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					Roadmap:

Up to now, the supply curve has served as a summary
  of the behavior of (competitive) firms.

In the next few chapters: A more detailed look at firm
   behavior.

First, in chapter 13:
   What are firms trying to achieve?
   How do a firm’s costs vary with the quantity of
   output it produces?
Basic behavioral assumption of the economic theory of
  the firm:
       Firms try to maximize profit.

Profit = total revenue - total cost.

Total revenue: the amount a firm receives for the sale
  of its output.

Total cost: the opportunity cost of the firm’s inputs.
Two kinds of opportunity costs of inputs:

Explicit costs: opportunity costs that require an outlay
  of money by the firm

  (wages of employees, payments for the purchase of
  raw materials, rent, utility bills, etc.)

Implicit costs: opportunity costs that do not require an
  outlay of money by the firm

  (Usually, these are opportunity costs of using
  resources already owned by the firm.)
The two most important implicit costs:

Opportunity costs of:

. . . owner’s labor (measured by foregone earnings),

. . . owner’s financial capital (measured by foregone
        return on next best alternative investment.)

“Accounting profit” vs. “Economic profit”
  Economists recognize explicit and implicit costs.
  Accountants generally recognize explicit costs only.
Example: Dave’s Dependable Do-dads.
If Dave weren’t running his own business, he would work
as a machinist for somebody else; salary = $50,000/yr.
Dave invests $300,000 of his savings in his business. Next best
alternative investment would pay interest @ 5%/yr.

2010 total revenue =                   $600,000
explicit costs =                        $530,000
(wages, raw materials, rent,
utility bills, etc.)
implicit costs =                        $ 65,000
(opportunity cost of Dave’s
labor ($50,000) and financial
capital ($300,000 @ 5% = $15,000))
Accounting profit =                     $70,000
Economic profit =                         $5,000
Accountants are mainly interested in keeping track of
  money flows.
Economists are mainly interested in predicting business
  decisions.

Dave’s positive economic profit (+$5,000) means that
  his business is more than covering all costs . . .

      . . . including the opportunity costs of the
      resources he owns and invests in business
      (his labor and financial capital).
This means Dave should keep the business going.
  (The resources he owns and has invested are earning
  a higher return than they would in their next-best
  alternative investments.)

Suppose that the “going wage” for machinists
  (opportunity cost of Dave’s labor) increases to
  $60,000/yr.

No change in accounting profit.

Economic profit falls to -$5,000 (negative!! $5,000).
Negative economic profit means that Dave would be
  better off investing his labor and financial capital in
  next-best alternatives.

He should close Dave’s Dependable Do-dads.



Recall second basic question in chapter 13:
  How do a firm’s costs vary with the quantity of
  output it produces?

First: How does a firm’s output vary with inputs?
For real-world firms, production usually requires many
  different kinds of inputs . . .

  . . . that differ in how rapidly their employment levels
  can be adjusted.

raw materials: usually pretty easy to change (up or
  down) the quantities that are delivered each month.

low-skill labor: usually pretty easy to hire more workers
  and train them -- or to lay off some current workers.
management/technical personnel: recruiting and
  training take a little longer than for low-skill workers.

specialized machinery: often a relatively long wait for
  delivery and installation.

build new (or expand current) factory: many months
  spent in planning and construction.

Simple “thought model” for analysis of firm decision-
  making:

  Two time frames for decision making: “short-run”
                                      and “long run”
Short-run: Some inputs (“variable inputs”) are freely
  variable; other inputs (“fixed inputs”) are absolutely
  fixed.

Long-run: All inputs are freely variable.

Let’s make it even a little simpler: Just two inputs.

All fixed inputs lumped together and called “factory.”

All variable inputs lumped together and called “labor.”
Technological factors determine how much output can
  be produced from given inputs.

From economist’s point of view, production technology
  summarized by:

production function: describes the relationship between
  the quantity of inputs used and the quantity of
  output produced.

Symbolically: Q = f(X1, X2, . . ., Xk),
  where Q is quantity of output and X1, X2, . . ., Xk are
  quantities of k different inputs.
A tabular presentation of a simple, two input, short-run,
production function. For a factory of given size . . .

  Quantity of   Quantity of      Marginal
     labor        output          product
 (workers/day) (widgets/day) (widgets/worker)

      0              0
                                    50
      1             50
                                    40
      2             90
                                    30
      3             120
                                    20
      4             140
                                    10
      5             150
Marginal product: the increase in output that arises
  from an additional unit of one input, holding other
  input(s) fixed.

Diminishing marginal product: the property of a
  production function whereby the marginal product
  declines as the quantity of the input increases.
       (http://en.wikipedia.org/wiki/Diminishing_returns)


A feature of almost all real-world production functions.

Why?
As “labor” (the variable input) increases, the size of the
  “factory” (the fixed input) is held fixed.

If both labor and factory were increasing (each extra
   worker brought with her some “extra factory”),
   perhaps we’d expect roughly equal increments to
   output with each increase in inputs.

When we add extra workers only, additional workers
 have to share materials and equipment, work in more
 crowded conditions, etc.

Output continues to increase with each extra worker,
  but by smaller and smaller increments.
A brief digression for those who know some calculus:

Our definition of marginal product . . .
      (increase in output for 1 unit increase in input)
      . . . is an approximation to the rate of change of
                     output with respect to the input.

Marginal products are partial derivatives.

With the production function represented by:

              Q = f(X1, X2, . . ., Xk),
. . . the marginal product of the second input, for
        example, is the partial derivative of
          f(X1, X2, . . ., Xk) with respect to X2:




Diminishing marginal product says that . . .

  . . . as X2 increases, holding X1, X3, . . . Xk fixed, . . .

          . . . this partial derivative decreases.
Recap: Production function (in tabular form, for
  example) describes how output varies, in the short-
  run as the variable input increases.

Next: How do costs vary, in the short-run, as output
  varies?

Definitions of some short-run cost functions:

fixed costs (FC): costs that do not vary with the
   quantity of output produced (costs of fixed inputs).

variable costs (VC): costs that do vary with the quantity
  of output produced (costs of variable inputs).
total costs (TC): costs of both fixed and variable inputs.
   TC = FC + VC.

average fixed cost (AFC): fixed costs per unit of output.
  AFC = FC ÷ Q.

average variable cost (AVC): variable costs per unit of
  output. AVC = VC ÷ Q.

average total cost (ATC): total costs per unit of output.
  ATC = TC ÷ Q.
Note: ATC = AFC + AVC.

marginal cost (MC): the increase in total cost that arises
  from an extra unit of production.

This “marginal cost” accompanies “total cost.”

How about “marginal fixed cost”? . . .

       . . . or “marginal variable cost”?
Building on the short-run production function from
  earlier . . .

  . . . and adding some extra assumptions:

Cost of factory = $30/day.
  (Firm has entered a long-term lease that calls for
  payment of rent = $30/day, even if the firm produces
  nothing at all.)

Workers are hired at a wage of $10/worker/day.
   The first two columns are the same as before:

  labor    output    FC VC       TC     AFC AVC ATC              MC
(wrkrs/d) (wdgt/d)    --- ($/day) ---    --- ($/widget) ---   ($/wdgt)

    0       0        30     0    30      --     --      --
                                                               0.20
    1       50       30    10    40     0.60 0.20 0.80
                                                               0.25
    2       90       30    20    50     0.33 0.22 0.55
                                                               0.33
    3      120       30    30    60     0.25 0.25 0.50
                                                               0.50
    4      140       30    40    70     0.21 0.29 0.50
                                                               1.00
    5      150       30    50    80     0.20 0.33 0.53
Recall: Marginal cost = the increase in total cost due to
  a 1 unit increase in production.

The data tell us the increases in total cost (DTC’s) due
  to output increases (DQ’s) of more than 1 unit.

Estimate marginal cost:

       MC = DTC ÷ DQ
Graphing the three average costs and marginal cost:
     Note: For best approximation graphing MC, I’ve plotted
           each value against midpoint of corresponding
           quantity range.
 ($/widget)
                                               MC



                                                ATC
                                                AVC
                                                AFC


                                             (widgets/day)
Three key things to note about this graph:

1. MC increases as output increases.

      MC = DTC ÷ DQ
         = wage ÷ [DQ due to additional worker]
        (because of the way our table is set up)

          = wage ÷ MP

Diminishing MP implies increasing marginal cost.
 2. There is a special relationship between MC and ATC.
($/widget)                                MC



                                          ATC




                          Q1      Q3 Q2         (widgets/day)


       Where MC < ATC, ATC is falling.          “Average-
       Where MC > ATC, ATC is rising.             marginal
                                                    rules”
       Where MC = ATC, ATC is “flat.”
Example: Cumulative GPA (“average”) and the grade in
  the next course you take (“marginal”).

  Cumulative GPA    Grade in “marginal” course.

        2.96
                             A (4.00)
        3.02
                             C+ (2.33)
        3.00
                             B (3.00)
        3.00
3. ATC is “U-shaped.”

  This follows from first two (increasing MC and
  “average-marginal rules”).

  Initially low MC pulls ATC down to start, but . . .

      . . . increasing MC eventually crosses ATC . . .

             . . . and, thereafter, pulls ATC up.
Summary:

The numbers in our example are hypothetical, . . .
  . . . but they do reflect one important feature of
        real-world production functions:
               diminishing marginal product.

We’ve seen how this feature leads to three key
 properties of short-run cost curves:
      1. Increasing MC
      2. “Average-marginal rules”
      3. “U-shaped” ATC.

				
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posted:7/26/2013
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