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Increasing Returns to Scale

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Increasing Returns to Scale

What do you think of when you hear that a business is growing? Perhaps you think of increasing output, profit, and workers — or maybe your mind immediately goes to lower costs. 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. Increasing returns to scale will often be the desirable goal for most businesses — continue reading to learn more about this concept!

Increasing Returns to Scale Explanation

The explanation for increasing returns to scale is all about outputs increasing by a greater percentage than inputs. Recall Returns To Scale - the rate at which output changes due to some change in input. 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.

Let's think about a simple example that we can use to further understand this concept.

Increasing Returns to Scale Grilling Burgers Increasing Returns to Scale Explained StudySmarterGrilling Burgers

Say you're a restaurant owner that only makes burgers. Currently, you employ 10 workers, have 2 grills, and the restaurant produces 200 burgers a month. Next month, you employ a total of 20 workers, have a total of 4 grills, and the restaurant now produces 600 burgers a month. Your inputs exactly doubled from the previous month, but your output has more than doubled! This is increasing returns to scale.

Increasing Returns to Scale is when the output increases by a larger proportion than the increase in input.

Returns to Scale is the rate at which output changes due to some change in input.

Increasing Returns to Scale Example

Let's look at an example of increasing returns to scale on a graph.

increasing returns to scales studysmarterFig 1. - Increasing Returns to Scale

What does the graph in Figure 1 above tell us? The graph above shows the long-run average total cost curve for a business, and the LRATC is the long-run average total cost curve. For our study of increasing returns to scale, it's best to direct our attention to points A and B. Let's go over why that is.

Viewing the graph from left to right, the long-run average total cost curve is downward sloping and decreasing while the quantity being produced is increasing. Increasing returns to scale is predicated on the output (quantity) increasing by a larger proportion than the increase of inputs (costs). 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.

However, at point B directly, there are no increasing returns to scale since the flat part of the LRATC curve means that outputs and costs are equal. At point B there are constant returns to scale, and to the right of point B there are decreasing returns to scale!

Increasing Returns to Scale Formula

Understanding the returns to scale formula will help us determine whether a firm has increasing returns to scale. The formula for finding increasing returns to scale is plugging the values for inputs to calculate a corresponding increase in output using a function such as this one: Q = L + K.

Let's look at the equation that is commonly used to figure out the returns to scale for a firm:

What does the formula above tell us? Q is output, L is labor, and K is capital. To get the returns to scale for a firm, we need to know how much of each input is being used — labor and capital. After knowing the inputs, we can find out what the output is by using a constant to multiply each input by.

For increasing returns to scale, we are looking for an output that increases by a larger proportion than the increase in inputs. If the increase in output is the same or less than the inputs, then we do not have increasing returns to scale.

The constant can be a number you decide to use as a test or a variable — it is your decision!

Increasing Returns to Scale Calculation

Let's look at an example of increasing returns to scale calculation.

Let's say that a function of the firm's output is:

With this equation, we have our starting point to begin our calculation.

Next, we have to use a constant to find the change in output resulting from the increase in production inputs - labor and capital. Let's say that the firm increases the amount of these inputs five fold.

What do you notice about the numbers in the parenthesis? They are the exact same as the initial equation that told us what Q was equal to. Therefore, we can say that the value inside the parenthesis is Q.

We can now say that our output, Q, increased 25 times based on the increase in inputs. Since the output increased by a larger proportion than the input, we have increasing returns to scale!

Increasing Returns to Scale vs Economies of Scale

Increasing returns to scale and economies of scale are closely related, but not exactly the same thing. Recall that increasing returns to scale occur when output increases by a larger proportion than the increase in input. Economies of Scale, on the other hand, are when the long-run average total cost declines as output rises.

Chances are if a firm has economies of scale they also have increasing returns to scale and vice versa. Let's look at a firm's long-run average total cost curve for a better look:

increasing returns to scales and economies of scale studysmarterFig 2. - Increasing Returns to Scale and Economies of Scale

The graph in Figure 2 above us gives us a good visualization of why increasing returns to scale and economies of scale are closely related. 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 on the graph. During this slope, the cost for the firm is decreasing as the quantity being produced increases — this is the exact definition of economies of scale! Recall: economies of scale is when the long-run average total cost decreases as output increases.

But what about increasing returns to scale?

Increasing returns to scale is when outputs increase by a greater proportion than inputs. Generally, if a firm has economies of scale then they will likely have increasing returns to scale as well.

Economies of Scale is when the long-run average total cost decreases as the output increases.


Increasing Returns to Scale - Key takeaways

  • Increasing Returns to Scale is when the output increases by a greater proportion than the increase in input.
  • Returns to Scale is the rate at which output changes due to some change in input.
  • Increasing returns to scale can be seen as the LRATC curve is decreasing.
  • The common formula used for returns to scale questions is the following: Q = L + K
  • Economies of scale is when the LRATC decreases and output increases.

Frequently Asked Questions about Increasing Returns to Scale

Increasing returns to scale is when the output increases by a greater proportion than the input.

You look at whether the inputs, labor and capital, increased by a smaller percentage than the output.

Increasing returns to scale can be caused when a firm is lowering costs as it is expanding.

Cost typically decreases in increasing returns to scale.

The formula for finding increasing returns to scale is plugging the values for inputs to calculate a corresponding increase in output using a function such as this one: Q = L + K

Final Increasing Returns to Scale Quiz

Question

What is increasing returns to scale?

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Answer

When the output increases by a greater proportion to the increase in input

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Question

What is economies of scale?

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Answer

Long-run average total cost decreases as output increases

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Question

What is returns to scale?

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Answer

The rate at which output changes by some change in input

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Question

What do you need to calculate increasing returns to scale?

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Answer

Inputs: Labor and Capital

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Question

What happens to cost during increasing returns to scale?

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Answer

Costs generally decrease during increasing returns to scale

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Question

What formula is used to calculate returns to scale?

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Answer

Q = L + K

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Question

What do you multiply labor and capital by to find the change in output?

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Answer

A constant

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Question

When does increasing returns to scale happen on the LRATC curve?

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Answer

When the LRATC curve is downward sloping

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Question

True or False: Increasing Returns to Scale and Economies of Scale generally occur together.

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Answer

True

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Question

Which of the following is NOT used in the returns to scale formula?

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Answer

Wages

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Question

True or False: Increasing returns to scale occur when the LRATC curve is upward sloping.

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Answer

False

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Question

Bob doubled his labor and capital for his restaurant business which resulted in Bob doubling his output! Did Bob see increasing returns to scale?

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Answer

No

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Question

Rick runs a shoe business and doubled his labor and capital which resulted in a 5x increase in output! Did Rick see increasing returns to scale?

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Answer

Yes

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Question

Ned sells 50 ice cream cones between himself and an employee per day. When he hires 2 more people, doubling his inputs. Use the formula to calculate the new output. Does Ned have increasing returns to scale?

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Answer

200 ice cream cones. Yes, Ned has increasing returns to scale.

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Question

If the current output is 5,000 units and inputs increase by 150%, what is the new output, and do we have increasing returns to scale?

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Answer

The new output is 11,250 units. Yes we have increasing returns to scale.

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Question

If the current output is 947 units per week with 10 workers, what would happen to output if 15 more workers were hired? What is the new level of output?

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Answer

The output would increase 225 times. The new level of output is 213,075 units per week.

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Question

The laundromat can process 340 loads per day in 34 washers. If the owner bought 10 more washers what would their new output be? 

(Round to the nearest whole number)

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Answer

The new output is 569 loads of laundry.

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Question

If management increases production inputs by 300% when existing inputs were already producing 14 units per month, how many units per month should the factory be producing?

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Answer

126 units.

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Question

The difference between increasing returns to scale and economies of scale is...

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Answer

that returns to scale deals with the changes in production while the other deals with changes in the long run average total cost.

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Question

Calculate the total output if there are 17 workers who can produce 12 pairs of shoes each in one day. 

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Answer

204 pairs of shoes.

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Question

Increasing returns to scale occur when output _________ by a _______ proportion than the increase in input.


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Answer

increases, larger,

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Question

If a firm has economies of scale they probably do not have increasing returns to scale.

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Answer

False, they probably do.

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Question

The long-run average total cost curve has a U shape.

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Answer

True.

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Question

As we move along the LRATC curve what is happening to the average cost?

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Answer

At first, it is decreasing, then it increases.

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Question

What happens if outputs increase by a lower proportion than inputs?

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Answer

Then it is not increasing returns to scale!

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Question

What is Q' in our calculations of increasing returns to scale?

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Answer

It is the new output after we increased the level of input.

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Question

What does the Y axis represent when graphing returns to scale?

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Answer

The average cost.

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Question

The X axis represents time when graphing increasing returns to scale.

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Answer

False, it represents the quantity produced.

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