# NCERT Solutions for class 12th Economics Part A Chapter 3 Production and Cost

#### NCERT Textbook Questions Solved

Question 1. Explain the concept of a production function.

Ans. It expresses the functional relationship between inputs and corresponding output. In other words, it shows the minimum quantities of various input required to produce a given level of output. Mathematically,
Q = F (L L1 K O)
Where Q is quantity produced, L L1 K O are land, labour, capital and organization respectively. There are two types of production function.

1. Production Function in the Short Run: Short run is a period of time when some factors are fixed and some are variable. Accordingly, output can be increased only by using more of a variable factor. Often, in the short period K (production capacity of a firm) is constant and L (labour) is variable. Short period, by definition, is too short for a firm to change its production capacity. Accordingly, production can be increased only by using more of L (labour).
2. Production Function in the Long Run: Long period is a period of time when all factors are variable. Accordingly, output can be increased only by using more of all factors of Production. In the long run, production will increase when all factors are increased in the same proportion.

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

Ans. Total Product (TP) refers to total quantity of goods produced by a firm during a given period of time with given number of inputs.
TP = AP X Q or ΣMP
For example, if 10 labours produce 60 kg. of rice, then total product is 60 kg. In the short-run, a firm can expand TP by increasing only the variable factors. However, in the long-run, TP can be raised by increasing both fixed and variable factors.

Shape of TP Curve: TP Curve starts from the origin, increases at an increasing rate, then increases at a decreasing rate, reaches a maximum and after that it starts falling. Thus as more units of variable factors are employed, it will not always increase the TP. It is illustrated with a TP Schedule in Table and a TP curve.

TP Schedule confirms that in the beginning total production increases at an increasing rate. TP starts increasing at a decreasing rate with the employment of the fourth unit of labour. When seventh unit of labour is employed, TP becomes stable at 30 units and with the employment of the eighth unit, it starts declining.

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

Ans. Average Product (AP)
Average product refers to output per unit of variable input. Average Product is also known as ‘Average Physical Product (APP)’ or ‘Average Return’
For example, if total product (TP) is 60 kg. of rice, produced by 10 labour (variable input), then average product will be 60 ÷ 10 = 6 kg.
AP is obtained by dividing TP by units of variable factor.

From the AP Schedule, it is clear that initially AP is zero when no labor is employed, then it increases till three units of labour are employed, reaches a maximum when four units of labour are employed and then starts declining.

Shape of AP Curve: AP curve starts from the origin, increases at a decreasing rate, reaches a maximum and then starts falling. AP curve is inverted-U shaped. As long as TP is positive, AP is positive. It can be illustrated with the help of an AP schedule given in Table and AP
The curve given in fig.

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

Ans. Marginal Product refers to addition to total product, when one more unit of variable factor is employed. Marginal Product (MP) is also known as ‘Marginal physical product (MPP)’ or ‘Marginal Return’.
MPn = TPn – TPn – 1
Where:
MPn = Marginal product of nth unit of variable factor; TPn = Total product of n units of variable factor;
TPn-1 = Total product of (n-1) units of variable factor; n = Number of units of variable factor.
For example, if 10 labours make 60 kg. of rice and 11 labours make 67 kg. of rice, then MP of 11th labour will be:
MP11 = TP11 – TP10 MP11 = 67 – 60 = 7 kg.
One More way to calculate MP:
MP is the change in TP when one more unit of variable factor is employed. However, when change in variable factor is greater than one unit, then MP can be calculated as:

Shape of MP Curve: The MP Curve rises initially, reaches a maximum and then starts falling. When TP is maximum, MP is Zero. When TP falls, MP is negative. It can be illustrated with a MP schedule given in Table
and MP curve given in fig.

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

Ans. Relationship between TP and MP:

1. When TP increases at an increasing rate, MP increases.
2. When TP increases at a decreasing rate, MP falls but it is positive.
3. When TP is maximum, MP is zero.
4. When TP starts falling, MP becomes negative.

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

Ans. Short run is a time period in which we cannot change all the factors of production. Some factors can be changed which are called variable factors and some cannot be changed which are fixed factors. However, in the long run all factors of production can be changed. No factor of production in the long run is fixed.

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

Ans. Law of diminishing returns or principle of diminishing marginal productivity is an economic law which states that if one input in the production of a commodity is increased while all other inputs are held fixed, a point will eventually be reached at which additions of the input yield progressively smaller, or diminishing, increases in output.

In the classic example of the law, a farmer who owns a given acreage of land will find that a certain number of labourers will yield the maximum output per worker. If he should hire more workers, the combination of land and labour would be less efficient because the proportional increase in the overall output would be less than the expansion of the labour force. The output per worker would therefore fall. This rule holds in any process of production unless the technique of production also changes.

Question 8. What is the law of variable proportions?

Ans. STATEMENT OF THE LAW: This law states that as more and more units of variable factors are employed on a
given quantity of fixed factors, TP first increases at an increasing rate(MP increases) then at a diminishing rate (MP falls but is positive), reaches its maximum(MP is 0),
and finally starts falling (MP becomes Negative).

Assumptions of Law of Variable proportions
1. It operates in the short run, as factors are classified as variable and fixed factors;
2. The law applies to all fixed factors including land;
3. This law applies to the field of production only;
4. The effect of change in output due to change in variable factor can be easily determined;
5. The state of technology is assumed to be constant during the operation of this law;
6. It is assumed that all variable factors are homogeneous.

Three Stages or Phases of Production

The law of variable proportion can be divided into three distinct stages. These three stages of the short-run law of production are graphically illustrated by the relationship between TP and MP curves. It is given in the schedule and figure.

Stage I: Stage of Increasing Returns

It goes from the origin to the point where the MP curve is maximum. In this stage, TP curve is increasing at an increasing rate. MP curve rises and reaches a maximum. A rational producer will not operate in this stage because
MP of the fined factor is negative in stage I.

Stage II: Stage of Diminishing Returns

It is the most important stage out of the three stages. Stage II of production ranges from the point where MP curve is maximum to the point where the MP Curve is zero. MP curve is positive but declining. TP curve increases at a decreasing rate and reaches a maximum. A rational producer will always operate in this state. The law of diminishing returns operates in stage II.

Stage III: Stage of Negative Returns

It covers the entire range over which MP curve is negative. In this stage, TP curve falls. A rational producer will not operate in this stage, even with free labour, because he could increase his output by employing less labour. It is a non-economic and an inefficient stage.
Saturation point is the point where mp is zero or tp is maximum.

Reasons for Increasing Returns:

1. Better Utilization of the Fixed Factor: In the first phase, the supply of the fixed factor (say, land) is too large, whereas variable factor are too few. So, the fixed factor is not fully utilized. When variable factors are increased and combined with fixed factors, then fixed factor is better utilized and output increases at an increasing rate.

2.Increased Efficiency of Variable Factor: As more and more units of labour are employed, the work gets divided according to skills and abilities which leads to specialization and hence improvement in efficiency. This leads to increasing returns to a factor.

Reasons for Diminishing Returns to a Factor:
The main reasons for occurrence of diminishing returns to a factor are:

1. Optimum Combination of Factors: Among the different combination between variable and fixed factor, there is one optimum combination, at which total product (TP) is maximum. After making the optimum use of fixed factor, the marginal returns of variable factor begins of diminish. For example, if a machinery (fixed factor) is at its optimum use, when 4 labours are employed, then addition of one more labour will increase TP by very less amount and MP will start diminishing.

2. Imperfect Substitutes: Diminishing returns to a factor occurs because fixed and variable factors are imperfect substitutes of one another. There is a limit to the extent of which one factor of production can be substituted for another. For example, labour can be substituted in place of capital or capital can be substituted in place of labour till a particular limit. But, beyond the optimum limit, they become imperfect substitutes of one another, which lead to diminishing returns.

Reasons for Negative Returns to a Factor:
The main reasons for the occurrence of negative returns to a factor are:

1. Limitation of Fixed Factor: The negative returns to a factor apply because some factors of production are of fixed nature, which cannot be increased with increase in variable factor in the short run.

2. Poor Coordination between Variable and Fixed Factor: When the variable factor becomes too excessive in relation to the fixed factor, then they obstruct each other. It leads to poor coordination between variable and fixed factors. As a result, total output falls instead of rising and marginal product becomes negative.

3. Decrease in Efficiency of Variable Factor: With continuous increase in variable factor, the advantages of specialization and division of labour start diminishing. It results in inefficiencies of variable factors, which is another reason for the negative returns to eventually set in.

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

Ans. When on doubling the inputs, output also get doubled, it is called constant returns to scale.

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

Ans. When on doubling the inputs, output gets more than doubled, it is called increasing returns to scale.

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

Ans. When on doubling the inputs, output gets less than doubled, it is called decreasing returns to scale.

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

Ans. Cost of producing a commodity is the payment made to the factors of production which are used in the production of that commodity.
A Cost function shows the functional relationship between output and cost of production. It gives the least cost combinations of inputs corresponding to different levels of outputs.
Cost function is given as: C = f(Q) Where,
C = Cost
Q = Output
Note: Q. No. 9, 10 and 11 have been deleted from course.

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

Ans. Total Cost: In short period, total cost comprises of fixed costs and Variable Cost:
TC = TFC + TVC
(TC = Total Cost, TFC = Total Fixed Cost; TVC = Total Variable Cost)
(a) Total Fixed Cost: Fixed Costs are the sum total of expenditure incurred by the producer on the purchase or hiring of fixed factors of production. These costs do not change with the change in volume of output. Whether the output is zero or maximum, fixed costs remain the same. These costs are also known as supplementary costs or Indirect Costs. Fixed costs include expenses like: (i) Rent (ii) Wages of permanent employees, (iii) Licence Fees, etc. Fixed costs are explained with the help of the following table and figure.

(b) Total Variable Costs or Prime Costs: Variable Costs are those which are incurred on the use of variable factors. When output changes, these costs also change. As the output increases, these costs also increase and as the output decreases, these costs also decrease. When output is zero, these costs are also zero. These costs are called Prime Costs or Direct Costs. Variable costs include expense like:
(i) Purchases of raw material,
(ii) Wages of casual labour,
(iii) Expenses on motive power or electricity,
(iv) Wear and tear expenses, etc. Variable costs are explained with the help of table and figure.

(c) Total Cost: It is defined as the aggregate of all costs of producing any given level of output. TC curve has been shown in the figure. It is an inverse S-shaped curve starting from the level of fixed cost. A change in TC is entirely due to change in TVC. TC curve is above the TVC curve by the amount of TFC. The vertical distance between TVC and TC curves is the amount of TFC.

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

Ans. Average Total Cost (ATC): Average Cost is the cost per unit of output produced. It is also called unit cost of production. The per unit cost explains the relationship between cost and output in a more realistic manner. From total fixed cost (TFC), total variable cost (TVC) and total cost (TC), we can obtain per unit costs. The kinds of ‘per unit costs’ are:
1. Average Fixed Cost
2. Average Variable Cost
ATC = AFC + AVC / TC ÷ Q

The AC curve as derived from TC curve is U-shaped. It shows that as the output increases the value of AC falls continuously till it reaches a minimum point. Beyond this point, the AC starts rising. The reason behind the U-shape of AC curve is the law of variable proportion.

(a) Average Fixed Cost (AFC)
Average fixed cost refers to the per unit fixed cost of production. It is calculated by dividing TFC by total output. AFC = TFC ÷ Q
Where: AFC = Average Fixed Cost; TFC = Total Fixed Cost; Q = Quantity of output
AFC falls with increase in output as TFC remain same at all levels of output. AFC curve is a rectangular hyperbola, i.e. area under AFC curve remains same at different points.

AFC does not touch any of the axis As AFC is a rectangular hyperbola, it approaches both the axes. It gets nearer and nearer to the axes, but never touches them. AFC can never touch the X-axis as TFC can never be zero. AFC curve can never touch the Y-axis because at zero level of output, TFC is a positive value and any positive value
divided by zero will be an infinite value.

(b) Average Variable Cost (AVC)
Average variable cost refers to the per unit variable cost of production. It is calculated by dividing TVC by total output.
AVC = TVC ÷ Q
Where: AVC = Average Variable Cost; TVC = Total Variable Cost; Q = Quantity of output
AVC initially falls with increase in output. Once the output rises till optimum level, AVC starts rising. It can be better understood with the help of Table. AVC initially falls with increase in output and after reaching its minimum level (Rs. 5), AVC starts rising.
Like AVC, average cost also initially falls with increase in output. Once the output rises till optimum level, AC starts rising.

Interrelation between ATC, AVC and AFC is as follows:
(a) The distance between ATC and AVC keep on falling because it is AFC which keeps on falling but ATC and AVC can never touch each other because AFC can never be zero.
(b) AVC reaches its minimum earlier than ATC because ATC is also falling because of AFC and if fall in AFC is more than rise in AVC, ATC will continue to fall.
(c) ATC and AVC both are U shaped due to law of variable proportion. AFC is rectangular hyperbola. It is shown as follows:

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

Ans. No, there cannot be any fixed cost in the long run because there are no fixed factors and cost of fixed factors is called fixed cost.

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

Ans. AFC curve looks like a rectangular hyperbola. It is so because TFC is fixed and as we keep on increasing quantity we get such values of AFC which give us a curve on which rectangle dram from any point taking x axis and y axis, they will have equal area because area will be equal to AFC × Q = TFC.

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

Ans. All of them look like u shaped due to law of variable proportion. When we get increasing returns in production in Ist stage of this law, AC, AVC and MC fall. When we start getting decreasing returns to a factor, AC, ATC and MC start rising. Therefore, it looks like U shaped.

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

Ans. 1. Both AVC and MC are derived from TVC by the formulas,

since MC is the changes in TVC or TC due to additional unit produced.
2. Both AVC and MC curves are U-shaped reflecting the law of Variable Proportion.
3. The minimum point of AVC curve will always occur to the right of the minimum point of MC curve.
4. When AVC is falling, then MC is below AVC.
5. When AVC is rising, then MC is above AVC.
6. When AVC is neither falling nor rising, then MC = AVC.
7. There is a range over which AVC is falling and MC is rising.

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

Ans. 1. SMC cuts SAC at the latter’s minimum because when AC is falling, then MC is below AVC.
2. When AVC is rising, then MC is above AC.
3. When AVC is neither falling nor rising, then MC = AC
Therefore, it can cut AC only at latter’s minimum.

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

Ans. Short run average cost curve is u shaped because of law of variable proportion. When we get increasing returns in production in Ist stage of this law MC falls. When we start getting decreasing returns to a factor, MC starts rising. A curve which first falls and then rises will look like U shaped. Therefore, it looks like U shaped.

Question 21. What do the long run marginal cost and the average cost curves look like?
Note:
Deleted from the course.

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

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.

Question 24. The following table gives the marginal product schedule of labour. It is also given that the total product of labour is zero at zero level of employment. Calculate the total and average product schedules of labour.

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.

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.

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.

Question 28. Let the production function of a firm be Q = 5L½ K½ . Find out the maximum possible output that the firm can produce with 100 units of L and 100 Units of K

Ans. Q = 5L½ K½
The maximum possible output that the firm can produce
with 100 units of L and 100 is as follows: Units of K.
Q = 5 × 1001/21001/2 Q = 5 × 10 × 10
Q = 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?

Ans. Q = 2L2K2
The maximum possible output that the firm can produce
with 5 units of L and 2 units of K is as follows: Q = 2 × 5222 Q = 2 × 25 × 4 Q = 200 units. The maximum possible output that the firm can produce with zero unit of L and 10 units of K is as follows: Q = 2 × 02102
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
Ans. Q = 5L + 2K
Q = 5(0) + 2(10)
Q = 20

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