Ncert Solutions for Class 12 Micro Economics Chapter 3 Production and Costs

Microeconomics Class 12 Chapter 3 questions and answers: Production and Costs ncert solutions

Textbook	NCERT
Class	Class 12
Subject	Economics
Chapter	Chapter 3
Chapter Name	Production and Costs class 12 ncert solutions
Category	Ncert Solutions
Medium	English

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Question 1: Explain the concept of a production function.

Answer 1: A production function is an economic concept that describes the relationship between the inputs a firm uses and the output it produces. It shows how different combinations of inputs, such as labor, capital, land, and technology, are transformed into a certain level of output.

• Inputs and Outputs:
  • Inputs, also known as factors of production, include labor (workers), capital (machinery, tools), land, and raw materials.
  • Output refers to the goods or services produced by combining these inputs.

A production function can be expressed as: Q = f(L,K,R,T)

where:

• Q is the quantity of output,
• L represents labor,
• K represents capital,
• R represents raw materials or land,
• T represents technology. The function f shows how inputs are transformed into output.

Question 2: What is the total product of an input?

Answer 2: The total product of an input refers to the total quantity of output produced by a firm using a given amount of that input, while holding other inputs constant. It represents the overall productivity of a specific input, such as labor or capital, in the production process.

Question 3: What is the average product of an input?

Answer 3: The average product of an input is a measure of the output produced per unit of a specific input, such as labor or capital. It is calculated by dividing the total product (TP) by the quantity of the input used. Essentially, it tells us how much output each unit of input contributes on average.

Formula:
Average Product (AP) = \(\frac{\text{Total Product (TP)}}{\text{Quantity of Input (X)}}\)

Where:

• AP is the average product of the input,
• TP is the total product (total output produced),
• X is the quantity of the input (e.g., number of workers or units of capital).

Question 4: What is the marginal product of an input?

Answer 4: The marginal product of an input refers to the additional output that is produced by adding one more unit of that input while keeping all other inputs constant. It shows how much extra output can be generated when the quantity of an input (such as labor or capital) is increased by one unit.

Question 5: Explain the relationship between the marginal products and the total product of an input.

Answer 5: The relationship between marginal product (MP) and total product (TP) is as follows:

1. Rising Marginal Product: When the marginal product of an input is increasing, the total product rises at an increasing rate. This occurs in the initial stages of production when inputs are used more efficiently.
2. Diminishing Marginal Product: As more units of an input are added, the marginal product begins to decrease due to the law of diminishing marginal returns. During this phase, total product continues to increase but at a decreasing rate.
3. Marginal Product Equals Zero: When the marginal product reaches zero, the total product is at its maximum. Adding more input beyond this point will no longer increase output.
4. Negative Marginal Product: If the marginal product becomes negative, the total product starts to decline, indicating overuse of the input.

Question 6: Explain the concepts of the short run and the long run.

Answer 6: Short Run: In the short run, at least one input (such as capital or machinery) is fixed, while other inputs (like labor) can be varied. Firms can increase production by using more of the variable input, but they cannot change all production factors. For example, a factory can hire more workers, but it cannot immediately expand its building size.

Long Run: In the long run, all inputs are variable. Firms have the flexibility to adjust all factors of production, including capital and labor, and can even enter or exit industries. This allows for more significant changes, such as building new factories or adopting new technologies.

Question 7: What is the law of diminishing marginal product?

Answer 7: According to the law of diminishing marginal product, there will initially be an increase in the total amount of production when one of the factors is increased while keeping the others constant.

Eventually, this strategy would not keep increasing production. For example, think of a factory where the machinery is a factor of production. Increasing the number of machines would initially increase production. But if the company keeps increasing the number of machines without correspondingly hiring new workers to operate them, the productivity will decrease.

Question 8: What is the law of variable proportions?

Answer 8: According to the law of variable proportions, if more and more units of the variable factor (labour) are combined with the same quantity of the fixed factor (capital), then initially the total product will increase but gradually after a point, the total product will start diminishing. Thus Law of variable proportions is the new name of the “Law of Diminishing Returns” of classical economics. Some economists also call it the Law of Non-Proportional Returns.

Question 9: When does a production function satisfy constant returns to scale?

Answer 9: Constant returns to scale is achieved when the change in the factors of production matches with the changes in the total output. This means that the efforts of the producer to improve production yield appropriate and equivalent returns.

Question 10: When does a production function satisfy increasing returns to scale?

Answer 10: Increasing returns to scale (IRS) holds when a proportional increase in all the factors of production leads to an increase in the output by more than the proportion. For example, if both the labour and the capital are increased by ‘n’ times, and the resultant increase in the output is more than ‘n’ times, then we say that the production function exhibits IRS.

Question 11: When does a production function satisfy decreasing returns to scale?

Answer 11: Decreasing returns to scale is when the change in the factors of production results in a decrease in the changes in the total output. This is an indication that the changes have proved to be detrimental to productivity instead of increasing productivity

Question 12: Briefly explain the concept of the cost function.

Answer 12: The cost function is the functional relationship between the cost of production and the output. It studies the behaviour of cost at different levels of output when technology is assumed to be constant. It can be expressed as: C = f(Q) where, C = cost, f = functional relativity and Q = units of output.

Question 13: What are the total fixed cost, total variable cost and total cost of a firm? How are they related?

Answer 13:

1. Total Fixed Cost (TFC): Total Fixed Cost refers to the costs that do not change with the level of output produced. These costs are constant, regardless of how much (or how little) a firm produces. Examples include rent, salaries of permanent staff, insurance, and depreciation of machinery. TFC remains the same even if production is zero.

2. Total Variable Cost (TVC): Total Variable Cost refers to costs that vary directly with the level of output. As production increases, variable costs rise, and as production decreases, they fall. Examples include raw materials, wages of hourly workers, and utility costs that fluctuate with production levels. TVC increases as output increases.

3. Total Cost (TC): Total Cost is the sum of both fixed and variable costs. It represents the total expense a firm incurs to produce a certain level of output. TC = TFC + TVC

Relationship between TFC, TVC, and TC:

• TFC is constant and does not change with output.
• TVC increases with the level of output.
• TC is the total of TFC and TVC, meaning as variable costs rise with more output, total costs also rise.

Question 14: What are the average fixed cost, average variable cost and average cost of a firm? How are they related?

Answer 14: 1. Average Fixed Cost (AFC): Average Fixed Cost is the total fixed cost per unit of output. Since total fixed costs (TFC) are constant, as output increases, the average fixed cost decreases.

• Formula:
  \(AFC = \frac{TFC}{Q}\)
• Where:
  • (TFC) is the total fixed cost,
  • (Q) is the quantity of output.

2. Average Variable Cost (AVC): Average Variable Cost is the total variable cost per unit of output. Since variable costs change with the level of output, AVC typically decreases initially as production becomes more efficient, but increases after a certain point due to diminishing returns.

• Formula:
  \(AVC = \frac{TVC}{Q}\)
• Where:
  • (TVC) is the total variable cost,
  • (Q) is the quantity of output.

3. Average Cost (AC) or Average Total Cost (ATC): Average Cost (also known as Average Total Cost) is the total cost per unit of output. It includes both fixed and variable costs.

• Formula:
  AC = \(\frac{TC}{Q} = \frac{TFC + TVC}{Q}\) = AFC + AVC
• Where:
  • (TC) is the total cost,
  • (Q) is the quantity of output,
  • (AFC) is the average fixed cost,
  • (AVC) is the average variable cost.

Relationship between AFC, AVC, and AC:

• AC (or ATC) is the sum of AFC and AVC.
• AFC decreases as output increases, because the fixed cost is spread over more units.
• AVC typically decreases initially and then increases due to diminishing marginal returns.
• AC decreases at first as both AFC and AVC decline, but eventually rises as AVC increases more sharply than AFC declines.

Question 15: Can there be some fixed cost in the long run? If not, why?

Answer 15: No, there cannot be any fixed cost in the long run. In the long run, a firm has enough time to modify factor ratio and can change the scale of production. There is no fixed factor as the firm can change quantity of all the factors of production and therefore there cannot be any fixed cost in the long-run.

Question 16: What does the average fixed cost curve look like? Why does it look so?

Answer 16: The Average Fixed Cost (AFC) curve is a rectangular hyperbola in shape. The area under the curve is constant because TFC is constant at all levels of output. AFC decreased as the output increases. So, AFC curve is downward sloping to the right.

Question 17: What do the short run marginal cost, average variable cost and short run average cost curves look like?

Answer 17: The curves of short-run marginal cost, Average variable cost and Average cost are of U-shaped.

Question 18: Why does the SMC curve cut the AVC curve at the minimum point of the AVC curve?

Answer 18: It can be explained by the following points:

• 1. When AVC (Average Variable Cost) falls, SMC (Short Marginal Curve) is lesser than AVC.
• 2. When AVC rises, SMC becomes more than AVC.
• 3. When AVC is constant and is minimum, SMC is equal to AVC.

Therefore, the SMC curve cuts the AVC curve at the minimum point.

Question 19: At which point does the SMC curve cut the SAC curve? Give reason in support of your answer.

Answer 19: SMC curve intersects SAC curve at its minimum point. This is because as long as SAC is falling, SMC remains below SAC and when SAC starts rising, SMC remains above SAC. Hence, SMC intersects SAC at its minimum point P, where SMC = SAC.

Question 20: Why is the short run marginal cost curve ‘U’-shaped?

Answer 20: The Marginal Curve (MC) is U-shaped as per the Law of Variable Proportion.

This can be explained as follows:

• 1. Shape of the Marginal Cost Curve (MC) depends on the Total Variable Cost (TVC).
• 2. As TVC increases at a diminishing rate, the total product increases at an increasing rate, which creates a gap in the curve leading to the fall of MC.
• 3. Now, as TVC increases at an increasing rate and the total product increases at a diminishing rate, making the marginal cost increase and rise upward.
• 4. The increasing returns and then constant returns, along with the rise in decreasing returns, make it appear like the letter U from the English alphabet; hence, it is named so.

Question 21: What do the long run marginal cost and the average cost curves look like?

Answer 21: The Long Run Marginal Cost (LMC) and Long Run Average Cost (LAC) are U-shaped, and the reason behind this is the law of returns to scale. As per this law, a company or a firm undergoes three stages in production which are IRS (Increasing Return to Scale), CRS (Constant Return to Scale) and DRS (Diminishing Return to Scale). The curve becomes U-Shaped due to the falling of LAC due to economies of scale (IRS); it attains constant output at the CRS level, and finally, if the firm experiences diseconomies of scale and if it is continuing production after this stage, it will see a rise or DRS.

Question 22: The following table gives the total product schedule of labour. Find the corresponding average product and marginal product schedules of labour.

L	TPL
0	0
1	15
2	35
3	50
4	40
5	48

Answer 22: The solution to this question is as follows:

L	TPL	AP=\(\frac{\Delta T P}{\Delta L}\)	MP=TPn−TPn−1
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.

L	APL
1	2
2	3
3	4
4	4.25
5	4
6	3.5

Answer 23: The solution to this question is as follows:

L	APL	TPL=APL×L	MP=TPn−TPn−1
1	2	2×1=2	2
2	3	3×2=6	6-2=4
3	4	4×3=12	12-6=6
4	4.25	4.25 × 4 = 17	17 – 12 = 5
5	4	4×5=20	320-17=3
6	3.5	3.5×6=21	21-20=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.

L	MPL
1	3
2	5
3	7
4	5
5	3
6	1

Answer 24: The solution to this question is as follows:

L	MPL	TPn=TPn−1+MPn	APL=\(\frac{TP_L}{ L}\)
1	3	3	\(\frac{3}{1}\) = 3
2	5	3 + 5 = 8	\(\frac{8}{2}\) = 4
3	7	8+7=15	\(\frac{15}{3}\) = 5
4	5	15 + 5 = 20	\(\frac{20}{4}\) = 5
5	3	20 + 3 = 23	\(\frac{23}{5}\) = 4.6
6	1	23 + 1 = 24	\(\frac{24}{6}\) = 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.

Q	TC
0	10
1	30
2	45
3	55
4	70
5	90
6	120

Answer 25: The solution to this question can be as follows:

Q	TFC	TVC	TC	AFC	AVC	SAC	SMC
0	10	0	10	–	–	–	–
1	10	20	30	10	20	30	20
2	10	35	45	5	17.5	22.5	15
3	10	45	55	3.33	15	18.33	10
4	10	60	70	2.5	15	17.5	15
5	10	80	90	2	16	18	20
6	10	110	120	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.

Q	TC
1	50
2	65
3	75
4	95
5	130
6	185

Answer 26: The solution to this question is as follows:

Q	TFC	TVC	TC	AFC	AVC	SAC	SMC
1	20	30	50	20	30	50	–
2	20	45	65	10	22.5	32.5	15
3	20	55	75	6.67	18.33	25	10
4	20	75	95	5	18.75	23.75	20
5	20	110	130	4	22	26	35
6	20	165	185	3.33	27.5	30.83	55

Question 27: A firm’s SMC schedule is shown in the following table. The total fixed cost of the firm is Rs 100. Find the TVC, TC, AVC and SAC schedules of the firm.

Q	TC
0	−
1	500
2	300
3	200
4	300
5	500
6	800

Answer 27: The solution to this question is as follows:

Q	TFC	TC	TVC	AVC	SAC
0	100	–	0	–	–
1	100	500	400	400.00	500.00
2	100	300	200	100.00	150.00
3	100	200	100	33.33	66.67
4	100	300	200	50.00	75.00
5	100	500	400	80.00	100.00
6	100	800	700	116.67	133.33

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.

Answer 28: To find the maximum possible output that the firm can produce with the given production function:

\(Q = 5L^{\frac{1}{2}} K^{\frac{1}{2}}\)

and the inputs:

• ( L = 100 ) (units of labor)
• ( K = 100 ) (units of capital)

Substitute ( L ) and ( K ) into the Production Function

We will substitute the values of ( L ) and ( K ) into the production function:

Q = \(5(100)^{\frac{1}{2}}(100)^{\frac{1}{2}}\)

Calculate \( (100)^{\frac{1}{2}} \)

\((100)^{\frac{1}{2}} = 10\)

Substitute Back into the Production Function

Now substitute this result back into the production function:

Q = 5(10)(10)

Calculate the Output

Q = 5 × 100 = 500

The maximum possible output that the firm can produce with 100 units of labor (L) and 100 units of capital (K) is 500 units.

Question 29: Let the production function of a firm be Q = 2L²K²
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? 

Answer 29:

• a) Q = 2L² K² …………(1)
• L = 5 units of labour
• K = 2 units of capital
• Putting these values in equation (1)
• Q = 2 (5)²(2)²
• = 2 (25) (4)
• Q = 200 units

• b) If L = 0 units and K = 100 units
• Putting these values in equation (1)
• Q = 2 (0)² (100)²
• Q = 0 units

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

Answer 30: To find the maximum possible output for the given production function:

Q = 5L + 2K

with:

• ( L = 0 ) (units of labor)
• ( K = 10 ) (units of capital)

Substitute the values into the production function

Substituting ( L = 0 ) and ( K = 10 ):

Q = 5(0) + 2(10)

Calculate the output

Q = 0 + 20 = 20

The maximum possible output for the firm with 0 units of labor and 10 units of capital is 20 units.