The Production Function Micro: Econ: 18 54 Module The Production Function KRUGMAN'S MICROECONOMICS for AP* Margaret Ray and David Anderson

What you will learn in this Module: Can you draw a production function, correctly labeled? Why is production often subject to diminishing returns to inputs? The purpose of this module is to introduce the production function and a key concept: short-run diminishing returns to a variable input (typically labor). Production functions, and short-run diminishing returns, are the foundation for cost functions and the ability to model a firm’s profit maximizing decision.

Production Functions A production function shows the relationship between a firm’s inputs and output. Generally, more inputs means more output, hence positive. A firm uses a production function to combine inputs (labor, capital, raw materials, land, etc) to get output. The output produced is a function of the inputs used for production. In general, more inputs create more output (the total product curve has a positive slope).  

Inputs and Output   Think of a production function like a cook with a recipe for soup. The cook adds varying quantities of ingredients, labor, heat and ingenuity to a fixed quantity of capital (a pot and stove). The inputs are combined and soupy output is produced. All goods and services, either simple (like soup) or complex (like 767’s), have a production function. So if the capital is fixed now, how much time must pass before they could expand it? It kind of depends and illustrates the difference between the short run and the long run. The short run is the time period that is too brief for a firm to alter its plant capacity. The capital, or plant size, is fixed in the short run. The long run is a period of time long enough for a firm to change the quantities of all resources employed, including the capital plant size. Variable Inputs: can be increased to increase production. Fixed Inputs: cannot be increased in the near term to increase production. The short run versus the long run Short run: at least one input is fixed. The time period that is too brief for a firm to alter its plant size (capital is fixed). Long run: all inputs may vary. A period of time long enough for a firm to vary all inputs, including capital (plant size). Long run:

Total Product The production function shows how firms can combine inputs to produce output. The simplified model has two inputs, capital (which is fixed) and labor (which is variable). Total product curves typically increase rapidly as the first workers are hired. This is due to specialization as workers perform tasks that are best suited to their talents.  As more workers are hired, total product continues to rise, but at a slower and slower rate. Opportunities to specialize have been exhausted and the plant can’t get any bigger! By the time the later worker are hired, the plant is too crowded with people. Eventually, an additional worker actually gets in the way of the production process and causes total output to fall.   Total Product (TP or Qs) is the total output produced by the firm. A graph of the firm’s TP when it uses different levels of a variable input (with a given level of fixed inputs)is the firm’s production function. When we graph it we make the Total Product Curve.

Total Product Curve  Diminishing marginal product of any input is a defining characteristic of production functions in the short run. The concept is really very simple. As you add more labor to a fixed quantity of capital, the next worker contributes less and less to the total than the workers who came before.   This is not the result of hiring inferior workers, they are assumed to be just as good as the workers that came before. It is a result of having less space and/or tools with which to work and this prevents the later workers from contributing as much as the workers who came before.

Total Product The production function shows how firms can combine inputs to produce output. The simplified model has two inputs, capital (which is fixed) and labor (which is variable). Total product curves typically increase rapidly as the first workers are hired. This is due to specialization as workers perform tasks that are best suited to their talents.  As more workers are hired, total product continues to rise, but at a slower and slower rate. Opportunities to specialize have been exhausted and the plant can’t get any bigger! By the time the later worker are hired, the plant is too crowded with people. Eventually, an additional worker actually gets in the way of the production process and causes total output to fall.   Discover the main differences between the Total Product Curve and the Production Function.

Marginal Product Marginal Product (MP) of an input is the additional output produced as a result of hiring one more unit of the input. When we graph it out we make the Marginal Product Curve. MPL = (Δ Total Output)/(Δ Labor) MPC = (Δ Total Output)/(Δ Capital) We can see the additional contribution of an additional worker by computing marginal product of the variable input, labor in this case.   Marginal Product of Labor = (Δ Total Output)/(Δ Labor) The MP is represented by the slope of the TP curve (slope = rise/run). A change in output is the rise and change in labor is the run.

Marginal Product Curve  Diminishing marginal product of any input is a defining characteristic of production functions in the short run. The concept is really very simple. As you add more labor to a fixed quantity of capital, the next worker contributes less and less to the total than the workers who came before.   This is not the result of hiring inferior workers, they are assumed to be just as good as the workers that came before. It is a result of having less space and/or tools with which to work and this prevents the later workers from contributing as much as the workers who came before.

Diminishing Returns The shape of the TP curve illustrates the principle of Diminishing Returns to an Input. Diminishing Returns to an Input: as more and more of a variable input is added to a fixed input, the additional output produced will decline.  Diminishing marginal product of any input is a defining characteristic of production functions in the short run. The concept is really very simple. As you add more labor to a fixed quantity of capital, the next worker contributes less and less to the total than the workers who came before.   This is not the result of hiring inferior workers, they are assumed to be just as good as the workers that came before. It is a result of having less space and/or tools with which to work and this prevents the later workers from contributing as much as the workers who came before.

Diminishing Returns  Diminishing marginal product of any input is a defining characteristic of production functions in the short run. The concept is really very simple. As you add more labor to a fixed quantity of capital, the next worker contributes less and less to the total than the workers who came before.   This is not the result of hiring inferior workers, they are assumed to be just as good as the workers that came before. It is a result of having less space and/or tools with which to work and this prevents the later workers from contributing as much as the workers who came before.

Diminishing Returns  Diminishing marginal product of any input is a defining characteristic of production functions in the short run. The concept is really very simple. As you add more labor to a fixed quantity of capital, the next worker contributes less and less to the total than the workers who came before.   This is not the result of hiring inferior workers, they are assumed to be just as good as the workers that came before. It is a result of having less space and/or tools with which to work and this prevents the later workers from contributing as much as the workers who came before.

“Spin-ishing” Returns Let’s generate some data, and graph it out. Let’s do a simplified model where we have fixed inputs [land] and variable inputs [labor]. 1 full rotation per student = 1 unit of output All workers need to coordinate or else production for that day doesn’t happen. The group with the highest Total Product will earn 2 dojo points per member.  Diminishing marginal product of any input is a defining characteristic of production functions in the short run. The concept is really very simple. As you add more labor to a fixed quantity of capital, the next worker contributes less and less to the total than the workers who came before.   This is not the result of hiring inferior workers, they are assumed to be just as good as the workers that came before. It is a result of having less space and/or tools with which to work and this prevents the later workers from contributing as much as the workers who came before.

Let’s Practice What are his fixed and variable inputs? Calculate and graph the marginal output of his variable input(s) Assume he buys a new machine that allows him to double the amount of drinks per pound of beans. Calculate and graph. Noel’s friend has a restaurant, so he lets Noel run a small coffee making business in his building. All Noel has to do is buy the machines and pay for the coffee beans. Lbs. of Coffee Beans Number of Drinks 1 10 2 18 3 24 4 28  Diminishing marginal product of any input is a defining characteristic of production functions in the short run. The concept is really very simple. As you add more labor to a fixed quantity of capital, the next worker contributes less and less to the total than the workers who came before.   This is not the result of hiring inferior workers, they are assumed to be just as good as the workers that came before. It is a result of having less space and/or tools with which to work and this prevents the later workers from contributing as much as the workers who came before.