Production And Costs - Class 11 Commerce Economics - Extra Questions

Output (units)	Average Fixed Cost (Rs.)	Marginal Cost (Rs.)	Average Variable Cost (Rs.)	Average Cost (Rs.)
1	60	20	20	80
2	30	18	19	49
3	20	16	18	38
4	15	18	18	33
5	12	23	19	31

Firstly, MC = MR is a necessary condition of producers equilibrium as this the point when profits are maximized.

Law of variable proportions is a short period concept when output can be increased only by increasing the application of the variable factor. Fixed factor (indicating scale of output) remains constant. 

Production function refers to the functional relationship between (physical) inputs and (physical) output.

Under short-run production function at least one of the factors of production remains fixed.
Under the long-run production function, all factors of production become variables.

Marginal cost curve cuts average cost curve only at its minimum point because it is only here that MC $$=$$ AC.

Production cost refers to the expenditure incurred by the producer (explicitly or implicitly) on the inputs for producing a given level of output.

Output  (Units)	ATC  (Rs.)	AVC  (Rs.)	MC  (Rs.)
1	54	30	30
2	36	24	18
3	32	24	24
4	33	27	36

$$ATC - AVC = AFC = 54 - 30 = 24$$ (when output$$ = 1$$) $$= TFC$$.

SMC (short run marginal cost) curve cuts the AVC (average variable cost) curve at the minimum point of the AVC curve because it is only here that SMC $$=$$ AVC

Marginal cost is an additional cost and additional cost cannot be fixed cost, it can only be variable cost. Accordingly, the sum total of marginal costs corresponding to different units of output becomes $$TVC$$.
$$\Sigma MC = TVC$$

Output (Units)	TC (RS.)	AFC   (Rs.)	TFC    (Rs.)	TVC    (Rs.)	AVC (Rs.)	MC (Rs.)
1	23	18	18	$$23 - 18 = 5$$	$$\dfrac{5}{1}=5$$	5
2	27	9	18	$$27-18=9$$	$$\dfrac{9}{2}=4.5$$	4
3	30	6	18	$$30-18=12$$	$$\dfrac{12}{3}=4$$	3

SMC curve cuts the SAC curve only at its lowest (or minimum) point because it is only here that SMC $$=$$ SAC.

When $$10\%$$ increase in all inputs leads to $$12\%$$ increase in output, unit cost of production $$\left(\dfrac{TC}{Q}\right)$$ must decline. Implying a fall in average cost.

Long run marginal cost (LMC) and the average cost (LAC) curves are U-shaped in accordance with the returns to scale.

Yes. Because in a stage of increasing returns, cost of producing every additional unit of output tends to fall. Accordingly, it would be irrational for the producer to stop production in this stage.

Given,                  $$ Q={ 5L }^{ 1/2 }{ K }^{ 1/2 } $$
                            $$ Q={ 5\left( 100 \right)  }^{ 1/2 }{ \left( 100 \right)  }^{ 1/2 } $$ 
                                $$ =5{ \left( { 10 }^{ 2 } \right)  }^{ 1/2 }{ \left( { 10 }^{ 2 } \right)  }^{ 1/2 } $$
                                $$ =5\times 10\times 10-500 $$
The maximum output the firm can produce with 100 units of L and 100 units of K is 500.

Given,                       $$ Q={ 2L }^{ 2 }{ K }^{ 2 } $$
                                  $$ Q={ 2\left( 5 \right)  }^{ 2 }{ \left( 2 \right)  }^{ 2 } $$
                                      $$=2\times 25\times 4 $$ 
                                      $$=200$$
The maximum possible output that the firm can produce with 5 units of $$L$$ and 2 units of $$K$$ is 200.

Short period production function of a firm is drawn on the assumption of a given technology. When new technology is available, the whole production function would shift: more output would be available from the same amount of inputs. In terms of costs, firm's AC curve would shift downward. Thus, the availability of new technology (relating to auto industry) would shift the AC curve (of a car manufacturer) downward. It would prompt him to produce more at the going/ prevailing price.

India meets its domestic demand for petrol and diesel largely through imports. Accordingly, a cut in their price in the international market leads to cut in price in the domestic market as well.
Transport firms use petrol and diesel as a major input. A cut in their price is expected to lower their cost of production. Other things remaining constant, it would lead to lower cost for the transportation of goods across different places.

TFC:   $$60,$$ $$60,$$ $$60,$$ $$60,$$ $$60,$$ $$60,$$ $$60$$;

Variable Input   Total Product    Marginal Product     Phases/Stages 

(i) AFC (of fourth unit)$$=Rs.20$$;  

Output (Units)	Total Variable Cost                   (Rs.)	Average Variable Cost                        (Rs.)	Marginal Cost               (Rs.)
1	2020	10	0
2	32	1616	1212
3	5454	18	22
4	80	2020	26

Output (kg)	Total Cost (Rs.)	Total Fixed Cost (Rs.)	Average Fixed Cost (Rs.)	Total Variable Cost (Rs.)	Average Variable Cost (Rs.)	Marginal Cost (Rs.)
$$0$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$	$$40$$ $$100$$ $$120$$ $$130$$ $$150$$ $$190$$	$$40$$ $$40$$ $$40$$ $$40$$ $$40$$ $$40$$	- $$40$$ $$20$$ $$13.3$$ $$10$$ $$8$$	- $$60$$ $$80$$ $$90$$ $$110$$ $$150$$	- $$60$$ $$40$$ $$30$$ $$27.5$$ $$30$$	- $$60$$ $$20$$ $$10$$ $$20$$ $$40$$

Output (Units)	Total Cost (Rs.)	Total Variable Cost (Rs.)	Marginal Cost (Rs.)
$$0$$ $$1$$ $$2$$	$$12$$      $$18$$     $$21$$	-      $$18 - 12 = 6$$     $$21 - 12 = 9$$	-     $$18 - 12 = 6$$     $$21 - 18 = 3$$

The fixed cost is to be incurred even when output is zero. Thus, in the above example, $$Rs. 12$$ is fixed cost. The variable cost is the difference between total cost and fixed cost.

Relation between Total Product $$(MP)$$ and Marginal Product $$(MP)$$:
(i) Up to $$3rd$$ unit of labour employment, $$MP$$ increases and $$TP$$ increases at increasing rate.
(ii) From $$4th$$ unit to $$6th$$ unit of labour employment, $$MP$$ decreases and $$TP$$ increases at diminishing rate.
(iii) At $$7th$$ unit of labour employment, $$MP$$ is zero and $$TP$$ is maximum.
(iv) At $$8th$$ unit of labour employment, $$MP$$ is negative and $$TP$$ starts declining.

The production function of a firm depicts the relationship between the inputs used in the production process and the final output produced. Algebraically, a production function is represented as, 
$$Qx = f(L, K)$$
Where, 
$$L$$ represents units of labour used (input 1) 
$$K$$ represents units of capital used (input 2) 
$$Q_x$$ represents the unit of output produced 

Output (Units)	TVC (Rs.)	TFC (Rs.)	MC (Rs.)	AFC (Rs.)
$$0$$ $$1$$ $$5$$	- $$400$$ $$1,600$$	$$500$$            $$500$$            $$50$$	-             $$400$$         $$\dfrac {1,600 - 400}{5 - 1} = \dfrac {1,200}{4} = 300$$	$$\infty$$   $$500$$   $$100$$

The total of the MC values between units 1 & 5 is 300.

Y – f (R, I, K, O, .......), 

Output (Units)	$$TC   (Rs.)$$	$$TFC   (Rs.)$$	$$TVC (Rs.)$$	$$AVC (Rs.)$$	$$MC (Rs.)$$
$$1$$ $$2$$ $$3$$ $$4$$	$$350$$ $$450$$ $$610$$ $$820$$	$$100$$ $$100$$ $$100$$ $$100$$	$$250$$ $$350$$ $$510$$ $$720$$	$$250$$   $$175$$   $$170$$   $$180$$	$$250$$   $$100$$   $$160$$   $$210$$

Output (Units)	Total Cost (Rs.)	Total Fixed Cost (Rs.)	Average Fixed Cost (Rs.)	Total Variable Cost (Rs.)	Average Variable Cost (Rs.)	Marginal Cost (Rs.)	Average Cost (Rs.)
$$0$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$	$$150$$ $$300$$ $$420$$ $$600$$ $$790$$ $$1,000$$ $$1,260$$	$$150$$ $$150$$ $$150$$ $$150$$ $$150$$ $$150$$ $$150$$	$$\infty$$ $$150$$ $$75$$ $$50$$ $$37.5$$ $$30$$ $$25$$	- $$150$$ $$270$$ $$450$$ $$640$$ $$850$$ $$1,110$$	- $$150$$ $$135$$ $$150$$ $$160$$ $$170$$ $$185$$	- $$150$$ $$120$$ $$180$$ $$190$$ $$210$$ $$260$$	$$\infty$$ $$300$$ $$210$$ $$200$$ $$197.5$$ $$200$$ $$210$$

(i) AFC of producing $$3\ units = Rs. 50$$.
(ii) AVC of producing $$4\ units = Rs. 160$$.
(iii) Least AC level of output $$= 4\ units$$.
(iv) MC of producing $$5th\ unit = Rs. 210$$.
(v) TVC of producing $$6\ units = Rs. 1,110$$.

Cost is the total expenditure incurred in producing a commodity. In economics, it is sum of total of actual expenditure incurred on inputs (i. e. explicit cost) and the imputed valued of inputs supplied by the owners (i. e. implicit cost).

	Fixed costs	Variable costs
Definition	Incurred on hiring fixed factors of production	Incurred on hiring variable factors of production
Variability	Remain constant irrespective of the units of output produced	Vary directly as per the variation in the output, then higher variable costs are incurred and vice-versa
Example	Salary of permanent staff, output produced, etc.	Wages of casual labours, cost of raw materials, etc.

Output	TFC	TVC	TC	AFC	AVC	AC
1	50	20	70	50	20	70
2	50	30	80	25	15	40
3	50	40	90	16.67	13.33	30
4	50	60	110	12.5	15	27.5
5	50	90	140	10	18	28

TFC = TC - TVC

Variable factors are the factors the supply of which can be changed by any desired quantity.

The factor for which quantity can neither be increased and nor decreased in the short run is called a fixed factor.

• Total utility is the sum total of marginal utility from the consumption of different units of a commodity. For example, a person consumes eggs and gains 50 utils of total utility. This total utility is the sum of utilities from the successive units (30 utils from the first egg, 15 utils from the second and 5 utils from the third egg). Summing up total utility is the amount of satisfaction (utility) obtained from consuming a particular quantity of a good or service within a given time period. It is the sum of marginal utilities of each successive unit of consumption.
• Marginal utility means addition to total utility when one or more unit of a good is consumed.For example, when a person increases the consumption of eggs from one egg to two eggs, the total utility increases from 30 utils to 45 utils.The marginal utility here would be the 15 utils of the 2nd egg consumed. Marginal utility, thus, can also be described as difference between total utility derived from one level of consumption and total utility derived from another level of consumption. Marginal utility is the difference of total utility.

The four factors of production are: 

The shape of average variable cost curve is U-shaped.

L	TPL	APL	MPL
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

The relationship between AC, AVC, and MC are :
1:When MC<AC and AVC both AC and MC fall.
2:When MC=AC and AVC both are minimum and constant.
3:When MC>AC and AVC both AC and MC rise.

The relationship between TVC and MC is:
1. When TVC increases at a diminishing rate, MC falls.
2. When TVS increases at an increasing rate, MC rises.

Return to scale refers to change in all input in the same proportion, change in scale of production. It is a long run phenomenon.

The assumptions of the law of variable proportion are:
1. The state of technology remains constant.
2. It is assumed that some inputs are kept fixed and while others are varied.
3. Units of variable factors are homogeneous

The relationship between TP and MP is as follows: 
1. When TP increases at an increasing rate, MP increases.
2. When TP increases at diminishing rate MP declines.
3. When TP reaches its maximum then MP becomes zero.
4. When TP begins to decline then MP becomes negative.

Returns to a factor refers to the behaviour of physical output owing to change in physical input of a variable factor, fixed factors remaining constant.

Assumptions of Law of Variable Proportions::
1. It operates in short run, as factors are classified as variable and fixed factor,
2. The law applies to all fixed factors including land.
3. Under law of variable proportions, different units of variable factor can be combined with fixed factor.
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. It is assumed that, factors of production become imperfect substitutes of each other beyond a certain limit.
6. The state of technology is assumed to be constant during the operation of this law.
7. It is assumed that all variable factors are equally efficient.

            Table: Law of Variable Proportions

Fixed Factor (Land) (acres)	Variable Factor (Labour)	Total Product (units)	Marginal Product (units)	Phase
1	1	10	10	Phase I: Increasing Returns to a Factor
1	2	30	20
1	3	45	15	Phase II: Diminishing Returns to a Factor
1	4	52	7
1	5	52	0
1	6	48	-4	Phase III: Negative Returns to a Factor

When total product is at maximum point then MP will be zero.

When total product decline then MP will be in negative.

Three stages of return to scale are:
1. Constant return to scale
2. Increasing returns to scale
3. Diminishing return to scale

Reasons for Increasing Returns to a Factor 

• Underutilisation of the fixed factor- In the first stage of production, there are not enough labour units to fully utilise the fixed factor. Therefore, the firm can increase its output just by combining more and more of labour inputs with the fixed factor, thereby  the output of the additional unit of labour (i.e. MP) tends to rise.
• Division of labour- The increase in the labour input enables the division of labour, which further increases the efficiency and productivity of the labour.
• Specialisation of labour- Due to the division of labour, specialisation of individual labour unit increases, which in turn raises the overall efficiency and productivity. Consequently, the MP curve rises and TP curve continues to rise.
  
  Reasons for Decreasing Returns to a Factor

• Fuller utilisation of fixed factor- In this stage, the fixed factor is utilised to its maximum level as more and more of labour inputs are employed.
• Imperfect substitutability between labour and capital- The variable factors are imperfect substitute for the fixed factor. Therefore, the firm cannot substitute labour for capital and as a result diminishing returns takes place.
• Optimum Proportion/ Ideal Factor Ratio- The optimum proportion (or ideal factor ratio) is a fixed ratio in which the labour and capital inputs are employed. These factors will be the most efficient if they are employed as per the optimum proportion.
  
  Reasons for Negative Returns to a Factor
  
  
• Over utilisation of the fixed factors- In the third stage of production, the variable factor is in excessive relative to the fixed factors. This leads to the over utilisation of the fixed factor, thereby negative returns to a factor sets-in. 
• Negative Marginal Product- Throughout this stage the TP curve is continuously falling, consequently, the additional product by the additional unit of labour becomes negative. This implies that in this stage of production, the cost of employing labour is substantially higher than its contribution to the total product.
• Problem of Management- With the increased number of labour units employed, it becomes hard for the management of the firm to efficiently manage them. Thus, due to the mismanagement and lack of responsibility, inefficiency is infused in the system.

1. When marginal cost is less than average cost, average cost falls and when marginal cost is greater than average cost, average cost rises.
2. It is illustrated in this figure that when marginal cost (MC) is above average cost (AC), the average cost rises, that is, the marginal cost (MC) pulls the average cost (AC) upwards.
   
3. As long as short-run marginal cost curve MC lies below short-run average cost curve, the average cost curve AC is falling.
4. When marginal cost curve MC lies above the average cost curve AC, the latter is rising.
5. At the point of intersection L where MC is equal to AC, AC is neither falling nor rising, that is, at point L, AC has just ceased to fall but has not yet begun to rise.
6. It follows that point L, at which the MC curve crosses the AC curve to lie above the AC curve is the minimum point of the AC curve. Thus, marginal cost curve cuts the average cost curve at the latter minimum point.

(i) Law of Variable Proportions (LVP) states that as we increase quantity of only one input keeping other inputs fixed, total product (TP) initially increases at an increasing rate, then at a decreasing rate and finally at a negative rate.

(ii)  (a) 1st Phase-Increasing return to a factor: This phase starts from 1st unit of labour till 6th unit of labour because here TP is increasing.
(b) 2nd Phase-Constant return to a factor: This phase starts from 7th unit of labour till 8th unit of labour because here TP is at constant.
(c) 3rd Phase-Decreasing return to a factor: This phase starts from 9th unit of labour because here TP in falling.

Total Product start to fall, if production continues by a producing firm in short run, even after Marginal Product becomes zero because of the following reasons:

1. Better utilisation of the fixed factor: In the first phase, the supply of the fixed factor (say, land) is too large, whereas variable factors are too few. So, the fix factor is not fully utilised when variable factors are increased and combined with fixed factor, then fixed factor is better utilised and output increases at increasing rate.
2. Increased efficiency of the variable factor: When variable factors are increased and combined with the fixed factor, then former is utilised in a more efficient manner. At the same time, there is greater cooperation and high degree of specialisation between different units of the variable factor.
3. Indivisibility of the fixed factor: Generally, the fixed factor which are combined with variable factors are indivisible. Such factors cannot be divided into smaller units. Once an investment is made is an indivisible fixed factor, then addition of more and more units of the variable factor, improves the utilisation of fixed factor. The increasing returns apply as long as optimum level of combination between variable and fixed factor is achieved.

The law of variable proportions states that as the quantity of factor increases while keeping the other factors constant the total product first increases with an increasing rate then increases with the decreasing rate and then diminishes. 
Schedule-There are three stages of law of variable proportion.
1.Stage I- Here, TP first increases with an increasing rate and MP and AP also increases up to a certain level. In the first phase there is better utilisation of fixed factor, increase efficiency of variable factors and indivisibility of fixed factors are responsible for the cause.
2. Stage II- Here, TP increases with the diminishing rate and MP and AP both starts to fall. The reason responsible for the diminishing return 2 factors are optimum combination of factors and imperfect substitute.
3.Stage III- Here, TP reduces and MP becomes negative and AP is also falling but is positive the factors responsible for negative returns to scale and limitation of fixed factors poor, coordination between variable and fixed factors, decreasing efficiency of variable factors.

When the quantity of one factor is varied, keeping the quantity of other factors con­stant, the proportion between the variable factor and the fixed factor is altered; the ratio of employ­ment of the variable factor to that of the fixed factor goes on increasing as the quantity of the variable factor is increased.

The law of variable proportions or diminishing returns, as stated above, holds good under the following conditions:

1. First, the state of technology is assumed to be given and unchanged. If there is improvement in the technology, then marginal and average products may rise instead of diminishing.

2. Secondly, there must be some inputs whose quantity is kept fixed.

The law has three stages as explained below:

(i) Stage I – The TPP increases at an increasing rate and the MPP increases too. The MPP increases with an increase in the units of the variable factor. Therefore, it is also called the stage of increasing returns. In this example, the Stage I of the law runs up to three units of labour (between the points O and L).

(ii) Stage II – The TPP continues to increase but at a diminishing rate. However, the increase is positive. Further, the MPP decreases with an increase in the number of units of the variable factor. Hence, it is called the stage of diminishing returns. In this example, Stage II runs between four to six units of labour (between the points L and M). This stage reaches a point where TPP is maximum (18 in the above example) and MPP becomes zero (point R).

(iii) Stage III – Now, the TPP starts declining, MPP decreases and becomes negative. Therefore, it is called the stage of negative returns. In this example, Stage III runs between seven to eight units of labour (from the point M onwards).

The equilibrium level of output will be 4 units. This is becuase at this point the two conditions of equilibrium (Using MR-MC approach) are met. this can be seen as follows:
We are given the Total Revenue (TR) and Total Cost (TC). From here, we can find Marginal Revenue (MR) and Marginal Cost (MC), as given in the following schedule.
 

Units	Total Revenue (TR)	Marginal Revenue (MR)	Total Cost (TC)	Marginal Cost (MC)
1	10	-	8	-
2	18	8	15	7
3	24	6	21	6
4	28	4	25	4
5	30	2	33	8

Here, as we can see, the first and the order conditions of equilibrium through MR-MC approach are being met at unit 4. That is, 
First Condition : $$MR = MC = 4$$
Second Condition : MC is rising from this point and meets MR from below.
Thus, equilibrium output is 4 units.

Production Possibility Frontier or Production Possibility Curve is the curve which shows the combinations of two goods and services that can be produced with fuller utilisation of a given amount of resources in the most efficient way and with a given production technology. 

Characteristics of PPF 
(a) Concave to the origin: PPF or PPC is concave to the origin. This is because the opportunity cost of producing a good in terms of the loss of the output of other good, tends to increase. 
(b) Downward sloping curve: PPC curve is downward sloping from left to right. This is because for production of every additional unit of one good, more and more units of other good has to be sacrificed. 

The behaviour of marginal product and total product as more and more units of only one input are employed while keeping other inputs as constant can be understood with the help of following diagram:  [Ref. image]
From the figure, we can analyse that initially as more and more units of one input (say, labour) are employed, the TP curve increases at an increasing rate till point I. After point I, the TP curve rises at a decreasing rate till the point B. The point I is also known as point of inflexion. This is because passing through the point I, the curvature of the TP curve changes from convex to concave. With successive rise in the labour units, the TP curve continues to rise and attains its maximum point B. Beyond this point, the TP curve starts falling when more units of labour are employed. On the other hand, MP initially increases at an increasing rate and attains its maximum point at M (point of inflexion). After point M, MP curve continues to fall and becomes zero at N. Finally. after point N, MP curve continues to fall and becomes negative. 
So, we can summarize: 
a. When TP increases at an increasing rate, MP also increases at an increasing rate. 
b. When TP increases at decreasing rate, MP attains its maximum point and starts falling. 
c. When TP reaches its maximum point, MP becomes zero. 
d. When TP starts falling, MP becomes negative and continues to fall. 

An SEZ offers multi-faceted infrastructural facility for the firms operating in the specified zone. It offers facilities of raw material, transportation, banking and insurance services. These facilities generate external economies for all the firms located in the SEZ. Due to the external economies, cost structure of an individual firm tends to be moderated. Unit cost of production is lowered.

Output

SMC

TFC

TVC

TC

AVC

SAC

0	-	100	0	100	-	-
1	500	100	500	600	500	600
2	300	100	800	900	400	450
3	200	100	1000	1100	333.33	366.67
4	300	100	1300	1400	325	350
5	500	100	1800	1900	360	380
6	800	100	2600	2700	433.33	450

As output increases and TFC remains fixed, AFC declines continuously. As the same volume of fixed cost is divided by the – larger volume of output, AFC must decline. Further, the AFC curve is a rectangular hyperbola in the sense that all rectangles formed by AFC are of equal sizes. The AFC curve is asymptotic to both the axes. This means that it touches neither the horizontal axis nor the vertical axis.

In the short period production function, rise in the average cost is related to the 'diminishing returns to a factor'. In the long period production function, on the other hand, rise in the average cost is related to diminishing returns to scale.

No, because all costs are variable costs in the long run and no factor is a fixed factor in the long run.