Outline Seven - Some Basics on Production Theory

Reading Assignment:  "The Structure of Capital" by Gene Callahan

The purpose of this section of the class is to provide tools that will help a manager to make better decisions about choosing which inputs to use in a production process, and what level of output to produce.  These tools are most appropriate in a basic factory setting -- where the firm is producing distinct outputs -- when marginal productivity, revenue and costs can all be determined pretty easily.

 It becomes less useful when marginal productivity, revenue or costs can't be determined easily.  For example, what is the marginal productivity of a teacher?  Lawyer?  Other professionals?  We will look more at this problem later.

So given that we can collect good information about our production process - the discussion falls into 2 parts.  The first part deals with ‘production theory’ or the right combinations of inputs to employ.  The second part addresses the appropriate level of output. 

The Firm:

In standard neoclassical theory -- a firm is given and a production function is stated:  Q = f (K, L), where K = capital and L = labor.

In reality, all capital and all labor are homogeneous.  They can't be put into a function in the sense that they can be aggregated.  So be careful with all of the assumptions that are made here!!  As a manager, your job will be much more complicated (and interesting).  More on this later.

So before we make this assumption and use this model -- let's go back a step and ask:

What is a firm?

Why do firms exist?

Also - realistically, the decision to even become a firm is an interesting one.  It is basically the Make or Buy decision.

Ronald Coase:

    Two modes of organization (or production)- The Make or Buy Decision:

The firm then is when internalization is used (when more than one input comes under the same ownership). Can be somewhat fuzzy.

        Internalization (types):

      Transactions Costs:

    Uncertainty:

    The Entrepreneur (the human action - the decision-maker):

NOTE:  Uncertainty is very important here.  Many institutions in our economy exist because of uncertainty. 

Uncertainty, to a large degree, is a major issue that economists should address but often assume away!!  When they do, they basically assume away some of the most important problems/issues that we face.

Entrepreneurs are very special people who take on uncertainty.  When uncertainty is increased by government changing the rules or by entrepreneurs not knowing how and when the government will change the rules, for example, entrepreneurship, economic growth and job creation are all hindered.

To sum up the reason firm's exist and the decision that entrepreneurs must make:

Capital and Reality - Production/Time and the Structure of Capital:  Remember the mainstream production function above - Q = f (K,L) - we need to be careful using this model.  Why?

The major problem with this model:  in reality, capital is not a "blob" or even a dollar amount we can add up.  Both in society and in a firm, capital is a structure that evolves over time with changing values and circumstances.  Something is a capital good because an entrepreneur sees value in it as such.  It is useful to him or her in producing a consumer good. 

Furthermore - the concept of capital can be viewed as a complex order of goods related to each other in particular ways.

It is similar to a puzzle - each piece fits with other pieces in a very particular way.  Trying to take a piece of one puzzle and put into another puzzle will not necessarily mean it will be productive.  It might not "fit" into the structure of that particular country or firm, for example.  So we must look at capital as being valuable only if it the entrepreneurs find that it adds value to the production processes.  For example - let's look at the a country or a firm as a "Hayekian Triangle" (after economist F. A. von Hayek):

The Hayekian Triangle as a Firm:  As a manager you must decide where and how the pieces of capital (including labor) should fit together to be the most productive.  For the economy, this is a spontaneous process.  But in the firm it must involve some planning.  This is a difficult job that needs to be constantly updated, changed, etc.

The Role of the Manager in the Production Process - Mainstream theory (with some of Deb's process points added in):

    Production within a firm (input acquisition and transformation) has two dimensions:

1.  Planning (or deciding what types of productive assets to acquire in the first place - will the capital you acquire "fit" with the capital you already have, for example), and

2.  Operating (day to day operations - making sure all inputs, including capital, are used to make day to day operations more productive).

In the operating dimension, the manager must attend to two issues.  These are easier said than done!

a. Produce on the Production Function.  A production function illustrates the maximum amount of output feasible given a particular set of inputs. NOTE (via Deb):  do we ever really know where this is?  All a manager can really do is, again, obtain a satisfactory level any given time given the information he or she has.

 If the workers do not work to maximum capacity, less will be produced.  One very important managerial function is to motivate workers to work efficiently. 

We will discuss worker motivation methods later.

b. Use the Right Level and combination of Inputs. The manager must decide the best amount of variable inputs to use and how each should be used.  (The right number of sales people, or waiters, etc.)  Again, these inputs are not homogeneous -- so where they are utilized in our "capital structure" is very important. 

To analyze this question (or at least the right level of inputs) we must characterize the productivity of inputs - using the standard model.

In standard neoclassical theory (as stated earlier) we have:  The Production Function for the firm.

We start by characterizing the way that inputs are converted or transformed into units of output.  The process is represented by a production function.  Again, which (assumes) illustrates the maximum amount of output available for a given combination of inputs. 

Although the production function that is appropriate for a particular circumstance is particular to that firm, the general issues underlying production analysis are illustrated in standard theory by considering a generic production function:

            Q         = F (K, L)

Where              Q         = units of output

                        K         = units of capital input (typically machines of some sort)

                        L          = units of labor input.

Most typically, production requires some combination of machines and labor.

Now, let's go back to our standard economic time horizons:

Time Horizons:

 In a short run some factors of production (usually capital) are fixed.  In the long run, all factors are variable.  Thus, the short run is an operating horizon, where the best amount of variable inputs are chosen.  In distinction, the long run is a planning horizon, where all inputs are variable.

Short Run - Operations

Long Run - Planning

Remember:  The amount of time necessary to define the short run varies across industry.  The short run in steel production, for example, is a much longer period of time than the short run for a pizza maker.  Nevertheless, in either environment, within the short run the same sort of issues are relevant.

Short Run Decisions 

As just mentioned, in the short run some factors are fixed.  Let us assume that K, capital is fixed at level K*, or

            Q         =          F (K*,L)

Then, the relevant problem is to determine the best amount of variable input L. 
In order to do this, we have to look at how productive labor inputs are relative to cost.

Measures of Productivity.  Now let’s consider the variable input.  First, we must define some terms. 

Total Product: (TP) is simply the maximum total output available from a given combination of inputs.

 Average Product (AP) is the average output for all units of a given input. The average product of the variable input labor

                         AP_L = Q/L

 Marginal Product (MP) is the change in output associated with the use of an additional input unit.

                        MP_L =Change in Q/Change in L

But wait -- Remember with variable inputs we will face the dreaded Diminishing Marginal Returns or Productivity:  As is the case in much of economic analysis, marginal decisions play a pivotal role in production analysis. 

This is why MP first increases, then decreases - or at least this is a very typical pattern, and reflects basic economic assumptions.  As a few resources are hired, there are gains from specializing the use of these inputs (for example, by dividing tasks and creating an assembly line).  After a while, however, factors begin to experience some crowding (e.g., workers on the line start getting in each others way.)  Thus, declining marginal productivity is a consequence of the law of diminishing marginal returns.  Eventually, crowding becomes so severe that marginal productivity is negative.  In this case, total output actually falls as extra units of input are hired.  No rational manager would use resources to the point of negative marginal productivity (unless they have other motives besides profit - which could happen with a manager - especially in the short run or in a not for profit business).

But notice also, that diminishing marginal productivity is not a consequence of “worse” or “lazy” workers. Rather it is a consequence of crowding or overuse of the fixed asset.

So again - note that this theory to a large degree assumes that inputs are homogeneous.  In reality, we can hire an additional worker and MP increases even with more overloading because that particular worker is so much more productive than others -- there's more going on here than just DMR.

 Graph:

Relationships between Productivity Measures.  The productivity measures are related systematically.  These interrelationships can be seen by plotting the curves:

Graphs: (see handout of graphs)

Notice that the Total Product curve first increases at an increasing rate (reflecting gains from specialization), then increases at a decreasing rate (the law of diminishing marginal returns) finally peaks out and decreases (indicating negative marginal productivity).

Three Stages of Production in the Short Run:

            Stage I:  zero to maximum Average total product –

            Stage II:  from maximum Average total product to where TP is maximized (MP is zero) –

            State III:  MP is negative -

According to economic theory, a profit making (rational) firm will always produce in Stage II.  Why? 

Reason:  A firm would never stop where there are increasing marginal returns, because if it is profitable to hire a worker who makes 6 units per hour, it should be profitable to hire a worker who makes more than 6 (unless marginal costs increase for some reason or there is not enough demand to justify more output).  Furthermore, if average product is increasing – under utilizing your fixed inputs (Stage I).  Similarly, a firm would stop hiring when there are negative marginal returns, because output could be increased by laying off workers and cutting production expenses (Stage III).  See graphs handed out in class.

Derived Demand and Best Use of a Single Input

So what is the right level of input to use in Stage II? 

Remember first – Derived Demand:  the value of an input is derived from the value of the output it produces.  If there is no value for the output ... there is no value for the input. 

So to determine the best use of an input – we must consider the output price (a proxy of consumer value).  Therefore we are "deriving" the value of the input from the value of the output (proxy = consumer price).

Value of the Marginal Product of Labor (also called marginal revenue product) – Therefore, to decide the appropriate level of a variable input to use, we must convert productivity into value. Do this by multiplying marginal productivity in units, by the value to the consumers (proxy for this is the price) of the units.

For labor (Marginal Revenue Product or Value of the Marginal Product)

            VMP_L = P_Q(MP_L).

(Similarly, for capital VMP_K = P_Q(MP_K).

Rule: Best Input Usage:  A manager should use an input L up to the point where VMP_L is as close to the wage (w) (or marginal cost) as possible without w exceeding VMP_L.

Notice that you can use the above theory to anticipate the response of a firm to changes in underlying conditions.  For example, what would be the effects of a change in the wage?  What would be the effects of a change in the price of the output?

What about multiple inputs -- how many to hire if  the inputs could substitute for each other?

 Now, let us suppose that a firm can vary all its factors of production (including machinery) - so this is a long run decision if the machines were fixed. 

             MP_i /P_i            =          MP_j /P_j             

Where i and j are two different inputs that could substitute for each other.

This is called the least cost combination of inputs. It is an important and general principle of hiring multiple inputs: A firm should hire resources until the marginal value per dollar spent is equal for all inputs.  It makes sense - if one input is giving you more productivity per dollar spent on it, hire more of it.  But as you hire more (or use more) the input experiences diminishing marginal returns -- until its marginal product per dollar spent is = to other inputs. 

Example:  Jones  Printing Co. is presently paying $10 per hour for labor, and $5 per hour for Printing Machines. 

- If the Marginal Productivity of labor is 100 pages per day, and the marginal productivity of machines is 150 per day what is the best combination of inputs?  Assume an 8 hour work day.

First, what is the marginal productivity per hour - 100/8 = 12.5 for labor and 150/8 = 18.75 for machines.

Then determine the marginal productivity per dollar spent for each:  12.5/10 = 1.25 for labor, and 18.75/5 = 3.75 for machines.

- Given this information, the firm should increase its use of machines (MP will drop) and decrease it use of labor (MP will increase) until the MP per dollar cost is equal for both.

Example: Suppose that Randolph Tire Co. Currently uses Labor and Rubber Banding Machines to finish tires (and they could be substituted for each other).  Suppose that labor is negotiating its contract, and asks for a 33% increase in salary.  Management argues that the consequence of such a wage increase will be a sharp reduction in the number of employees. Employees don’t believe management. They firmly believe that management will continue to employ the same number of workers even after a substantial wage increase.

Explain management’s position using marginal productivity theory.

The Long Run Production Function

            Remember, in the long run all inputs can vary – so the size of the firm can change.

            There are increasing returns, constant returns or decreasing returns to scale.  Same as economies of scale, constant returns to scale and diseconomies of scale.

Let’s define these more specifically with respect to productivity or output.

Increasing returns to scale:  an increase in a firm’s inputs by some proportion results in an increase in output by a greater proportion.

Constant returns to scale:

Decreasing returns to scale:

We will review reasons for these in the next (cost) section.  Right now, let’s think about how a manager might determine (measure) returns to scale.

Maybe an output elasticity:

% Change in Q/% Change in all inputs

So if our output elasticity is:

>1 =

=1 =

< 1 =

Or, going back to the neoclassical production function:

Q = f (K, L)

Let’s put proportional increases (assume both K and L are increased in the same proportion) = p

And the proportion that Q increases = h

So:  hQ = f(pK, pL)

If h > p:

If h = p:

If h < p:

Question:  Betty is thinking of increasing the size of her bakery by adding a new room with new bakery equipment - such as a new mixer and oven.  Looking at how productive her current (and similar) inputs are, she estimates her output elasticity to be 1.5.  Ceteris paribus, should she expand her business?  Why or why not?

What other factors should she also consider when making this decision?

Derived demand?

Cost?