases as output increases

B) Increases as output increases

C) Remains constant

D) Is equal to MC

Hint: TC - TVC = TFC, and TFC does not change with output level.

17. Average Revenue (AR) is always equal to:

A) Profit

B) Price

C) Marginal Revenue

D) Total Cost

Hint: AR = Total Revenue / Quantity = (Price × Quantity) / Quantity.

18. Which curve is not U-shaped?

A) AC

B) MC

C) AVC

D) AFC

Hint: Look for the curve that is a rectangular hyperbola.

19. Opportunity Cost is also known as:

A) Alternative Cost

B) Money Cost

C) Sunk Cost

D) Real Cost

Hint: It is the value of the next best alternative forgone.

20. Break-even point occurs where:

A) TR = TC

B) TR > TC

C) TR < TC

D) MC = MR

Hint: It is the point of no profit and no loss.

21. When TR increases at a constant rate, MR is:

A) Increasing

B) Decreasing

C) Constant

D) Zero

Hint: This happens in perfect competition where price is constant.

22. The long run is a period in which:

A) All factors are fixed

B) All factors are variable

C) At least one factor is fixed

D) Supply is fixed

Hint: In the long run, firms can change all inputs, including the size of the factory.

23. Explicit costs are:

A) Non-monetary costs

B) Payments made to outsiders

C) Self-employed resource costs

D) Normal profits

Hint: These are out-of-pocket expenses recorded in accounting books.

24. If Price falls as output increases, then:

A) MR = AR

B) MR > AR

C) MR < AR

D) MR = 0

Hint: To sell an extra unit, the firm must lower the price of all units, making MR fall faster than AR.

25. Marginal Revenue can be:

A) Positive only

B) Zero only

C) Negative only

D) Positive, Zero, or Negative

Hint: MR depends on the elasticity of demand; it becomes negative when TR starts falling.

--- End of Assignment 2. Please review all sections before final submission. ---

Submission & Guidelines

1. Step 1: Solve the Business Math problems on paper, scan them, and upload to the portal.
2. Step 2: Draw neat, labeled diagrams for the Accounting and Economics sections.
3. Step 3: Use the "Hint" sections to double-check your logic before final submission.
4. Contact: Managing Director, Focus Edge Education Network for any technical queries.