The Production Function

In This Lecture We build a model to describe a “generic” production process. • The most common characteristics in production processes • Translate those characteristics into a “model” – a set of equations and graphs-. ©2001Claudia Garcia-Szekely

Factors of Production • To produce, an entrepreneur uses factors of production. • Factors of production are: • Labor (workers) • Land (a farm) • Capital (equipment, buildings) ©2001Claudia Garcia-Szekely

The Concept of Plant • A “plant” is the factory (space) where production takes place and • All the equipment necessary to produce • In other words is everything needed to produce, except workers and raw materials. ©2001Claudia Garcia-Szekely

Short Run vs. Long Run • The short run is defined as the period of time when the plant size is fixed. • The long run is defined as the time period necessary to change the plant. • The duration of the long run (and thus that of the short run) depends on the nature of the production process… ©2001Claudia Garcia-Szekely

The Nature of production • For a coffee shop: the long run is the time it takes to expand the coffee shop. • For a steel mill: the long run is the time it takes to expand the plant – to build an addition, add the new equipment- • The long run can be as short as a few weeks or as long as several months, depending on what is involved in expanding capacity to produce. ©2001Claudia Garcia-Szekely

Short Run vs. Long Run • In the short run, at least one factor of production is fixed (unchangeable) • In the long run, all factors of production can be changed… are “variable” ©2001Claudia Garcia-Szekely

Firms plan in the Long Run • At any point in time, a firm is restricted by (committed to) a specific plant size… • Firms never operate (produce) in the long run. • The long run is the planninghorizon…when all inputs are variable until you commit to a specific plant size. ©2001Claudia Garcia-Szekely

In the Short Run • Plant size is fixed. • This means that production is restricted to the capacity that you have in place at the moment. • To increase production, the only adjustment possible is to hire more workers or more labor hours (longer shifts). ©2001Claudia Garcia-Szekely

The Production Function (TP) • This function represents the relationship between the number of workers and the TOTAL number of units of output produced holding all other factors of production (the plant size) constant. • For a coffee shop, output would be measured in “number of coffee cups a day” • For a steel mill, output would be measured in “tons of steel produced a day” ©2001Claudia Garcia-Szekely

Rise Run AP: slope of ray from origin… Q AP (of 10 workers) = 15 TP 150 units Slope = 150/10 = 15 L 10

AP: slope of ray from origin… Q What happens to the Slope of the ray as L Increases up to Lo? AP Increases up to L0 The ray gets steeper: The slope increases L Lo L increases

AP: slope of ray from origin… What happens to the Slope of the ray as L Increases past Lo? Q AP Decreases after to L0 The ray gets flatter: The slope decreases L Lo L increases

AP: Slope of ray from origin… Q Q AP (slope of ray) Decreases after L0 AP (slope of ray) Increases up to L0 Lo Lo

Marginal Product (MP) The additional output that can be produced by adding one more unit of labor, holding everything else constant. MP = DQ/DL The slope of the Total Product Function ©2001Claudia Garcia-Szekely

Rise Run MP: Slope of the Production Function Slope = 30/3 = 10 Q MP = 10 TP 160 units 30 130 units 3 L 9 12

Choosing the Slope of the Production Function… To choose the slope we must consider the following: • The Slope of the Production Function is: (Rise) DQ / (Run) DL • How does production (Q) CHANGES when a new worker (L) is hired? ©2001Claudia Garcia-Szekely

What happens to output as we hire more and more workers? • Remember that the plant size is fixed. • That means that you will be hiring more workers to SHARE the EXISTING EQUIPMENT and the EXISTING SPACE. ©2001Claudia Garcia-Szekely

A Coffee Shop • The plant will be the store, the tables, the coffee machines, etc. • When you add your first three workers, • One will make the coffee, the second will be the waiter and the third will manage the register. ©2001Claudia Garcia-Szekely

If you add a fourth worker • With two waiters, more customers can be served… • Output would probably increase a lot as you add more and more workers AT THE BEGINNING. • Eventually, adding new workers would begin to be counterproductive… • Workers will now need to wait to use the equipment… ©2001Claudia Garcia-Szekely

The most likely scenario • For most production processes, • Adding the first workers will be favorable to production as specialization increases productivity. • Eventually, adding more and more workers to a FIXED PLANT size would result in decreases in productivity due to “crowded conditions”. ©2001Claudia Garcia-Szekely

The Law of Diminishing Marginal Product. • As more of a variable input (labor) is added to a fixed input (plant), additions to output get smaller and smaller.. Note that adding workers increases output but the increases become smaller and smaller as more workers are hired. ©2001Claudia Garcia-Szekely

Choosing a Graph to show Diminishing Marginal Product To draw the production function we must choose a graph that shows: • The more workers we have the more output would be produced. For this, we need to draw and INCREASING FUNCTION. ©2001Claudia Garcia-Szekely

Drawing a Typical Production Function • As we add more and more workers, additions to output - may increase at the beginning but - eventually decrease. For this, we need to draw a function with a slope that increases at the beginning, reaches a maximum and then decreases. ©2001Claudia Garcia-Szekely

The Relationship between AP and MP • If MP (10) > AP (9), then the Average Product increases. • If MP (11) < AP (12), then the AP will decrease. • If MP = AP, then the AP is not increasing or decreasing: it is at the maximum point. ©2001Claudia Garcia-Szekely

The Production Function