M. COM. SEM-I-MANAGERIAL ECONOMICS-PRODUCTION FUNCTION

 MANAGERIAL ECONOMICS-PRODUCTION FUNCTION

M. COM. SEMESTER-I

 Production function is a concept in managerial economics that describes the relationship between the inputs used in the production process and the resulting level of output. In other words, it is a mathematical equation that shows how much output can be produced from a given set of inputs. The production function can be used to analyze the efficiency of the production process and to determine the optimal level of production given the resources available.

The general form of a production function is as follows:

Q = f(K, L)

where Q is the level of output, K is the quantity of capital input, and L is the quantity of labor input. The production function shows how the level of output (Q) is affected by the amount of capital and labor used in the production process.

Example: A company produces widgets using two inputs: labor and capital. The company's production function is given by:

Q = 5K^(0.5) L^(0.5)

where Q is the quantity of widgets produced, K is the amount of capital used, and L is the amount of labor used.

Using this production function, we can see that if the company uses 4 units of capital and 9 units of labor, the output can be calculated as:

Q = 5(4)^(0.5) (9)^(0.5) = 60

Therefore, with the given amounts of capital and labor, the company can produce 60 widgets.

Production functions can be used to analyze how changes in inputs affect the level of output. For example, if the company increases the amount of capital input to 16 units while keeping the amount of labor input at 9 units, the output can be calculated as:

Q = 5(16)^(0.5) (9)^(0.5) = 120

Therefore, by increasing the amount of capital input, the company is able to produce 120 widgets, which is twice the amount of the original output.

Similarly, the production function can be used to determine the optimal level of production given the resources available. This involves calculating the marginal product of each input and determining the point at which the marginal cost of each input equals the marginal revenue of the output. This point represents the level of production at which the company can maximize its profits.

Assumptions in Production Function

The assumptions of the production function are:

• Fixed inputs: The inputs used in production are assumed to be fixed in the short run, meaning that their quantity cannot be changed. For example, the size of the factory building, the number of machines, and the land area used for production are all considered fixed inputs in the short run.
• Variable inputs: The inputs used in production that can be changed in the short run are called variable inputs. Examples of variable inputs include labor, raw materials, and energy.
• Homogeneous units of inputs and output: The inputs and outputs used in production are assumed to be homogeneous. This means that they are identical and interchangeable, so the production function can be expressed in terms of the number of units of input used and the number of units of output produced.
• Constant returns to scale: The production function assumes that the increase in output resulting from an increase in inputs is proportional. In other words, if you double the inputs, the output will also double. This is known as constant returns to scale.
• Efficient use of inputs: The production function assumes that the inputs are used efficiently to produce the maximum possible output.

These assumptions help in building a simplified model of the production process, which allows producers to analyze the relationship between inputs and outputs and make informed decisions about how to maximize production.

Average Production Function

The average production function is a concept in production analysis that shows the relationship between the amount of a product produced and the average amount of inputs used in production. It is calculated by dividing total output by the number of units of the variable input used.

For example, let's consider a bakery that produces cakes. The bakery uses a variable input, such as labor, and a fixed input, such as capital. The table below shows the bakery's total output and the number of units of labor employed in each production period:

To calculate the average product of labor, we divide the total output by the units of labor employed:

As we can see from the table, the average product of labor initially increases as more units of labor are employed, but then begins to decrease. This pattern is consistent with the law of diminishing marginal returns, which states that as more and more of a variable input is added to a fixed input, the marginal product of the variable input will eventually decrease.

The average product of labor is a useful concept in production analysis because it provides information about the productivity of each unit of the variable input used in production. It can be used by firms to determine the most efficient level of production and to make decisions about hiring or laying off workers.

Marginal Product

Marginal product is the additional output produced by using one more unit of a specific input while holding all other inputs constant. It is an important concept in production analysis as it helps to determine the optimal level of input usage to maximize output.

Assume we are producing cupcakes, and the following table shows the relationship between the number of workers and the cupcakes they produce in an hour:

Here, total product refers to the total number of cupcakes produced per hour, while marginal product refers to the additional output produced by adding one more worker. The marginal product is calculated by finding the difference between the total product at a given level of labor input and the total product at the previous level of labor input.

For example, when there is only one worker, the total product is 10 cupcakes per hour. When we add a second worker, the total product increases to 25 cupcakes per hour. The marginal product of the second worker is therefore 25 - 10 = 15 cupcakes per hour.

Law of Diminishing Marginal Returns

The law of diminishing marginal returns is a fundamental concept in economics that states that as more and more units of a variable input are added to a production process, while other inputs are held constant, the additional output or marginal product (MP) that is gained from each additional unit of input will eventually decrease. This means that the marginal product of each additional unit of input will eventually become smaller and smaller, leading to diminishing returns.

Assume we are producing cupcakes, and the following table shows the relationship between the number of workers, the cupcakes they produce in an hour and marginal product:

Here, total product refers to the total number of cupcakes produced per hour, while marginal product refers to the additional output produced by adding one more worker.

If we plot this on a graph, it will look like following:

We can observe the law of diminishing marginal returns in this example. As we add more workers, the marginal product of each additional worker decreases. For instance, when we add a third worker, the marginal product is only 17 cupcakes per hour, compared to 15 for the second worker. This is because the fixed resources (such as oven space and baking equipment) become more crowded as we add more workers, which limits their productivity.

The law of diminishing marginal returns is an important concept to keep in mind when trying to optimize production processes. It suggests that there is an optimal level of input that maximizes output, and that going beyond this level may actually lead to lower levels of productivity. By monitoring and adjusting production processes in response to the law of diminishing marginal returns, companies can help to ensure that they are using their resources efficiently and effectively.