NCERT Solutions for Class 11 Economics Chapter 3 - Production And Costs

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1. Explain the concept of a production function.

Ans. Production function expresses the maximum quantity of a commodity that can be produced per unit of time, with given amount of inputs when the best production technique is used. It is expressed in terms of the equation :
Q_x = f(L, K)
where Q_x = Production of commodity
L = Labour
K = Capital
(It is assured that labour and capital are the only two factors used for production)

2. What is the total product of an input?

Ans. Total product refers to the total amount of a commodity produced during some period of time along with different factors of production.

3. What is the average product of an input?

Ans. Average product refers to the production unit of variable factor.
$$\text{Therefore Average product}=\frac{\text{Total Product}}{\text{Output}}$$

4. What is the marginal product of an input?

Ans. Marginal proudct is the change in total production sesulting from change in the unit of a variable factor.

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

Ans. The relationship between TP and MP are :
(i) When TP increases at an increasing rate, MP increases.
(ii) When TP increaes at a diminishing rate, MP declines.
(iii) When TP reaches its maximum, MP becomes zero.
(iv) When TP begins to decline, MP becomes negative.

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

Ans. Short-run production function refers to a situation where a firm makes changes in the only output by changing its variable factors and all the other inputs are fixed. Time period in which firm make these change in said to be short run.
Long-run production function refers the change in output when all inputs used in the production of good are changed simultaneously and in the some proportion. In this case scale of production is changed.

7. What is the law of diminishing marginal product?

Ans. Law of diminishing marginal product states that as more and more unit of a variable factor are applied to the given quantity of a fixed factor, total product increase at a diminishing rate and marginal product falls.

8. What is the law of variable proportions?

Ans. Samuelson defines this law as follows: “An increase in some inputs relative to other fixed inputs will in a given state of technolgy, cause output to increase at an increasing rate but after a point, the extra output resulting from the same additions of extra input will become less and less.

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

Ans. There is a situation of constant returns to a scale when a proportional increase in all the factors of production leads to an equal proportional increase in the output.

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

Ans. Increasing returns to scale holds when a proportional increase in all the factors of production leads to an increase in the output by more than the proportion.

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

Ans. When an additional unit of variable factor gives lesser and lesser amount of output, it satisfies decreasing returns to scale.

12. Briefly explain the concept of the cost function.

Ans. 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.

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

Ans. Total Fixed Cost is incurred by a firm in order to acquire the fixed factors of production and it does not change with the change in output.
Total Variable Cost is incurred by a firm on variable inputs of the firm used for production and it does change with the change in output.
For instance, wages of labour, fuel expenses, etc.
Total Cost is the sum total of total variable cost and total fixed cost.
Thus,
TC = TFC + TVC.

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

Ans. Average Fixed Costs (AFC): Average fixed cost refers to the per unit fixed cost of production. It is calculated by dividing TFC by total output i.e.,
AFC =TFC/Q
where,
AFC = Average Fixed Cost
TFC = Total Fixed Cost
Q = Quantity of output.
Average Variable Cost (AVC): Average variable cost refers to the per unit variable cost of production.
It is calculated by dividing TVC by the total output.
AVC =TVC/Q
where
AVC = Average Variable Cost
TVC = Total Variable Cost
Q = Quantity of output
Average Total Cost (ATC) Or Average Cost (AC): Average cost refers to the per unit total cost of production. It is calculated by dividing TC by the total output.
AC =TC/Q
where
AC = Average Cost
TC = Total Cost
Q = Quantity of output
The average cost is also defined as the sum of the average fixed cost and average variable cost.
AC = AFC + AVC
Like AVC, average cost also initially falls with an increase in output. Once the output rises to the optimum level, AC starts rising.

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

Ans. No, there can’t be any fixed cost in the long run since all costs are variable costs in the long run and no factor is a fixed factor in the long run as fixed costs exists only in the short-run.

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

Ans. 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.

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

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

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

Ans. It is because when AVC falls, SMC is less than AVC. When AVC starts rising, SMC is more than AVC. Hence, it happens only when AVC is constant and at its minimum point that SMC is equal to AVC. Therefore, the SMC curve cuts the AVC curve when it is minimum.

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

Ans. 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.

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

Ans. The marginal cost curve is U-shaped in the short run because of the “law of variable proportions”. According to this law, MC curve initially slopes downward till it reaches its minimum point and thereafter, it starts rising. Therefore, it leads to a U-shape of the curve when presented graphically.

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

Ans. Both MC and AC curves, in the long run, are U-shaped cost curves. This U-shape is a little less flat than the U-shape of the short-run MC and AC curves i.e., long-run MC and AC curves are a little flatter in shape. This behaviour is in accordance with the returns to scale.

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

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

$$\text{Ans. APL}=\frac{TP_L}{L}\\APL=\frac{\Delta TP_L}{\Delta L}$$

Labour	TP_L	MP_L	AP_L
0	0	—	0
1	15	15	15
2	35	20	17.5
3	50	15	16.67
4	40	10	10
5	48	8	9.6

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

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.

Ans. TPL = AP_L × L

$$MPL=\frac{\Delta TP_L}{\Delta L}$$

Labour	AP_L	TP_L	MP_L
1	2	2 × 1 = 2	2
2	3	3 × 2 = 6	4
3	4	4 × 3 = 12	6
4	4.25	4.25 × 4 = 17	5
5	4	5 × 4 = 20	3
6	3.5	3.5 × 6 = 21	1

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	MP_L
1	3
2	5
3	7
4	5
5	3
6	1

Ans. TPn = TP_{n – 1} + MP

$$AP_L=\frac{TP_L}{L}$$

Labour	MP_L	TP_L	AP_L
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

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

Ans. TVC = TC –TFC

$$AVC=\frac{TVC}{Q}\\SAC =\frac{TC}{Q}\\AFC =\frac{TFC}{Q}$$
SMC = TC_n – TC_{n – 1}

Quantity	TC	TFC	AFC	SAC	TVC	AVC	SMC
0	10	10	—	—	0	0	0
1	30	10	10	30	20	20	20
2	45	10	5	22.5	35	17.5	15
3	55	10	3.33	18.33	45	15	10
4	70	10	2.5	17.5	60	15	15
5	90	10	2	18	80	16	20
6	120	10	1.67	20	110	18.33	30

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 ₹5. Find the TVC, TFC, AVC, AFC, SAC and SMC schedules of the firm for the corresponding values of output.

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

Ans. MC = TVC_n – TVC_{n – 1}
MC = 30 – 0
MC
= 30

Q	TC	TFC (4 × 5)	TVC (TC – TFC)	AFC = TFC/θ	SAC = TC/Q	SMC (TC _n – TC _{n – 1})
1	50	20	30	20	50	50 – 20 = 30
2	65	20	45	10	32.5	65 – 50 =15
3	75	20	55	6.67	25	75 – 65 =10
4	95	20	75	5	23.75	95 – 75 =20
5	130	20	110	4	26	130 – 95 =35
6	185	20	165	3.33	30.8	185 – 130 =55

27. A firm’s SMC schedule is shown in the following table. The total fixed cost of the firm is ₹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

Ans. TVC = SMC
$$SAC=\frac{TC}{Q}\\TC = TVC + TFC\\AVC =\frac{TVC}{Q}$$

Q	SMC	TFC	TVC	AVC	TC	SAC
0	—	100	0	—	100	—
1	500	100	500	500	600	600
2	300	100	800	400	900	450
3	200	100	1000	333.3	1100	333.7
4	300	100	1300	325	1400	350
5	500	100	1800	360	1900	380
6	800	100	2600	433.3	2700	450

28. Let the production function of a firm be
Q = 5L^1/2K^1/2
Find out the maximum possible output that the firm can produce with 100 units of L and 100 units of K.

Ans. Given : Q = 5, K = 100 units, L = 100 units
Qx = F(X₁.X₂)
Q = 5(100)^1/2 (100)^1/2
Q = 5(102)^1/2(102)^1/2
Q = 5 × 10 × 10
Q = 500 units
The maximum output, the firm can produce with 100 units of L and 100 units of K is 500 units.

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. Given, Q = 2L²K²
L = 5, K = 2
Q_x = f(X₁.X₂)
Q = 2(5)².(2)²
Q = 2 × 25 × 4
Q = 200 units
Maximum possible outut with 0 unit of L and 10 units of K is 0 units.