CBSE Class 12 Economics Chapter 5: Production - NCERT Solutions

Solution: A production function is a fundamental concept in economics that describes the technical relationship between the quantities of various physical inputs (such as labor, capital, raw materials) and the quantity of physical output of a product that can be produced by a firm. It essentially shows the maximum output a firm can achieve with a given set of inputs, assuming the technology remains constant.

The general mathematical form of a production function can be represented as:

$$q\; =\; f(x1\; :\; x2)$$

Where:

• $q$ represents the quantity of output produced.
• $f$ denotes the function representing the technology or process.
• $x1$ represents the quantity of the first input (e.g., labor).
• $x2$ represents the quantity of the second input (e.g., capital or machinery).

This function indicates how changes in the amount of inputs affect the total output.

Solution: The total product (TP) of an input refers to the total volume of goods and services that a firm is able to produce using a specific combination of inputs during a given period of time. When considering a variable input, like labor, while keeping other inputs fixed, the total product is the total output generated by employing a certain number of units of that variable input.

Solution: The average product (AP) of an input measures the productivity per unit of a variable factor. It is calculated by dividing the total product (TP) by the total number of units of the variable input employed. For example, if a firm produces 100 units of output using 10 units of labor, the average product of labor is 10 units of output per unit of labor.

The formula for Average Product is:

$$AP\; =\; \backslash frac\{\backslash text\{Total\; Product\; (TP)\}\}\{\backslash text\{Units\; of\; Variable\; Input\; (L)\}\}$$

Solution: The marginal product (MP) of an input is the additional output produced when one more unit of a variable input is employed, while all other inputs are held constant. It measures the change in total product resulting from a small change in the variable input.

It can be calculated using the formula:

$$MP\; =\; \backslash frac\{\backslash text\{Change\; in\; Output\}\}\{\backslash text\{Change\; in\; Input\}\}\; =\; \backslash frac\{\backslash Delta\; q\}\{\backslash Delta\; L\}$$

Where $\backslash Delta\; q$ is the change in total output and $\backslash Delta\; L$ is the change in the unit of labor (or variable input).

Solution: The Law of Variable Proportions describes how the total product (TP), average product (AP), and marginal product (MP) of a variable input change when it is added to a fixed input. The behavior of TP and MP is closely linked and can be understood through three distinct phases:

1. Phase I: Increasing Marginal Returns When a firm starts employing more units of a variable input (like labor) with fixed inputs (like capital), the marginal product initially rises. This is because the fixed inputs are initially underutilized, and adding more variable inputs allows for better specialization and efficiency. During this phase, the total product increases at an increasing rate (the TP curve is convex upwards). This phase continues until the point of inflexion on the TP curve, which corresponds to the maximum point of the MP curve.
2. Phase II: Diminishing Marginal Returns After the point of inflexion, as more units of the variable input are added, the marginal product begins to fall, but it remains positive. This is because the fixed inputs become increasingly crowded or overutilized relative to the variable input. While each additional unit of input adds to the total output, it adds less than the previous unit. The total product continues to increase during this phase, but at a diminishing rate (the TP curve is concave upwards). This phase is crucial for optimal production decisions as it represents the stage where total product is maximized.
3. Phase III: Negative Marginal Returns If the firm continues to add more units of the variable input beyond a certain point, the marginal product becomes negative. This means that adding an extra unit of the variable input actually reduces the total output. This occurs when the variable input becomes excessively large relative to the fixed inputs, leading to inefficiency, congestion, and coordination problems. In this phase, the total product starts to fall.

Relationship Summary:

• When MP is rising, TP increases at an increasing rate.
• When MP is falling but positive, TP increases at a diminishing rate.
• When MP is zero, TP is at its maximum.
• When MP is negative, TP falls.

The diagram typically shows the TP curve rising, peaking, and then falling, while the MP curve rises to a peak, falls, becomes zero, and then turns negative. The point where MP is maximum corresponds to the point of inflexion on the TP curve. The point where MP is zero corresponds to the maximum point on the TP curve.

Solution: The concepts of the short run and the long run are crucial in production theory and refer to the time horizon over which a firm can adjust its inputs.

1. Short Run:

The short run is a period during which a firm cannot change some of its factors of production, known as fixed factors. These typically include things like the size of the factory building, the amount of heavy machinery, or land. However, the firm can change other factors, called variable factors, such as the number of workers employed, the amount of raw materials used, or the quantity of power consumed. In essence, the short run is characterized by the presence of at least one fixed factor.

Example: A bakery operating with a fixed oven capacity might hire more bakers or buy more flour (variable factors) but cannot immediately build a larger bakery (fixed factor).

2. Long Run:

The long run is a period of time during which a firm can adjust all of its factors of production. This means that all inputs, including capital (machinery, buildings) and labor, can be varied. In the long run, a firm can expand its scale of operations by investing in new machinery, building larger facilities, or adopting new technologies. There are no fixed factors in the long run; all factors are considered variable.

Example: Over a longer period, the bakery can decide to purchase more ovens, expand its premises, or even relocate to a larger facility, thus changing all its factors of production.

Important Note: The terms 'short run' and 'long run' do not refer to specific calendar durations like a month or a year. Instead, they are functional concepts defined by the ability of the firm to change its factors of production. The length of the short run and long run can vary across industries depending on how quickly factor inputs can be adjusted.