Economics 101

Production and Costs: The Theory of the Firm

The Circular Flow Model
Recall that in our initial discussion of the economy we identified two broad groups of economic actors (or units); they were households and firms. In our study of demand we looked at households as consumer units effecting demand for goods and services in the product market. On the supply side of the product market are the economic (or business) firms. They are the producers (and sellers) of goods and services. In this section we are going to look the behavior of an economic firm.

Production and Production Costs
Questions to be asked:

How do firms decide what to produce and how much to produce?
What factors constitute a firmís costs?
How do firms determine what price(s) to charge
What determines a firmís profit?
What determines the shape and the position of a (firmís) supply curve?

Business Firm
A business firm is an economic unit engaged in the production of one of more economic goods or services.
Applying the technology available to it, a business firm combines economic resources (factors of production) to produce one or more goods for the purpose of making profits.
A business firm buys economic resources (inputs) and sells the goods it produces (outputs).

Production and Costs
To produce a good or a service a firm needs economic resources or factors of production. In economics,  the factors of production used by a firm in the production of a good or a service are generally referred to as inputs. What a firm produces is called output. A firm has to pay for the inputs it needs. Therefore, inputs, on the one hand, generate costs and, on the other hand, generate output.
We first study the relationship between inputs and the output; that is "production function". Then we look at the relationship between the output and costs; that is cost function.

Note: Studying the relationship between costs and inputs without regard to the output produced from the inputs is not useful. That is why we study the relationship between costs and output.

Inputs: Factors of Production
Factors of production:
The primary factors of production are land and labor.
Capital is another important factor of production.
In economics we distinguish between physical capital and financial capital.
Physical capital: tools,  machinery, equipment, buildings
Note: Non-physical assets such as copy rights and patent rights are functionally similar to physical capital.
Financial capital: Financial assets representing physical capital (stocks) or used to acquire physical capital are financial capital.

In addition to land, labor and capital businesses often use intermediate goods (raw materials and supplies) in the production process.
Entrepreneurial Services: In market economies the function of entrepreneurs is also very important. The function of an entrepreneur is to acquire and combine all the needed factors of production to produce a good. An entrepreneur takes chances (risks) in the hope of making profits.

Cost of production is simply the sum of the costs of all inputs used in production.

Production Costs = Costs of Inputs

Production in the Short Run versus Production in the Long Run

In the theory of the firm the distinction between short run and long run is not necessarily based on the length of time. It is rather based on the degree of the variability of inputs.
In the short run at least one of the factors of production remains unchanged (fixed).
In the long run all factors of production are variable.
In a two-input production process, in the short run, only one input is variable.

In a two-input production model, in the short run, the changes in the output (physical product) are the result of changes in the variable input.
Production in the Long Run
In the long run all inputs used in the production process by the firm are variable.
In a two-input production model, in the long run, both inputs (say, capital and labor) are variable.
In the long run the level of the output of a firm can change as a result of changes in any or all inputs.
A Short-Run Production (Function) Analysis
Our model:
A firm using two inputs:
Capital (K); Fixed Input
Labor (L);    Variable input

We examine the relationship between the variable
input (labor) and the output.

We examine how changes in labor (the variable input)
affect the out put.

Output Measures
Total (Physical) Product (output), TPP: The total amount of output produced by the firm over a certain period
Average (Physical) Product (of the variable input), APP: Total (Physical) Product divided by the number units of the variable input
Marginal (Physical) Product (of the variable input), MPP: The change in total product resulting from employing one additional unit of the variable input


Average (Physical) Product and Marginal Physical Product


                                                             Change in  TPP
Marginal Physical Product =  MPP =   ---------------------
                                                             Change in V. Input

                                                           Total Physical Product
Average Physical Product = APP =    -------------------------
                                                                Total V. Input

The ďLawĒ of Diminishing Return
Increases in the amount of any one input, holding the amounts all other inputs constant, would eventually result in decreasing marginal product of the variable input.

Explanation: Unless all inputs are perfectly and infinitely substitutable, as we increase the amount of one input, while keeping other inputs constant, at some point the productive effectiveness of that input starts to decline.

Output and the Firmís Revenue

Total Revenue (TR) = Price x Total P. Product

Marginal Revenue Product: The change (increase) in revenue resulting from the output produced by one additional unit (MPP) of the variable input

                   MRP = MPP x Price



Optimal Input Level:

Input Price = MRP

Wage = $5
Optimal Input= 7

Optimal Output =60
Optimal Input/Output



Plotting the Cost Measures


                     K= 10                                            K= 20                                               K= 30

Return to Scale


Optimal Input Combinations
Recall that in our short-run analysis to decide how many units of labor to employ we equalized the revenue resulted from hiring one additional unit of labor (MRP) and the price of labor (wage).

   This rule can be generalized and applied to all inputs.
        MPP *  PRICE  =  MRP=   Wage

      MPPK * PRICE =   MRPK  =   Price of Capital

Marginal Product and the Input Price
Each time a firm wants to increase its  output it would have to buy (hire) additional inputs.
Additional input generates costs, on the one hand, and generates output, on the other hand.
If the inputs are added one unit at a time,
            Change in cost = the price of input
                Change in output = MPP
The cost of each additional unit of out put will be:

 Change in cost           or                Input Price
Change in output                               MPP

MPP, Input Price and Marginal Cost
Recall our definition for marginal cost:
                      Change in Cost
     MC    =  -------------------
                    Change in Output

When we increase our input one input/one unit at a time:

                                         Change in cost  =  Input price

                                        Change in Output = MPP

Choosing the Optimal Mix of Inputs
One approach to choosing the optimal (least costly) mix of inputs is to compare the (marginal) cost of producing one extra unit of out put across different inputs.
The firm would likely use the input that increases its output at the lowest cost by comparing

Input Price
    --------------       across all available inputs.

                       Production Table                                               (Marginal) Cost-per-Unit Table

Choosing The Optimal Mix of Inputs: An Alternative Approach
Comparing the (physical) output of the (marginal) dollars spent across all inputs:
    MPP of any input
    Price of that input

                 MPPL          MPPK           MPPm
                --------         --------         ---------
                 Wage             PK                 Pm

Optimal Input Choice: The General Rule
For any given level of total output, a profit maximizing firm would want to minimize its cost. Alternatively put, for any given level of total cost, it would want to choose the mix of inputs that would maximize its output.
The firm can achieve this objective by making sure that it is getting the highest amount of output out of each dollar spent on inputs.
The rule: Equalize MPP per dollar across all inputs
MPPa/Pa  =  MPPb/Pb  =   MPPc/Pc  =   MPPd/Pd

Optimal Mix and Changes in Input Prices
Starting from an optimal position,
                                            MPL        MPK
                                            ------  =  -------
                                            Wage        PK

A change in the price of one input would disturb the equilibrium and would require adjustments in the input mix.