Production and Cost Theory: Law of Variable Proportions, Returns to Scale, Cost and Revenue Curves for SSC CGL Economics

Production theory explains how inputs are turned into output, and cost theory explains how much it costs. SSC CGL Finance and Economics asks about the production function, the laws of production, the types of costs and the profit-maximising condition. This guide on production and cost theory for SSC explains the concepts with formulas, a worked cost table, solved examples and practice questions.

Production Function

The production function shows the relation between inputs and the maximum output: Q = f(L, K), where L is labour and K is capital. In the short run at least one factor (usually capital) is fixed. In the long run all factors are variable.

Product Concepts

Law of Variable Proportions (Short Run)

When one input is increased while the others are fixed, the marginal product first rises, then falls and may become negative. It is also called the law of diminishing returns.

The MP curve cuts the AP curve at the maximum point of AP. TP is maximum when MP = 0.

Returns to Scale (Long Run)

Cost Concepts

Worked Cost Table

Here the fixed cost is 10 (the TC at zero output). The MC falls to 8 at the third unit and then rises, and the AC keeps falling till it is cut by the rising MC.

Revenue Concepts

Profit Maximisation and Break-Even

• Profit = TR − TC.
• A firm maximises profit where MC = MR, and the MC curve cuts the MR curve from below.
• The break-even point is where TR = TC, with zero profit.
• The shutdown point in the short run is where the price equals the minimum AVC.
• Economies of scale make long-run average costs fall as output rises.

Solved Examples

Example 1. TC at 3 units is 38 and at 4 units is 50. Find the marginal cost of the 4th unit.
50 − 38 = 12.

Example 2. At 5 units of output the TC is 100 and the FC is 20. Find the AVC.
VC = 80, so AVC = 80/5 = 16.

Example 3. A firm sells a product at 50 rupees and the AC is 40 rupees at an output of 100 units. Find the profit.
(50 − 40) × 100 = 1,000 rupees.

Example 4. The marginal product of labour is 0 at the 6th worker. What is the state of the total product?
It is at its maximum.

Quick Tips

• Memorise the relation between MP and AP, and MC and AC.
• Remember MC = MR for profit maximisation.
• Learn the three stages of the law of variable proportions.
• Fixed cost is the cost at zero output.

Quick Revision Points

• TC = FC + VC; AC = TC/Q; MC = ΔTC/ΔQ.
• MC cuts AC and AVC at their minimum points.
• Short run: law of variable proportions; long run: returns to scale.
• Profit is maximum where MC = MR.
• TP is maximum when MP = 0.

Practice Questions With Answers

1. What is the formula for total cost?
   Answer: FC + VC
2. At what point does the MC curve cut the AC curve?
   Answer: At its minimum point
3. Where is the total product maximum?
   Answer: Where MP = 0
4. What is the profit-maximising condition?
   Answer: MC = MR
5. Which cost does not change with output?
   Answer: Fixed cost
6. TC at 10 units is 200 and at 11 units is 215. Find the MC.
   Answer: 15
7. What is the law of diminishing returns another name for?
   Answer: Law of variable proportions
8. If output doubles when all inputs double, what are the returns to scale?
   Answer: Constant returns to scale
9. What is AR equal to?
   Answer: Price
10. At the break-even point, what is the profit?
    Answer: Zero

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Finance and Economics notes page, read the previous topic Demand, Supply and Elasticity and the next topic Market Structures.

Frequently Asked Questions

What is a production function?

The relationship between inputs and the maximum output produced.

What is the law of variable proportions?

When one input increases and others are fixed, the marginal product first rises and then falls.

What are returns to scale?

The change in output when all inputs are changed in the same proportion in the long run.

What is marginal cost?

The additional cost of producing one more unit.

What is the difference between fixed and variable costs?

Fixed costs do not change with output; variable costs change with output.

What is average cost?

Total cost divided by output.

Why is the AC curve U-shaped?

Because of the economies of scale at first and diseconomies later.

What is the break-even point?

The output at which total revenue equals total cost.

What is the shutdown point?

The point where price equals the minimum average variable cost.

What is marginal revenue?

The additional revenue from selling one more unit.

Is this topic asked in SSC CGL?

Yes. It is part of the micro-economics syllabus of the Finance and Economics paper.

What is the short run?

A period in which at least one input cannot be changed.