Chapter 5 Production Solutions
Question - 1 : - Explain the concept of a production function.
Answer - 1 : -
The production function of a firm depicts the relationship between the inputs used in the production process and the final output. It specifies how many units of different inputs are needed in order to produce the maximum possible output. Production function is written as:
Qx = f (L, K)
Where
Qx represents units of output x produced.
L represents unitsof labour employed.
K represents unitsof capital employed.
The above equation explains that Qx, units of output x are produced by employing L and K unitsof labour and capital respectively and by a given technology. As the givenlevel of technology appreciates, the output will increase with the same levelof capital and labour units.
What is the total product of an input?
Answer - 2 : - Total product is defined as the sum total of output produced by a firm by employing a particular input. It is also known as the Total Physical Product and is represented as 
Where, ∑ represents summation of all outputs and Qx represents units of output x produced by an input.
What is the average product of an input?
Answer - 3 : - Average product is defined as the output produced by per unit of variable factor (labour) employed. Algebraically, it is defined as the ratio of the total product by units of labour employed to produce the output, i.e. 
Where,
TP = Total product
L = units of labour employed
What is the marginal product of an input?
Answer - 4 : -
Marginal Product is defined as the additional output produced 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.
Where,
TPn = Total product produced by employing n units of labour
TPn−1 = Total product produced by employing (n − 1) units of labour
Explain the relationship between the marginal products and the total product of an input.
Answer - 5 : -
Relationship between marginal products (MP) and the total product (TP) can be represented graphically as
1) TP increases at an increasing rate till point K, when more and more units of labour are employed. The point 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 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) MP is derived from TP by
Explain the concepts of the short run and the long run.
Answer - 6 : -
Short run:
In short run, a firm cannot change all the inputs, which means that the output can be increased (decreased) only by employing more (less) of the variable factor (labour). It is generally assumed that in short run a firm does not have sufficient or enough time to vary its fixed factors such as, installing a new machine, etc. Hence, the output levels vary only because of varying employment levels of the variable factor.
Algebraically, the short run production function is expressed as
Where,
Qx = units of output x produced
L = labour input
= constant units of capital
Long run:
In long run, a firm can change all its inputs, which means that the output can be increased (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 required levels of output. The law that explains this long run concept is called returns to scale. The long run production function is expressed as
Qx = f (L, K)
Both L and K are variable and can be varied.
Question - 7 : - What is the law of diminishing marginal product?
Answer - 7 : -
Law of diminishing Marginal Product
According to this law, if the units of the variable factor keeps on increasing keeping the level of the fixed factor constant, then initially the marginal product will rise but finally a point will be reached 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.
Question - 8 : - What is the law of variable proportions?
Answer - 8 : -
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.
Question - 9 : - The following table gives the total product schedule of labour. Find the corresponding average product and marginal product schedules of labour.
Answer - 9 : -
| L | TPL |
| 0 | 0 |
| 1 | 15 |
| 2 | 35 |
| 3 | 50 |
| 4 | 40 |
| 5 | 48 |
Answer
| L | TPL | |  |
| 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 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.
Answer - 10 : -
| L | APL |
| 1 | 2 |
| 2 | 3 |
| 3 | 4 |
| 4 | 4.25 |
| 5 | 4 |
| 6 | 3.5 |
Answer
| L | APL | TPL = AP × L |
 |
| 1 | 2 | 2 × 1 = 2 | 2 |
| 2 | 3 | 3 × 2 = 6 | 6 − 2 = 4 |
| 3 | 4 | 4 × 3 = 12 | 12 − 6 = 6 |
| 4 | 4.25 | 4.25 × 4 = 17 | 17 − 12 = 5 |
| 5 | 4 | 4 × 5 = 20 | 20 − 17 = 3 |
| 6 | 3.5 | 3.5 × 6 = 21 | 21 − 20 = 1 |