The Production Function

1
The Production Function

• Production Function The maximum amount of
  output that can be produced for a given amount of
  input.
• Q f(X, Y)

2
Returns to Scale vs. Returns to a Factor

• Returns to Scale The output effect of a
  proportional increase in all inputs. LONG RUN
• Return to a Factor The relation between output
  and variation in only one input. SHORT RUN

3
Short Run Production

• The Short Run- A period of time in which at least
  one input used in production is fixed.
• The Long Run A period of time just long enough
  that all resources can be varied.
• Law of Diminishing Returns As a variable input
  increases, holding all else constant, the rate of
  increase in output eventually diminishes.
• Law of Diminishing Marginal Returns As
  additional units of the variable resource are
  used in combination with a fixed amount of other
  resources, total output at first rises, initially
  quite rapidly then more slowly, and eventually
  declines.

4
Total, Marginal, and Average Product

• Total Product the whole output from a
  production system.
• Marginal Product change in output associated
  with a one-unit change in a single input.
• Average Product Total product divided by units
  of input employed.
• UNDERSTAND HOW THESE ARE RELATED!!!

5
The Stages of Production

• Stages of Production
• Increasing Returns
• Decreasing Returns
• Negative Returns
• Do not confuse returns with returns to scale.

6
Marginal Product vs. Average Product

• Marginal Product - the additional output that
  will be forthcoming from an additional worker,
  other inputs constant.
• The change in total product that occurs in
  response to a unit change in a variable input
  (ceteris paribus).
• The amount of output produced by the last unit of
  the input hired.
• Change in total product / Change in an input
• Slope of the total product curve
• Rate of change in total product
• Average Productivity - output per worker.
• Total product / Inputs hired
• Average Product is Maximized AP MP

7
On the Hiring of Workers

• Why do firms hire workers? Return to Cost-Benefit
  Analysis
• Cost The wage the worker is paid. This is
  generally set in the market, not by the firm.
• Cost Wage
• Benefit The productivity of the worker
  (marginal product) the value of this
  productivity in the market place
• Benefit Marginal Revenue Product

8
Marginal Revenue Product

• Marginal Revenue Product The amount of revenue
  generated by employing the last input unit.
• MRP Marginal Product of input Marginal
  Revenue of output
• MRP The value of the input to the firm
• In words The value of an input is determined by
  the inputs productivity and the value of that
  production in the marketplace.

9
Profit Maximizing Hiring

• If W gt MRP What action should the firm take?
• If W lt MRP What action should the firm take?
• The firm will maximize profits with respect to
  the hiring of workers when
• Wage Marginal Revenue Product

10
Stages of Production, Again

• In what stage of production, then, do firms
  operate? Only in stage two.
• In stage one, increases in the labor force will
  increase the MRP. If it made sense to hire the
  previous workers, and the next worker offers a
  higher MRP, then it makes sense to hire the next.
  Hence firms will not stop hiring workers in
  Stage One.

11
More History

• J.B. Clark (1847-1938) The first American
  economist to contribute to the history of
  economic thought.
• Ethical implications of Marginal Productivity
  Theory Labor, Capital, and Land are paid
  according to their economic contribution to the
  social product. Therefore analysis contending
  that labor is exploited are naive.
• Critique of Clarks position
• Violation of Humes Dictum That what ought to
  be cannot be derived from what is (i.e.
  normative statements cannot be derived from
  positive statements, or in other words, what a
  person should earn is not relative to what the
  person does earn).
• Conclusion depends upon perfectly competitive
  goods and/or factor markets.
• How do you measure a workers marginal product?

12
Measuring MRP

• Joan Robinson (1933) What is actually meant by
  exploitation is usually that the wage is less
  than the marginal revenue product.
• In most industries the measure of MRP is
  difficult. Sports are the exception.
• The Gerald Scully approach
• i. Estimate the value of a win.
• Revenue f(wins, ...)
• ii. Estimate the value of the players actions in
  terms of wins.
• Wins f(player and team statistics)
• iii. Compare a players estimated MRP to the
  players wage.
• The Anthony Krautman approach
• If the market is competitive..... Salary MRP
• Salary f(player statistics)
• From this we can learn the value of a players
  statistics and thus analyze the value of non-free
  agents.

13
Cost Functions

• Cost Function The cost-output relation.
• Depend upon the underlying production function
  and input prices.
• Short-run cost functions Basis for day-to-day
  operating decisions.
• Long-run cost functions Basis for long-range
  planning.
• REMEMBER HOW SHORT-RUN AND LONG-RUN ARE DEFINED.

14
The Short Run

• Short-Run Cost Curve Cost-output relation for a
  specific plant and operating environment.
• Total Cost Total Fixed Cost (TFC) Total
  Variable Cost (TVC)
• Fixed Cost Expense that does not vary with
  output.
• Variable Cost Expense that fluctuates with
  output.
• CONNECT SHORT-RUN TOTAL COST TO TOTAL PRODUCT.

15
Marginal vs. Average Cost

• Marginal Cost Change in Total Cost (TC) /
  Change in Output (Q)
• Marginal Cost Change in TVC / Change in Q WHY?
• Average Total Cost TC / Q
• Average Fixed Cost TFC / Q
• Average Variable Cost AVC / Q
• ATC MC when ATC is minimized. WHY?
• CONNECT SHORT-RUN MC AND ATC TO MARGINAL PRODUCT
  AND AVERAGE PRODUCT.

16
The Long-Run

• Long-Run Cost Curves Cost-output relation for
  the optimal plant in the present operating
  environment.
• Economies of Scale Decreasing long-run average
  cost
• Economies of Scope Cost reduction from
  producing complementary products.
• Note the difference between economies of scale
  and scope. Scale is focused on cost-savings from
  increased production. Scope is focused on
  cost-savings from increases in product lines.

17
RETURNS TO SCALEDefined

• Constant Returns to Scale When a given
  percentage increase in all inputs leads to an
  identical percentage increase in output.
• Increasing Returns to Scale When a given
  percentage increase in all inputs leads to an
  larger percentage increase in output.
• Decreasing Returns to Scale When a given
  percentage increase in all inputs leads to a
  smaller percentage increase in output.

18
Returns to Scale

• Increasing Returns to Scale or Economies to Scale
  decreasing long-run average costs.
• Specialization of Labor
• Larger, more efficient, equipment
• Learning curve average cost reduction over time
  due to production experience.
• Decreasing Returns to Scale or Diseconomies of
  Scale increasing long-run average cost
• Lengthening of the managerial chain hampers the
  flow of information and the decision-making
  process.
• Motivation and supervision of workers becomes
  increasingly difficult.
• NOTE Returns to Scale is dictated by the size of
  the market.

19
Long-Run Average Cost

• Capacity Output level at which short-run
  average costs are minimized.
• If a firm moves beyond capacity the firm may
  want to consider building a larger plant.
• BE ABLE TO ILLUSTRATE THIS STORY IN THE SHORT-RUN
• Minimum Efficient Scale Output level at which
  long-run average costs are minimized.
• BE ABLE TO ILLUSTRATE LONG-RUN AVERAGE COST AND
  IDENTIFY THE LEVEL OF OUTPUT CORRESPONDING TO MES.

20
Firm Size and Plant Size

• Multi-plant Economies of Scale Cost advantages
  from operating multiple facilities in the same
  line of business or industry.
• Multi-plant Diseconomies of Scale Cost
  disadvantages from operating multiple facilities
  in the same line of business or industry.

21
The Economics of Multi-Plant Operations

• Elements needed for problem
• Equation for Demand Curve
• Short-run Total Cost Function
• Steps in Solving the Problem
• Solve for profit maximizing output, price, and
  profit.
• Solve for average cost minimizing output.
• Solve for MC when firm produces at capacity.
• Set MR equal to MC at capacity to determine
  optimal multi-plant operation.
• Determine the optimal number of plants.
• Determine price and profit when firm employs the
  optimal number of plants.

22
Business BuzzwordsDownsizing and Outsourcing

• Downsizing divesting unrelated businesses or
  removing jobs in middle management.
• Reduces inefficiency
• Law of Diminishing Returns
• Moving to a new short run cost function
• Problems
• Can increase costs because of lost specialization
• Can reduce moral and productivity

23
Outsourcing and Efficiency Wages

• Outsourcing the process of purchasing services
  that used to be performed in-house. Why is this
  necessary?
• Shirking - the behavior of a worker who is
  putting forth less than the agreed to effort.
• Solutions to shirking Outsourcing and Efficiency
  Wages
• Why would firms pay efficiency wages? In other
  words, why do higher wages elicit higher
  productivity.
• a. The Gift exchange hypothesis
• b. Worker turnover
• c. Worker quality