Production Function

1. Production Functions

Production is about transforming factors of production into goods and services. Production implies more than just making physical goods and services. It can include any process or service that creates value.

EXAMPLE

Moving finished products from the manufacturer to a retail store creates value, because it makes the product more accessible to customers. Wholesalers buy large quantities of goods and then resell them to large buyers, who distribute the product among their shops.

Every firm has a unique technical recipe for producing each of its goods or services. When we speak of a technical recipe, it is simply a collection of instructions on how to produce an object.

think about it

Suppose you wanted to open a tea shop as a gathering place for tea lovers. What factors of production would you need? What teas would you serve? How many workers would you hire? What physical equipment would you purchase? What would be your operating instructions for the tea shop? What hours would you be open? Would workers be paid by the hour or would they earn salaries? How large would your shop be? How many customers do you want to seat in your tea shop? Your answers form the basis of the technical recipe for your business model.

The technical recipe that provides instructions for the firm is called a production function. The production function is a mathematical expression describing the relationship between inputs and outputs. The production function states the quantity of output that can be obtained from using different combinations of factor inputs (land, labor, capital, entrepreneurship) given a level of productivity.

Let’s review the elements of the production function formula.

• Outputs are the yield or the quantity of output.
• Outputs depend upon the quantity of inputs used.
• The A in the formula represents the productivity of resources.
• The technical recipe assumes the firm will use the most efficient production method available and not waste resources.
• There is a symbol (f) in the formula. The f is shorthand for the word function. In mathematics, a function is an expression that defines a relationship between two variables. In the formula, the f indicates that the output is dependent on the inputs (or factors or production) identified between the brackets.
• Inputs are the factors of production (ingredients) needed to produce the product. The factors (land, labor, capital, technology, entrepreneurship) are noted within the brackets.

formula to know

Production Function

where A represents the productivity of resources

The mathematical expression for the production function is a shorthand way of writing the production function. It is similar to a cookie recipe stating a yield, listing the ingredients, and the process for making two dozen cookies. The only thing missing in the production function is specifying the exact amount of each input, such as two cups of flour as in a cookie recipe. A good production function, however, will have the right mix of ingredients in the right quantities, and will use the right technical process to produce the greatest yield from that combination of inputs.

big idea

Every firm has a unique technical recipe for producing each of its goods or services.

Production functions are specific to each product. Different products have different production functions. A firm selling children’s swing sets will have a production function that is different from firms selling pastries. The amount of labor a farmer uses to produce a bushel of wheat is likely different than that required to produce an automobile. Firms in the same industry may have somewhat different production functions, since each firm may produce its product a little differently. One pizza restaurant may make its own dough and sauce, while another may buy premade. A sit-down pizza restaurant probably uses more labor (to handle table service) than a purely take-out restaurant.

IN CONTEXT
Consider pizza making. The pizza maker takes flour, water, and yeast to make dough. Similarly, the pizza maker may take tomatoes, spices, and water to make pizza sauce. The pizza maker rolls out the dough, brushes on the pizza sauce, adds cheese and other toppings, and uses a wooden tool to put the pizza into the oven to bake. Once baked, the pizza goes into a box (if it’s for takeout), and the customer pays for the product. What are the inputs (or factors of production) in the production process for this pizza?

For pizza making, the factors of production fit into the following resource categories.

• Land as Natural Resources: If the pizza place uses a wood-burning oven, we would include the wood as a raw material. If the establishment heats the oven with natural gas, we would count this as a raw material. Don’t forget electricity for lights. If, instead of pizza, we were looking at an agricultural product, like wheat, we would include the land the farmer used for crops.
  
• Labor: When we talk about production, labor means human effort, both physical and mental. The pizza maker is the primary example of labor here. The pizza maker needs to be strong enough to roll out the dough and insert and retrieve the pizza from the oven, but they also need to know how to make the pizza, how long it cooks in the oven, and assorted other aspects of pizza-making. The business may also have one or more people to work the counter, take orders, and receive payment.
  
• Capital: When economists use the term capital, they do not mean financial capital (investment funds). Rather, they mean physical, man-made capital, such as the machines, equipment, and buildings that one uses to produce the product. In the case of pizza, the capital includes the pizza-making tools, the oven, the building, and any other necessary equipment (for example, tables and chairs).
  
• Technology: Technology refers to the process or processes for producing the product. How does the pizza chef combine ingredients to make pizza? How hot should the oven be? How long should the pizza cook? What is the best oven to use? Should the restaurant make its own dough, sauce, cheese, and toppings, or should it buy them?
  
• Entrepreneurship: Production involves many decisions and much knowledge, even for something as simple as pizza. Who makes those decisions? Ultimately, it is the entrepreneur, the person who creates the business, whose idea it is to combine the inputs to produce the outputs.

hint

Capital includes physical goods, buildings, and intellectual discoveries. Any resource that qualifies as capital must have been produced itself, and can be used to produce other goods and services. Money, however, is not part of capital. A firm cannot use money to directly produce other goods. Firms can, however, use money to acquire capital for the production of goods and services. Money is a form of financial capital.

terms to know

Production Function

A mathematical expression describing the relationship between inputs and outputs.

2. Total Physical Product Curve

The production function is important because it gives the answer to the question: What is the maximum output that the firm can produce with different combinations of inputs assuming some level of productivity? We assume one variable changes at a time, while all other conditions remain constant, or ceteris paribus. It is typical to allow the quantity of labor, or the number of workers, to vary, while holding the other inputs constant.

We can visualize a typical production function that relates inputs to outputs by plotting the quantity of inputs (land, labor, capital, and entrepreneurship) on the x-axis, and the quantity of output (yield) on the y-axis. This curve represents the total physical amount of output possible given different quantities of inputs.

In the production function graph below, the inputs are the number of workers used. Notice that this production function is a sigmoid curve or S-shaped curve. This S-shaped pattern is a common growth pattern that can also be found in biology and mathematics. The curve begins at zero where no inputs are being used, and no output is produced. Next, notice the shallow rise of the curve from zero, which then builds to a peak before tapering off.

did you know

Learning follows an S-shaped growth pattern. When you begin a new course you know very little. Slowly your understanding grows, and over time your learning accelerates as concepts build on one another. Your learning follows the growth pattern of an S-shaped curve.

The production function shows the total physical amount of output possible given different quantities of inputs and assuming a level of productivity. Along the curve, the maximum physical output is shown for different quantities of inputs, such as land, labor, physical capital, and technology.

• The firm cannot produce at any point above the curve because resources are not currently available.
• Producing at any point under the curve is productively inefficient, because the firm has the ability to produce more.
• By choosing a point along the curve, the total physical output is maximized.

hint

You might recall that these same outcomes occurred in the production possibilities model that you learned about in the lesson on the scarcity principle.

In the next lesson, you will learn what the particular sections of the curve mean for production, and you will be introduced to both numeric and graphical examples of a firm’s production function.

terms to know

Sigmoid Curve

An S-shaped curve.