# Returns to scale. Returns to Scale and Cobb Douglas Function: With Diagrams & Examples 2022-10-21

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Returns to scale refer to the relationship between the output of a production process and the inputs used in that process. When a firm increases all of its inputs by a certain percentage, the percentage change in output will be either greater than, equal to, or less than the percentage change in inputs.

If the percentage change in output is greater than the percentage change in inputs, the production process is said to exhibit increasing returns to scale. This occurs when the firm is able to take advantage of economies of scale, which are cost advantages that arise from producing at a larger scale. For example, a firm may be able to purchase raw materials at a lower price due to bulk discounts, or it may be able to spread out its fixed costs over a larger number of units produced.

If the percentage change in output is equal to the percentage change in inputs, the production process exhibits constant returns to scale. This means that the firm is neither gaining nor losing efficiency as it increases or decreases the scale of production.

If the percentage change in output is less than the percentage change in inputs, the production process exhibits decreasing returns to scale. This occurs when the firm experiences diseconomies of scale, which are cost disadvantages that arise from producing at a larger scale. For example, the firm may have difficulty coordinating and managing a larger number of employees, or it may face higher transportation costs due to the larger volume of goods being produced.

In the short run, a firm may experience increasing, constant, or decreasing returns to scale depending on the specific production process and the inputs used. In the long run, however, all firms will experience constant returns to scale because they can adjust all of their inputs in response to changes in the scale of production.

Understanding returns to scale is important for firms because it can help them make informed decisions about the optimal scale of production. If a firm is experiencing increasing returns to scale, it may be more cost-effective to produce at a larger scale. On the other hand, if a firm is experiencing decreasing returns to scale, it may be more cost-effective to produce at a smaller scale.

In conclusion, returns to scale refer to the relationship between the output of a production process and the inputs used in that process. A firm may experience increasing, constant, or decreasing returns to scale depending on the specific production process and the inputs used. Understanding returns to scale can help firms make informed decisions about the optimal scale of production.

So, with the additional 2 barbers, production would increase from 250 to 313 clients. Similarly, when a business reduces its inputs, the outputs decrease in the same proportion. What Is Returns to Scale? In general, congestion charges should be paid by the associated bilateral transaction. Looking at the graph from left to right, we can see that the LRATC long-run average total cost curve is downward sloping up to point B, then slopes upward to the right of point B. Namely, when the off diagonal elements in the above defined Q matrix are nonzero then there are interactions between variables. For some such units, there may be decreasing returns to scale, as required by standard equilibrium theory. A regular example of constant returns to scale is the commonly used Cobb-Douglas Production Function CDPF.

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## What Is Returns to Scale Economics?

Consequently, it is critical for businesses to evaluate the results of increasing their inputs on the total outputs. Knowing this, we can see why points A and B should be of focus for us — this is where the firm is able to increase output while costs are still going down. Concepts from financial portfolio theory have been adapted where decision makers are assumed willing to reduce expected return to achieve a reduction in the variance of return. Returns to scale is the variation, or change, in productivity that is the outcome from a proportionate increase of all the input. Thus, if we double the inputs, the output will increase but by less than double. Lesson Summary Let's review. There are many additional modeling techniques for handling other forms of uncertainty.

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## Returns to Scale in Economics: Definition & Examples

Once we know the inputs that we are given, we can find the output by multiplying the inputs by some constant of our choosing. The organization's production is efficient if it is able to maintain its current level of output with fewer inputs or resources or when it is able to increase output with the same level of input. However, your output of computers did not triple, it only doubled. As a result, the business serves over 200,000 customers. For example, a grocery store has 100 employees and five stores and serves 100,000 customers annually. This assumption can be relaxed within linear programming by specifying multiple activities, but its formal relaxation requires nonlinear programming techniques.

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## Constant Returns to Scale

For example, division of labor increases efficiency leading to higher output. A growing business will look different to everyone, but returns to scale is an important concept that all business owners will have to take into account. QP formulations are commonly used to allow objective function interactions. Recall that decreasing returns to scale is when the output increases by a smaller proportion than the increase in inputs. This is increasing returns to scale! An example of constant returns to scale is a luxury car manufacturer that makes 100 cars in one factory with 500 employees decides to build another factory and hire 500 more employees to work there. If the grocery store above serves 220,000 customers in the subsequent year after doubling its stores and number of employees, it increases its output by more than 100%.

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## Constant returns to scale

Increasing returns to scale simply means that the output that is produced by a firm will increase by a larger amount than the number of inputs that were increased — inputs being labor and capital, for example. Recall the definition for decreasing returns to scale: when the output increases by a smaller proportion than the increase in inputs. The outputs are the final goods and services. Thus, the single-minded pursuit of centralized energy supply led to a North American electric power system that was interconnected on a multistate basis and included gigawatt-scale generating plants. Now let's say that in year 2, you now have 150 employees and 60 machines producing 1,000 computers a year. Increasing returns to scale is predicated on the output quantity increasing by a larger proportion than the increase of inputs costs.

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## Returns to Scale and Cobb Douglas Function: With Diagrams & Examples

Constant Returns to Scale Benefits A business that achieves constant returns to scale benefits in a number of ways. More strictly, envelope is a geometrical term, referring to the piece-wise linear locus of tightest closure around a given collection of points. When increasing returns to scale occurs, it results in economies of scale. For example, if a business raises its input by 10% and the output increases by 20%, the company can be said to be experiencing increasing returns to scale. The surprising connection between Tinbergen's idea of maximizing a social welfare function and DEA was discovered fairly recently, in a 2010 paper by Cooper, Thore, and Tarverdyan printed in the volume Global Operations Management, ed. In this case, the company has increased its input by 100% and realized a 100% increase in output. If a firm is undergoing decreasing returns to scale, then the firm will likely be going through diseconomies of scale.

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## Increasing Returns to Scale: Meaning & Example StudySmarter

The latter occurs when a business realizes outputs that are higher than the inputs. The right-hand side of the LRATC curve visually portrays this definition — output is increasing by a smaller proportion than the cost shown by the upward sloping curve. Migrants from Brazil or from Portuguese-speaking areas in Africa easily meld with society. A key assumption of the input-output model is that output is related to input use through fixed coefficients. Inputs refer to the things that are used in the production of goods and services, such as capital, labor, and supplies. Decreasing Returns to Scale Explanation The explanation regarding decreasing returns to scale is made simpler once we understand returns to scale.

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## Decreasing Returns to Scale: Meaning & Example StudySmarter

This is quite often unrealistic in that parameters in agriculture are often subject to weather variations and other random events. The demand for the car increases, and the manufacturer decides to create another factory in a different location and hires 500 employees to work in the factory. NPP plant costs began in the mid-1970s. For example, when modeling an agricultural operation in a sequential setting, planting decisions are made under planting and harvesting season uncertainty but harvesting decisions are made with knowledge of what happened during planting season e. Is there anything you notice about the numbers in the parenthesis? In this case, there is no economy of scale. In this case, the business has doubled its inputs and outputs and hence realizes constant returns to scale. Decreasing Returns to Scale When the output increases less than proportionately as all the inputs increase proportionately, we call it decreasing returns to scale or diminishing returns to scale.

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