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NCERT Class 11 Economics Chapter 11 Production and Costs
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Production and Costs
Chapter: 11
PART – (B) INTRODUCTORY MICROECONOMICS
TEXTUAL QUESTION ANSWERS
1. Explain the concept of a production function.
Ans: Production function refers to the functional relationship between physical inputs and physical outputs.
It is expressed in terms of the equation:
Qₓ = f(L, K)
Where, Qₓ = Production of good X
L = Labour (Variable Factor)
K = Capital (Fixed Factor)
2. What is the total product of an input?
Ans: Total Product is the sum total of output produced by all units of labour along with other factors of production. In other words, it is defined as total quantity of goods and services produced by a firm in a given period of time.
The shape of the TP curve is steep from the origin then begins to flatten and eventually drops off.
3. What is the average product of an input?
Ans: Average product is a way used by companies to measure the total output produced using a particular combination of inputs. It is defined as the output per unit of factor inputs or the average of the total product per unit of input and can be calculated by dividing the Total Product by the inputs (variable factors).
4. What is the marginal product of an input?
Ans: Marginal Product is an addition made to the total product by employing an additional unit of variable input, keeping the other inputs unchanged.
The marginal product curve is generally inverted ‘U’ shape.
5. Explain the relationship between the marginal product and the total product of an output.
Ans: There is a close relationship between the marginal product and the total product of an input. For any level of employment of a factor input, if we add up the marginal product for every unit of that factor up to that level, we get the total product of that factor at that level of employment.
The relationship between MP and TP is as follows:
| Factors | MP | TP |
| 0 | — | — |
| 1 | 10 | 10 |
| 2 | 14 | 14 + 10 = 24 |
| 3 | 16 | 24 + 16 = 40 |
| 4 | 10 | 40 + 10 = 50 |
| 5 | 6 | 50 + 6 = 56 |
| 6 | 1 | 56 + 1 = 57 |
6. Explain the concepts of the short run and the long run.
Ans: The short-run is a period when some factors of production are fixed and some are variable. Output can be increased only by increasing the application of the variable factor. In the short run, the scale of production remains constant. The long run is a period when all factors of production are variable.
7. What is the law of diminishing marginal product?
Ans: Diminishing marginal returns are an effect of increasing input in the short-run, while at least one production variable is kept constant, such as labor or capital. Returns to scale, on the other hand, are an impact of increasing input in all variables of production in the long run.
8. What is the law of variable proportions?
Ans: The law of variable proportions is as follows: “If a producer increases the units of a variable factor while keeping other factors fixed, then initially the total product increases at an increasing rate, then it increases at a diminishing rate, and finally starts declining.”
9. When does a production function satisfy constant returns to scale?
Ans: Constant returns to scale (CRS) is a property of production function that holds when a proportional increase in all inputs results in an increase in output by the same proportion.
10. When does a production function satisfy increasing returns to scale?
Ans: Output per unit of labor input increases as the scale of production rises, hence increasing returns to scale. When average costs decline as output increases, it means that it becomes cheaper to produce the average unit as the scale of production rises, hence resulting in economies of scale.
11. When does a production function satisfy decreasing returns to scale?
Ans: Decreasing returns to scale DRS holds when a proportional increase in all the factors of production leads to an increase in the output by less than the proportion.
12. Briefly explain the concept of the cost function.
Ans: A cost function is a mathematical formula used to calculate the total cost of production for a given quantity of output. It represents the relationship between the cost of production and the level of output, incorporating various factors such as fixed costs, variable costs, and total costs.
13. What are the total fixed cost, total variable cost and total cost of a firm? How are they related?
Ans: In the figure, units of output are shown on the OX-axis and costs on Y-axis. The TFC curve represents fixed cost. It is horizontal and parallel to the X-axis. It shows that TFC is fixed and does not change with the change in the level of output. At the zero level of output it is not zero. It is equal to total cost at the zero level of output as TFC and TC both starts from the same point, i.e., at the point above origin. The TVC curve represents variable cost. It starts from 0 showing that variable cost is zero at zero level of output. It is positively sloped showing that variable cost increases with the increase in the level of output. Initially variable cost increases at the diminishing rate and after a certain limit it increases at the increasing rate. TC curve represents total cost. It is the vertical summation of total fixed cost and total variable cost curves. The vertical distance between TC and TVC curves remains constant. At zero level of output TC = TFC; because at this level of output, there is no variable cost.
14. What are the average fixed cost, average variable cost and average cost of a firm? How are they related?
Ans: Average Fixed Cost: Average fixed cost is the fixed cost per unit of output. It is obtained by dividing the total fixed cost by the number of units produced.
Average Variable Cost: Average variable cost is the variable cost per unit of output. It is obtained by dividing average cost by the number of units produced.
Average Cost: Cost per unit is called average cost. It is calculated by dividing total cost by units produced.
Relationship between AFC, AVC and AC:
(a) AC = AFC + AVC
(b) AFC = AC – AVC
(c) AVC = AC – AFC
15. Can there be some fixed cost in the long run? If not, why?
Ans: No costs are fixed in the long run. A firm can build new factories and purchase new machinery, or it can close existing facilities. In planning for the long run, a firm can compare alternative production technologies or processes.
16. What does the average fixed cost curve look like? Why does it look so?
Ans: The average fixed cost (AFC) curve looks like a rectangular hyperbola. It happens because the same amount of fixed cost is divided by increasing output. As a result, , AFC curve slopes downwards and is a rectangular hyperbola, i.e., the area under AFC remains the same at different points.
17. What do the short run marginal cost, average variable cost and short run average cost curves look like?
Ans: Short run marginal cost, average variable cost and short run average cost look like “U” shaped. It is due to the law of variable proportions. It may be shown as under:
18. Why does the SMC curve cut the AVC curve at the minimum point of the AVC curve?
Ans: Marginal cost curve cuts average cost curve only at its minimum point because it is only here that MC = AC.
The marginal cost curve always intersects the average total cost curve at its lowest point because the marginal cost of making the next unit of output will always affect the average total cost. As a result, so long as marginal cost is less than average total cost, average total cost will fall.
19. At which point does the SMC curve cut the SAC curve? Give reason in support of your answer.
Ans: The SMC curve always intersects the SAC curve at its minimum point.
20. Why is the short run marginal cost curve ‘U’ shaped?
Ans: The correct option is B U-shaped The U shape of SAC curve is directly due to the law of variable proportions, since in the short run some factors are fixed and some are variable. Initially, the average cost falls up to the optimum capacity level of output due to increasing returns to variable factor and it increases thereafter due to diminishing returns to the variable factor.
21. What do the long run marginal cost and the average cost curves look like?
Ans: Long run marginal cost and the average cost curves are U-shaped, but they are flatter as shown below:
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 |
Ans:
| L | TPL | APL | MPL |
| 0 | 0 | – | – |
| 1 | 15 | 15.00 | 15 |
| 2 | 35 | 17.50 | 20 |
| 3 | 50 | 16.67 | 15 |
| 4 | 40 | 10.00 | -10 |
| 5 | 48 | 9.60 | 8 |
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 | 1 | 2 | 3 | 4 | 5 | 6 |
| APL | 2 | 3 | 4 | 4.25 | 4 | 6 |
Ans:
| L | APL | TPL | MPL |
| 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 |
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:
| L | 1 | 2 | 3 | 4 | 5 | 6 |
| MPL | 3 | 5 | 7 | 5 | 3 | 1 |
Ans:
| L | MPL | TP | AP |
| 0 | – | – | – |
| 1 | 3 | 3 | 3.00 |
| 2 | 5 | 8 | 4.00 |
| 3 | 7 | 15 | 5.00 |
| 4 | 5 | 20 | 5.00 |
| 5 | 3 | 23 | 4.6 |
| 6 | 1 | 24 | 4.00 |
25. The following table shows the total cost schedule of a firm. What is the total fixed cost schedule of this firm? Calculate TVC, AFC, AVC, SAC and SMC schedules of the firm:
| Y | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| TC | 10 | 30 | 45 | 55 | 70 | 90 | 100 |
Ans: Total Fixed Cost Schedule of a firm:
| Y | FC | TC |
| 0 | 10 | 10 |
| 1 | 10 | 30 |
| 2 | 10 | 45 |
| 3 | 10 | 55 |
| 4 | 10 | 70 |
| 5 | 10 | 90 |
| 6 | 10 | 120 |
At zero level of output, TC = FC. In the table TC at zero level of output is 10. Hence, FC will be 10. The fixed cost remains constant. So, the fixed cost will be 10 at 0 level of output.
TVC, AFC, AVC, SAC and SMC schedules of the firm:
| Y | TC | TFC | TVC | AVC | SAC | SMC |
| 0 | 10 | 10 | – | – | – | – |
| 1 | 30 | 10 | 20 | 20.00 | 30 | 20 |
| 2 | 45 | 10 | 35 | 17.5 | 22.5 | 15 |
| 3 | 55 | 10 | 45 | 15.00 | 18.33 | 10 |
| 4 | 70 | 10 | 60 | 15.00 | 17.50 | 15 |
| 5 | 90 | 10 | 80 | 16.00 | 18.00 | 20 |
| 6 | 120 | 10 | 110 | 18.33 | 20.00 | 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 value of output:
| Q | 1 | 2 | 3 | 4 | 5 | 6 |
| TC | 50 | 65 | 75 | 95 | 130 | 185 |
Ans:
| Q | TC | TFC | TVC | AFC | AVC | SAC | SMC |
| 0 | 20 | 20 | – | – | – | – | – |
| 1 | 50 | 20 | 30 | 20 | 30 | 50.00 | 30 |
| 2 | 65 | 20 | 45 | 10 | 22.5 | 32.5 | 15 |
| 3 | 75 | 20 | 55 | 6.67 | 18.33 | 25.0 | 10 |
| 4 | 95 | 20 | 75 | 5 | 18.75 | 23.75 | 20 |
| 5 | 130 | 20 | 110 | 4 | 22 | 26.0 | 35 |
| 6 | 185 | 20 | 165 | 3.33 | 27.5 | 30.83 | 55 |
Here AFC at 4 units of output is ₹5. With this information, we will calculate TFC by multiplying 4 × 5. TFC will be ₹20. At all levels of output TFC will be ₹20 and TC will also be ₹20 at zero level of output.
27. A firm’s SMC schedule is shown in the following table. The total fixed cost of the firm is ₹100. Find TVC, TC, AVC and SAC schedules of the firm:
| Q | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| SMC | – | 500 | 300 | 200 | 300 | 500 | 800 |
Ans:
| Y | SMC | TFC | TC | TVC | AVC | SAC |
| 0 | – | 100 | 100 | – | – | – |
| 1 | 500 | 100 | 600 | 500 | 500 | 600 |
| 2 | 300 | 100 | 900 | 800 | 400 | 450 |
| 3 | 200 | 100 | 1100 | 1000 | 333.33 | 366.67 |
| 4 | 300 | 100 | 1400 | 1300 | 325.00 | 350.00 |
| 5 | 500 | 100 | 1900 | 1800 | 360.00 | 380.00 |
| 6 | 800 | 100 | 2700 | 2600 | 433.33 | 450.00 |
28. Let the production function of a firm be: Q = 5 L1/2 K1/2 .
Find out the maximum possible output that the firm can produce with 100 units of L and 100 units of K.
Ans: Q = 5L1/2 K1/2 or Maximum Output
= 5 × 1001/2 × 100 1/2
= 5 × 10 × 10
= 50 × 10 = 500
29. Let the production function of a firm be: Q = 2L2 K2
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 Land 10 units of K?
Ans: (i) Q = 2 L2 K2
or Output = 2 × 5222 = 2 × 25 × 4
= 200 units
(ii) The maximum output would be zero with zero units of L and 10 units of K. The reason is that the production function, our assumption is that if any input becomes zero, then the production would also be zero. Since here labour is zero, the output would also be zero.
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: In production function, our assumption is that if any input becomes zero, the production would also be zero. Since here labour is zero, the output would also be zero.
