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

1. Explain the concept of a production function. 

Ans: Production function, in economics, is a comparison that expresses the connection between the numbers of productive influences  (such as labour and capital) used and the amount of product attained. The production function is written as: 

$Q x=f(L, K)$ Where

Where $Q x$ represents units of output $x$ produced.

L represents units of labour employed.

$K$ represents units of capital employed.

The above equation explains that $Q x$, units of output $x$ are produced by employing L units of labour and $K$ units of capital for a given technology. As the given level of technology escalates, the output will increase with the same level of capital and labour units.

2. What is the total product of input? 

Ans: We can describe the total product as the total volume or amount of final output formed by a firm using given inputs in a given period of time. It is also known as the total physical Product and is denoted as:

$T \mathrm{P}=\sum Q_{\mathrm{x}}$

Where, $\Sigma$ represents the summation of all outputs $Q_{x}$ represents units of output $x$ produced by an input.

3. What is the average product of an input? 

Ans: Average product is definite as the output per unit of factor inputs or the average of the total product per unit of input and can be considered by dividing the Total Product by the inputs (variable factors). Algebraically, it is explained as the ratio of the total product by units of labour employed to construct the output, i.e. $A P=\frac{T P}{L}$

Where,

$T P=$ Total product

$L=$ units of labour employed

4. What is the marginal product of an input? 

Ans: Marginal Product is distinct as the additional output constructed because of the employment of an additional unit of labour. In other words, it is the change in the total output brought by employing one additional unit of labour. Algebraically, it is expressed as the ratio of the change in the total product to the change in the units of labour employed, i.e. $M P_{L}=\frac{\Delta J P}{\Delta L}=$ Change in total product/Change in total units Or, $M P_{L}=T P_{n}-T P_{n-1}$

Where, $T P n=$ Total product produced by employing $n$ units of labour

TPn - 1 = Total product produced by employing $(n-1)$ units of labour.

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

Ans: According to the Law of Variable Proportion, when only one input is enlarged while all other inputs are kept persistent, Marginal Product and Total Product behave in the following manner: Connection  between marginal products (MP) and the total product (TP) can be denoted graphically as

(Image will be uploaded soon)

1. TP increases at an increasing rate till point $\mathrm{K}$ when more and more units of labour are employed. The point $\mathrm{K}$ is known as the point of inflexion. At this point, MP(second part of the figure) attains its maximum value at point U.

2. After point K, TP increases but at a decreasing rate. Simultaneously, MP starts falling after reaching its maximum level at point U.

3. When the TP curve reaches its maximum and becomes constant at point B, MP becomes zero.

4. When TP starts falling after B, MP becomes negative.

5. $\mathrm{MP}$ is derived from TP by $M P_{L}=\frac{\Delta T P}{\Delta L}$

Or, $M P_{L}=T P_{n}-T P_{n-1}$

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

Ans: Short run: In the short run, a firm cannot change all the inputs, which means that the output can be enlarged (decreased) only by employing more (less) of the inconstant factor (labour). It is generally presumed that in the short run a firm does not have adequate or sufficient time to vary its fixed factors such as, installing a new machine, building, plant etc. Hence, the output levels vary only because of varying employment levels of the variable factor (labour, raw material etc). 

Algebraically, the short-run production function is expressed as 

Where, $Q_{x}=f(L, K)$

$Q x=$ units of output $x$ produced

$L=$ labour input

$K=$ constant units of capital

Thus, in the short run, there will be some factors of production that are fixed at predetermined levels, eg: a farmer has a fixed amount of land.

Long run:

In the long run, a firm can change all its inputs, which means that the output can be enlarged (decreased) by employing more (less) of both the inputs - variable and fixed factors. In the long run, all inputs (including capital) are variable and can be changed according to the need levels of output. The law that clarifies this long-run concept is called returns to scale. The long-run production function is expressed as $Q x=f(L, K)$

Both $L$ and $K$ are variable and can be varied.

In other words, it is the time period where supplies can adjust themselves to change in demand.

7. What is the law of diminishing marginal product? 

Ans:  Law of diminishing Marginal Product 

According to this law, if the units of the variable factor keep on increasing keeping the level of the fixed factor constant, then initially the marginal product will rise but finally, a point will get to after which the marginal product of the variable factor will start falling. After this point, the marginal product of any additional variable factor will be zero, and can even be negative. 

For eg: It is usually possible to increase the output of a farm by adding more labour, fertilizers or water, but only up to a certain extent. If it were otherwise, any farm could feed the entire world.

8. What is the law of variable proportions? 

Ans: Law of Variable Proportions 

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.

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

Ans: Constant returns to scale will hold when a proportional enlargement in all the factors of production leads to an equal proportional increase in the output. For example, if both labour and capital are increased by $10 \%$ and if the output also increases by $10 \%$, then we say that the production function evinces constant returns to scale.

Algebraically, sustained returns to scale exists when $f(n L, n K)=n. f(L, K)$

This implies that if both labour and capital are increased by ' $n$ ' times, then the production also increases by ' $n$ ' times.

In other words, constant returns to scale occur when increasing the number of inputs lead to an equivalent increase in the output.

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

Ans: Increasing returns to scale (IRS) holds when a comparable increase in all the factors of production leads to an increase in the output by more than the proportion. In other words, when increases in inputs lead to a bigger comparable increase in output, it is referred to as increasing returns to scale. 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. 

Algebraically, IRS exists when $f(n L, n K)>n. f(L, K)$

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

Ans: Decreasing returns to scale (DRS) holds when a proportional enlarge in all the factors of construction leads to an increase in the output by less than the proportion. Or DRS mainly occurs when increasing inputs lead to a proportionally smaller increase in output. For example, if both labour and capital are increased by 'n' times but the effect increase in output is less than 'n' times, then we say that the construction function exhibits DRS. 

Algebraically, DRS exists when $f(n L, n K)<n. f(L, K)$

12. Briefly explain the concept of the cost function. 

Ans: The functional relationship between the cost of production and the output is called the cost function. It is conveyed as

$C=f(Q x)$

Where,

$C=$ Cost of production

$Q x=$ Units of output $x$ produced $/$ Quantity produced of $x$ goods

In other words, the output-cost relationship for a firm is depicted by the cost function.

The cost function depicts the least cost amalgam of inputs connected with different output levels.

The cost function of a firm depends on two things:

• Production Function
• Price of the factors of production. Higher the output of a firm, higher would be the production cost.

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

Ans: Total Fixed Cost (TFC) 

This refers to the costs sustained by a firm in order to acquire the fixed factors for production like the cost of machinery, buildings, depreciation, etc. The cost which does not change with the change in output is called TFC. In the short run, fixed factors cannot vary and accordingly the fixed cost remains the same through all output levels. These are also called overhead costs. In other words, fixed costs are the total outlay of the purchase or hiring of fixed factors of production. 

Total Variable Cost (TVC) 

This refers to the costs incurred by a firm on variable inputs for production. As we increase quantities of variable inputs, accordingly the sustained variable cost also goes up. It is also called 'Prime cost' or 'Direct cost' and includes expenses like - wages of labour, fuel expenses, etc. 

The cost which changes with the change in output is called TVC. 

Total Cost (TC) 

The sum of total fixed cost and total variable cost is called the total cost. Total cost = Total fixed cost + Total variable cost

TC = TFC + TVC 

Relationship Between TC, TFC, and TVC 

1. TFC curve remains constant throughout all the levels of output as the fixed factor is constant in the short run. 

2. TVC rises as the output is increased by employing more and more labour units. Till point Z, TVC rises at a decreasing rate, and so the TC curve also follows the same pattern. 

3. The difference between TC and TVC is equivalent to TFC. 

4. After point Z, TVC rises at an increasing rate and therefore TC also rises at an increasing rate. 

5. Both TVC and TFC is derived from TC i.e. TC = TVC +TFC 

6. Eg: if TFC is 15, TVC is 5, and then TC will be 15+5=20. 

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

Ans: Average Fixed Cost: 

It is defined as the fixed cost per unit of output. / Production. 

Where, 

TFC = Total fixed cost 

Q = Quantity of output produced 

Average Variable Cost: 

It is defined as the variable cost per unit of output./ production 

Where, 

TVC = Total variable cost 

Q = Quantity of output produced 

Average Cost: 

It is defined as the total cost per unit of output/production. The average cost is derived by dividing total cost by quantity of output. 

AC is also defined as the sum total of average fixed cost and average variable cost. AC = AFC + AVC 

Relationship between AC, AFC, AVC: 

1. AVC and AFC are derived from AC as AC = AFC +AVC. 

2. The plot for AFC is a rectangular hyperbola and falls continuously as the number of output increases. 

3. The minimum point of AVC will always exist to the left of the minimum point ofAC; i.e., point 'Z' will always lie to point M'. 

4. AFC being a rectangular hyperbola falls throughout; this causes the difference between AC and AVC to keep decreasing at higher output levels. However, it should be noted that AVC and AC can never intersect each other. If they intersect at any point, it would imply that AC and AVC are equal at that point. However, this is not possible as AFC will never be zero because it is a rectangular hyperbola that never touches the x-axis. 

5. AC inherits its shape from AVC's shape and it is because of the law of variable proportions that both the curves are U-shaped. 

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

Ans: Average Fixed Cost:

It is defined as the fixed cost per unit of output. / Production.

$A F C=\frac{T F C}{Q}$

Where,

$\mathrm{TFC}=$ Total fixed cost

Q = Quantity of output produced

Average Variable Cost:

It is defined as the variable cost per unit of output./ production $A V C=\frac{T V C}{Q}$

Where,

$T V C=$ Total variable cost

$\mathrm{Q}$ = Quantity of output produced

Average Cost:

It is defined as the total cost per unit of output/production. The average cost is derived by dividing total cost by quantity of output.

$A C=\frac{\Gamma C}{Q}$

$\mathrm{AC}$ is also defined as the sum total of average fixed cost and average variable cost. $\mathrm{AC}=$ $\mathrm{AFC}+\mathrm{AVC}$

Relationship Between AC, AFC, AVC: 

1. AVC and AFC are derived from AC as AC = AFC +AVC. 

2. The plot for AFC is a rectangular hyperbola and falls continuously as the quantity of output increases. 

3. The minimum point of AVC will always exist to the left of the minimum point ofAC; i.e., point 'Z' will always lie to point M'. 

4. AFC being a rectangular hyperbola falls throughout; this causes the difference between AC and AVC to keep decreasing at higher output levels. However, it should be noted that AVC and AC can never intersect each other. If they intersect at any point, it would imply that AC and AVC are equal at that point. However, this is not possible as AFC will never be zero because it is a rectangular hyperbola that never touches the x-axis. 

5. AC inherits its shape from AVC's shape and it is because of the law of variable proportions that both the curves are U-shaped.

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

Fixed costs are not permanently fixed; they will change over time but are fixed in relation to the quantity of production for the relevant period. For example, a company may have unexpected and unpredictable expenses unrelated to production, such as warehouse costs and the like that are fixed only over the time period of the lease.  

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

Ans: Average fixed cost curve looks like a rectangular hyperbola. It is defined as the ratio of TFC to output. We know that TFC remains constant throughout all the output levels and as output increases, with TFC being constant, AFC decreases. 

The average fixed cost curve is depreciatingly sloped. Average fixed cost is relatively high at small quantities of output, then declines as production increases 

When the output level is close to zero, AFC is infinitely large and by contrast, when the output level is very large, AFC tends to zero but never becomes zero. AFC can never be zero because it is a rectangular hyperbola and it never intersects the x-axis and thereby can never be equal to zero.

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

Ans: The short-run marginal cost (SMC), average variable cost (AVC) and short-run average cost (SAC) curves are all U-shaped curves. The reason behind the curves being U- shaped is the law of variable comparable. In the initial stages of production in the short run, due to increasing returns to labour, all the costs (average and marginal) fall. In addition to this in the short run MP of labour also enlarge, which implies that more output can be produced per additional unit of labour, leading all the cost curves to fall. Subsequently, with the advent of constant returns to labour, the cost curves become constant and reach their minimum point (representing the optimum combination of capital and labour). Beyond this optimum combination, additional units of labour increase the cost, and as the MP of labour starts falling, the cost curve starts rising due to decreasing returns to labour.

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

Ans: The SMC curve always intersects the AVC curve at its minimum point. This is because to the left of the minimum point of AVC, SMC is below AVC. SMC and AVC both fall but the former falls at a faster rate. At the minimum point K, AVC is equal to SMC. Beyond K, AVC and SMC both rise but the latter rises at a faster rate than the former and also SMC lies above AVC. Therefore, the only point where SMC and AVC are equal is where SMC intersects AVC, i.e., at the minimum point of the AVC curve.

(Image will be uploaded soon)

20. At which point does the SMC curve intersect the SAC curve? Give a reason in support of your answer. 

Ans: SMC curve intersects the 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. SMC intersects SAC at its minimum point P, where SMC = SAC. 

(Image will be uploaded soon)

21. Why is the short-run marginal cost curve 'U'-shaped? 

Ans: The SMC curve is a U-shaped curve due to the law of variable proportions or law diminishing returns. In order to understand the reason behind the U-shape of SMC, let us divide the SMC curve (UAB) into three different parts according to the law of variable proportions: 

1. UA part corresponds to increasing returns to factor. 
2. Minimum point A corresponds to constant returns to factor. 
3. AB part corresponds to decreasing returns to factor. 

In the initial construction stages, the falling part of SMC (UA) is due to the application of increasing returns to factor. Then the SMC stops falling and reaches its minimum point 'A' due to the existence of constant returns to a factor. 

After the minimum point A, SMC starts rising (i.e. 'AB' part of SMC) due to the onset of decreasing returns of variable factors. This trend of the SMC curve (initially falling, then becoming constant at its minimum point and then rising) makes it look like the English alphabet - 'U'. 

In other words, Due to the operation of the law of variable proportion, MP first rises, reaches its maximum point and then declines. Since increasing returns means diminishing costs and diminishing returns implies increasing cost, therefore, MC first falls because of increasing returns, reaches its minimum and then rises due to the operation of diminishing returns. As a result, the MC curve becomes U-shaped.

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

Ans: The long-run marginal cost (LMC) and long-run average cost (LAC) are U shaped curves. The reason behind them being U-shaped is due to the law of returns to scale. It is argued that a firm generally experiences IRS during the initial period of production followed by CRS, and lastly by DRS. Consequently, both LAC and LMC are U-shaped curves. Due to the IRS, as the output increases, LAC falls due to economies of scale. Then falling LAC experiences CRS at the Q1 level of output which is also called the optimum capacity. Beyond the Q1 level of output, the firm experiences diseconomies of scale and if the firm continues to produce beyond the Q1 level, the cost of production will rise.

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

Ans:

24. 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:

25. 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.

Ans:

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.

Ans:

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

Ans: $\mathrm{Q}=5 \mathrm{~L}^{1 / 2} \mathrm{~K}^{1 / 2}$....Equation (1)

$\mathrm{L}=100$ units of labour

$\mathrm{K}=100$ units of capital

Putting these values in equation (1)

$\mathrm{Q}=(100)^{1 / 2}(100)^{1 / 2}$

$=5(10)(10)$

$=500 \text { units }$

Thus, the maximum possible output that the firm can produce is 500 units.

27. Let the production function of a firm be $\mathrm{Q}=2 \mathrm{~L}^{2} \mathrm{~K}^{2}$

Find out the maximum possible output that the firm can produce with 5 units of $L$ and 2 units of $\mathrm{K}$. What is the maximum possible output that the firm can produce with zero units of $L$ and 10 units of $K$?

Ans: 

(a) $Q=2 L^{2} K^{2} \ldots . .(1)$

$L=5$ units of labour

$\mathrm{K}=2$ units of capital

Putting these values in equation (1)

$\mathrm{Q}=2(5)^{2}(2)^{2}$

$=2(25)(4)$

$\mathrm{Q}=200 \text { units }$

(b) If $\mathrm{L}=0$ units and $\mathrm{K}=100$ units

Putting these values in equation (1)

$\mathrm{Q}=2(0)^{2}(100)^{2}$

$\mathrm{Q}=0 \text { units }$

28. Find out the maximum possible output for a firm with zero units of L and 10 units of K when its production function is Q = 5L = 2K. 

Ans: 

Q = 5L + 2K (1) equation (1) 

If L = 0 and K = 10, then putting these values in equation (1) 

Q = 5 (0) + 2 (10) 

= 20 units of maximum output

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Chapter 3 - Production and Costs

Chapter 3 of Microeconomics Class 12 contains the concept of Production and Costs. In the previous chapter of NCERT Microeconomics Class 12, you must have learned about the behaviour of consumers. In Ch 3 Microeconomics Class 12, you will discover the behaviour of a producer. The highlighted concepts of the production function, the short run, and the long run, the law of diminishing marginal product and law of variable proportions, etc. have been well covered under this topic. These concepts have been explained in a simple and lucid language which will help students to understand the chapter better.

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