Class 12: Introductory Micro-economics
Class 12: Introductory Micro-economics Chapter 3: Production and Costs
Question 1. Explain the concept of a production function.
A production function is the functional relationship between the quantity of inputs used and the maximum quantity of output that can be produced with a given level of technology during a given period.
It shows how inputs such as labour, capital, land, and entrepreneurship are transformed into output.
The production function can be expressed as:
$$ Q=f(L,K) $$Where:
- \(Q\) = Quantity of output
- \(L\) = Labour
- \(K\) = Capital
- \(f\) = Functional relationship between inputs and output
The production function assumes that technology remains constant.
Question 2. What is the total product of an input?
Total Product (TP) of an input is the total quantity of output produced by employing a given quantity of that input, while keeping other inputs constant.
For example, the total quantity of wheat produced by employing a certain number of workers on a fixed piece of land is the Total Product of labour.
Question 3. What is the average product of an input?
Average Product (AP) of an input is the output produced per unit of that input.
It is calculated as:
$$ AP=\frac{TP}{L} $$Where:
- \(AP\) = Average Product
- \(TP\) = Total Product
- \(L\) = Units of labour employed
Question 4. What is the marginal product of an input?
Marginal Product (MP) of an input is the additional output produced by employing one more unit of that input while keeping other inputs constant.
It is calculated as:
$$ MP=\frac{\Delta TP}{\Delta L} $$Where:
- \(MP\) = Marginal Product
- \(\Delta TP\) = Change in Total Product
- \(\Delta L\) = Change in Labour
Question 5. Explain the relationship between the marginal product and the total product of an input.
The relationship between Total Product (TP) and Marginal Product (MP) is as follows:
- When MP is positive, TP increases.
- When MP is rising, TP increases at an increasing rate.
- When MP is falling but positive, TP increases at a decreasing rate.
- When MP becomes zero, TP reaches its maximum.
- When MP becomes negative, TP starts decreasing.
Question 6. Explain the concepts of the short run and the long run.
Short Run
The short run is a period during which at least one factor of production remains fixed, while other factors can be varied to change output.
Long Run
The long run is a period during which all factors of production are variable. A firm can change the scale of production by varying all inputs.
Question 7. What is the law of diminishing marginal product?
The Law of Diminishing Marginal Product states that when additional units of a variable input are employed with fixed inputs, the marginal product of the variable input eventually begins to decline after a certain point.
This happens because the fixed inputs become insufficient relative to the increasing variable input.
Question 8. What is the law of variable proportions?
The Law of Variable Proportions states that when more and more units of a variable input are combined with fixed inputs, the total product initially increases at an increasing rate, then at a decreasing rate, and may eventually decline.
This law operates in the short run where at least one factor of production remains fixed.
Question 9. When does a production function satisfy constant returns to scale?
A production function satisfies constant returns to scale when all inputs are increased in the same proportion and output also increases in the same proportion.
For example, if all inputs are doubled, output also doubles.
$$ f(tL,tK)=tf(L,K) $$Question 10. When does a production function satisfy increasing returns to scale?
A production function satisfies increasing returns to scale when all inputs are increased in the same proportion but output increases by a greater proportion.
For example, if all inputs are doubled, output becomes more than double.
$$ f(tL,tK)>tf(L,K) $$Question 11. When does a production function satisfy decreasing returns to scale?
A production function satisfies decreasing returns to scale when all inputs are increased in the same proportion but output increases by a smaller proportion.
For example, if all inputs are doubled, output increases by less than double.
$$ f(tL,tK)Question 12. Briefly explain the concept of the cost function.
A cost function shows the relationship between the cost of production and the quantity of output produced. It indicates the minimum cost incurred in producing different levels of output, given the prices of inputs and the available technology.
The cost function can be expressed as:
$$ C=f(Q) $$Where:
- \(C\) = Total Cost
- \(Q\) = Quantity of Output
Question 13. What are the total fixed cost, total variable cost and total cost of a firm? How are they related?
Total Fixed Cost (TFC) is the cost that does not change with the level of output. It is incurred even when output is zero.
Total Variable Cost (TVC) is the cost that varies directly with the level of output. It increases as production increases.
Total Cost (TC) is the total expenditure incurred in producing a given level of output.
The relationship among these costs is:
$$ TC=TFC+TVC $$Question 14. What are the average fixed cost, average variable cost and average cost of a firm? How are they related?
Average Fixed Cost (AFC) is the fixed cost per unit of output.
$$ AFC=\frac{TFC}{Q} $$Average Variable Cost (AVC) is the variable cost per unit of output.
$$ AVC=\frac{TVC}{Q} $$Average Cost (AC) is the total cost per unit of output.
$$ AC=\frac{TC}{Q} $$The relationship among them is:
$$ AC=AFC+AVC $$Question 15. Can there be some fixed cost in the long run? If not, why?
No. There cannot be any fixed cost in the long run because all factors of production are variable in the long run. A firm can change the quantity of every input, so no cost remains fixed.
Question 16. What does the average fixed cost curve look like? Why does it look so?
The Average Fixed Cost (AFC) curve is a downward-sloping rectangular hyperbola.
It slopes downward because total fixed cost remains constant while output increases. Therefore, fixed cost is spread over more units of output, causing AFC to continuously decline.
$$ AFC=\frac{TFC}{Q} $$Question 17. What do the short run marginal cost, average variable cost and short run average cost curves look like?
The Short Run Marginal Cost (SMC), Average Variable Cost (AVC), and Short Run Average Cost (SAC) curves are all U-shaped.
Initially, these costs decrease due to increasing marginal product. After a certain level of output, they begin to increase because of the law of diminishing marginal product.
Question 18. Why does the SMC curve cut the AVC curve at the minimum point of the AVC curve?
The SMC curve cuts the AVC curve at its minimum point because:
- When \(SMC
- When \(SMC>AVC\), the AVC rises.
- Therefore, AVC is minimum when \(SMC=AVC\).
Question 19. At which point does the SMC curve cut the SAC curve? Give reason in support of your answer.
The SMC curve cuts the SAC curve at the minimum point of the SAC curve.
This is because:
- When \(SMC
- When \(SMC>SAC\), the SAC rises.
- Therefore, SAC is minimum when \(SMC=SAC\).
Question 20. Why is the short run marginal cost curve 'U-shaped'?
The Short Run Marginal Cost (SMC) curve is U-shaped because of the Law of Diminishing Marginal Product.
Initially, marginal product increases, so the cost of producing an additional unit decreases and SMC falls. After a certain point, marginal product starts diminishing, causing the cost of producing an additional unit to rise. As a result, the SMC curve becomes U-shaped.
Question 21. What do the long run marginal cost and the average cost curves look like?
The Long Run Marginal Cost (LMC) and Long Run Average Cost (LAC) curves are generally U-shaped.
Initially, they decline due to economies of scale. After reaching the minimum point, they rise because of diseconomies of scale.
Like the short-run curves, the LMC curve cuts the LAC curve at its minimum point.
Question 11. When does a production function satisfy decreasing returns to scale?
A production function satisfies decreasing returns to scale when all inputs are increased in the same proportion but output increases by a smaller proportion.
For example, if all inputs are doubled, output increases by less than double.
$$ f(tL,tK)Question 12. Briefly explain the concept of the cost function.
A cost function shows the relationship between the cost of production and the quantity of output produced. It indicates the minimum cost incurred in producing different levels of output, given the prices of inputs and the available technology.
The cost function can be expressed as:
$$ C=f(Q) $$Where:
- \(C\) = Total Cost
- \(Q\) = Quantity of Output
Question 13. What are the total fixed cost, total variable cost and total cost of a firm? How are they related?
Total Fixed Cost (TFC) is the cost that does not change with the level of output. It is incurred even when output is zero.
Total Variable Cost (TVC) is the cost that varies directly with the level of output. It increases as production increases.
Total Cost (TC) is the total expenditure incurred in producing a given level of output.
The relationship among these costs is:
$$ TC=TFC+TVC $$Question 14. What are the average fixed cost, average variable cost and average cost of a firm? How are they related?
Average Fixed Cost (AFC) is the fixed cost per unit of output.
$$ AFC=\frac{TFC}{Q} $$Average Variable Cost (AVC) is the variable cost per unit of output.
$$ AVC=\frac{TVC}{Q} $$Average Cost (AC) is the total cost per unit of output.
$$ AC=\frac{TC}{Q} $$The relationship among them is:
$$ AC=AFC+AVC $$Question 15. Can there be some fixed cost in the long run? If not, why?
No. There cannot be any fixed cost in the long run because all factors of production are variable in the long run. A firm can change the quantity of every input, so no cost remains fixed.
Question 16. What does the average fixed cost curve look like? Why does it look so?
The Average Fixed Cost (AFC) curve is a downward-sloping rectangular hyperbola.
It slopes downward because total fixed cost remains constant while output increases. Therefore, fixed cost is spread over more units of output, causing AFC to continuously decline.
$$ AFC=\frac{TFC}{Q} $$Question 17. What do the short run marginal cost, average variable cost and short run average cost curves look like?
The Short Run Marginal Cost (SMC), Average Variable Cost (AVC), and Short Run Average Cost (SAC) curves are all U-shaped.
Initially, these costs decrease due to increasing marginal product. After a certain level of output, they begin to increase because of the law of diminishing marginal product.
Question 18. Why does the SMC curve cut the AVC curve at the minimum point of the AVC curve?
The SMC curve cuts the AVC curve at its minimum point because:
- When \(SMC
- When \(SMC>AVC\), the AVC rises.
- Therefore, AVC is minimum when \(SMC=AVC\).
Question 19. At which point does the SMC curve cut the SAC curve? Give reason in support of your answer.
The SMC curve cuts the SAC curve at the minimum point of the SAC curve.
This is because:
- When \(SMC
- When \(SMC>SAC\), the SAC rises.
- Therefore, SAC is minimum when \(SMC=SAC\).
Question 20. Why is the short run marginal cost curve 'U-shaped'?
The Short Run Marginal Cost (SMC) curve is U-shaped because of the Law of Diminishing Marginal Product.
Initially, marginal product increases, so the cost of producing an additional unit decreases and SMC falls. After a certain point, marginal product starts diminishing, causing the cost of producing an additional unit to rise. As a result, the SMC curve becomes U-shaped.
Question 21. What do the long run marginal cost and the average cost curves look like?
The Long Run Marginal Cost (LMC) and Long Run Average Cost (LAC) curves are generally U-shaped.
Initially, they decline due to economies of scale. After reaching the minimum point, they rise because of diseconomies of scale.
Like the short-run curves, the LMC curve cuts the LAC curve at its minimum point.
Question 22. The following table gives the total product schedule of labour. Find the corresponding average product and marginal product schedules of labour.
Average Product (AP) and Marginal Product (MP) are calculated using:
$$ AP=\frac{TP}{L} $$ $$ MP=\frac{\Delta TP}{\Delta L} $$| Labour (\(L\)) | Total Product (\(TP\)) | Average Product (\(AP\)) | Marginal Product (\(MP\)) |
|---|---|---|---|
| 0 | 0 | — | — |
| 1 | 15 | 15 | 15 |
| 2 | 35 | 17.5 | 20 |
| 3 | 50 | 16.67 | 15 |
| 4 | 40 | 10 | -10 |
| 5 | 48 | 9.6 | 8 |
Question 23. The following table gives the average product schedule of labour. Find the total product and marginal product schedules. It is given that the total product is zero at zero level of labour employment.
Given:
$$ AP=\frac{TP}{L} $$Therefore,
$$ TP=AP\times L $$Marginal Product is calculated as:
$$ MP=\Delta TP $$| Labour (\(L\)) | Average Product (\(AP\)) | Total Product (\(TP\)) | Marginal Product (\(MP\)) |
|---|---|---|---|
| 0 | — | 0 | — |
| 1 | 2 | 2 | 2 |
| 2 | 3 | 6 | 4 |
| 3 | 4 | 12 | 6 |
| 4 | 4.25 | 17 | 5 |
| 5 | 4 | 20 | 3 |
| 6 | 3.5 | 21 | 1 |
Question 24. The following table gives the marginal product schedule of labour. It is also given that total product of labour is zero at zero level of employment. Calculate the total and average product schedules of labour.
Given:
$$ TP_0=0 $$Total Product (TP) is obtained by adding Marginal Product (MP) successively.
Average Product (AP) is calculated as:
$$ AP=\frac{TP}{L} $$| Labour (\(L\)) | Marginal Product (\(MP\)) | Total Product (\(TP\)) | Average Product (\(AP\)) |
|---|---|---|---|
| 0 | — | 0 | — |
| 1 | 3 | 3 | 3 |
| 2 | 5 | 8 | 4 |
| 3 | 7 | 15 | 5 |
| 4 | 5 | 20 | 5 |
| 5 | 3 | 23 | 4.6 |
| 6 | 1 | 24 | 4 |
Question 25. The following table shows the total cost schedule of a firm. What is the total fixed cost schedule of this firm? Calculate the TVC, AFC, AVC, SAC and SMC schedules of the firm.
Since Total Cost at zero output is ₹10,
$$ TFC=10 $$The required formulas are:
$$ TVC=TC-TFC $$ $$ AFC=\frac{TFC}{Q} $$ $$ AVC=\frac{TVC}{Q} $$ $$ SAC=\frac{TC}{Q} $$ $$ SMC=\Delta TC $$| \(Q\) | \(TC\) | \(TFC\) | \(TVC\) | \(AFC\) | \(AVC\) | \(SAC\) | \(SMC\) |
|---|---|---|---|---|---|---|---|
| 0 | 10 | 10 | 0 | — | — | — | — |
| 1 | 30 | 10 | 20 | 10 | 20 | 30 | 20 |
| 2 | 45 | 10 | 35 | 5 | 17.5 | 22.5 | 15 |
| 3 | 55 | 10 | 45 | 3.33 | 15 | 18.33 | 10 |
| 4 | 70 | 10 | 60 | 2.5 | 15 | 17.5 | 15 |
| 5 | 90 | 10 | 80 | 2 | 16 | 18 | 20 |
| 6 | 120 | 10 | 110 | 1.67 | 18.33 | 20 | 30 |
Question 26. The following table gives the total cost schedule of a firm. It is also given that the average fixed cost at 4 units of output is Rs 5. Find the TVC, TFC, AVC, AFC, SAC and SMC schedules of the firm for the corresponding values of output.
Given:
$$ AFC=\frac{TFC}{Q} $$At \(Q=4\),
$$ 5=\frac{TFC}{4} $$ $$ TFC=20 $$The required formulas are:
$$ TVC=TC-TFC $$ $$ AFC=\frac{TFC}{Q} $$ $$ AVC=\frac{TVC}{Q} $$ $$ SAC=\frac{TC}{Q} $$ $$ SMC=\Delta TC $$| \(Q\) | \(TC\) | \(TFC\) | \(TVC\) | \(AFC\) | \(AVC\) | \(SAC\) | \(SMC\) |
|---|---|---|---|---|---|---|---|
| 1 | 50 | 20 | 30 | 20 | 30 | 50 | — |
| 2 | 65 | 20 | 45 | 10 | 22.5 | 32.5 | 15 |
| 3 | 75 | 20 | 55 | 6.67 | 18.33 | 25 | 10 |
| 4 | 95 | 20 | 75 | 5 | 18.75 | 23.75 | 20 |
| 5 | 130 | 20 | 110 | 4 | 22 | 26 | 35 |
| 6 | 185 | 20 | 165 | 3.33 | 27.5 | 30.83 | 55 |
Question 27. A firm's SMC schedule is shown in the table. The total fixed cost of the firm is Rs 100. Find the TVC, TC, AVC and SAC schedules of the firm.
Given:
- \(TFC=100\)
Marginal Cost (SMC) values are:
500, 300, 200, 300, 500, 800
Total Variable Cost is obtained by cumulative addition of SMC values.
$$ TC=TFC+TVC $$ $$ AVC=\frac{TVC}{Q} $$ $$ SAC=\frac{TC}{Q} $$| \(Q\) | \(SMC\) | \(TVC\) | \(TC\) | \(AVC\) | \(SAC\) |
|---|---|---|---|---|---|
| 0 | — | 0 | 100 | — | — |
| 1 | 500 | 500 | 600 | 500 | 600 |
| 2 | 300 | 800 | 900 | 400 | 450 |
| 3 | 200 | 1000 | 1100 | 333.33 | 366.67 |
| 4 | 300 | 1300 | 1400 | 325 | 350 |
| 5 | 500 | 1800 | 1900 | 360 | 380 |
| 6 | 800 | 2600 | 2700 | 433.33 | 450 |
Question 28. Let the production function of a firm be
$$ Q=5L^{\frac{1}{2}}K^{\frac{1}{2}} $$Find out the maximum possible output that the firm can produce with 100 units of \(L\) and 100 units of \(K\).
Substituting the given values:
$$ Q=5(100)^{\frac12}(100)^{\frac12} $$ $$ =5\times10\times10 $$ $$ =500 $$Answer: The maximum possible output is 500 units.
Question 29. Let the production function of a firm be
$$ Q=2L^2K $$Find out the maximum possible output that the firm can produce with 5 units of \(L\) and 2 units of \(K\). What is the maximum possible output that the firm can produce with zero unit of \(L\) and 10 units of \(K\)?
(i) When \(L=5\) and \(K=2\)
$$ Q=2(5)^2(2) $$ $$ =2\times25\times2 $$ $$ =100 $$Maximum possible output = 100 units.
(ii) When \(L=0\) and \(K=10\)
$$ Q=2(0)^2(10)=0 $$Maximum possible output = 0 unit.
Question 30. Find out the maximum possible output for a firm with zero unit of \(L\) and 10 units of \(K\) when its production function is
$$ Q=5L+2K $$Substituting the given values:
$$ Q=5(0)+2(10) $$ $$ =20 $$Answer: The maximum possible output is 20 units.