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Production Analysis and Estimation

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Title: Production Analysis and Estimation


1
Production Analysis and Estimation
  • The Production Process
  • The Short Run Total, Marginal, and Average
    Product
  • The Long Run Input Combination Choice
  • Measuring the Value of an Input
  • Returns to Scale

2
The Production Function
  • Production Function The maximum amount of
    output that can be produced for a given amount of
    input.
  • Presumes the level of technology, training, etc.
    If these change, you need to estimate a new
    production function.
  • Q f(X, Y)

3
The Production FunctionDefinitions
  • Discrete Production Functions a production
    function with distinct input patterns.
  • Continuous Production Function a production
    function where inputs can be varied in an
    unbroken marginal fashion.
  • 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

4
Short Run Production
  • The Short Run- A period of time in which at least
    one input used in production is fixed.
  • Law of Diminishing Returns As a variable input
    increases, holding all else constant, the rate of
    increase in output eventually diminishes.
  • 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
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.

6
Optimal Level of a Single Input
  • To maximize profits the firm equates Marginal
    Revenue and Marginal Cost. WHY?
  • The same principle applies to the question How
    much of an input should I employ?
  • Marginal Cost of an input Input Price
  • Marginal Revenue of an input MRP
  • The firm maximizes profits in the hiring of a
    worker when MRP Price of the input.
  • IN WHAT STAGE OF PRODUCTION DO FIRMS OPERATE?

7
The Input Demand Function
  • See pages 284-287.
  • Elements needed for problem
  • Demand curve P a bQ
  • Total cost for parts TC c dQ
  • Labor supply Ls ePL
  • Hours of labor required for each unit of output.
  • Steps in solving the problem
  • Solve for the profit maximizing relationship
    between the price of labor and output.
  • Utilizing hours of labor required for each unit
    of output, solve for labor demand
  • Equate labor demand and supply to ascertain the
    profit maximizing wage rate.
  • Solve for profit maximizing level of worker
    hours, output, price, and profit.

8
Long Run Production
  • The Long Run A period of time necessary for all
    inputs used in production to be varied.
  • Question What combination of inputs should a
    firm hire to efficiently produce its chosen level
    of output?
  • Technical Efficiency Least-cost production of a
    target level of output.

9
Optimal Combination of Multiple Inputs
  • NOTE We will not be discussing isoquants or
    isocost lines.
  • The answer to the long-run question depends upon
    relative prices and relative productivities.
  • Equation 7.13 and 7.14
  • Px / Py MPx/MPy
  • MPx/Px MPy/Py
  • MP1/P1 MP2/P2 ...... MPn/Pn
  • In words The optimal input proportions are
    employed when an additional dollar spent on any
    input yields the same increase in output.

10
Profit Maximization in the Long-Run
  • THREE STATEMENTS TO DEFEND
  • A firm that minimizes long-run costs is not
    necessarily profit maximizing.
  • To be profit maximizing, though, one must
    minimize long-run costs.
  • A firm profit maximizes by employing a quantity
    of each input so that each inputs MRP equals its
    price.

11
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.

12
Output Elasticity
  • Output Elasticity The percentage change in
    output associated with a 1 change in all inputs.
  • If E gt 1 Increasing Returns to Scale
  • If E 1 Constant Returns to Scale
  • If E lt 1 Decreasing Returns to Scale

13
Production Functions, Again
  • The Linear Production Function
  • Imposes Constant Returns to Scale
  • The Marginal Product of any one input is
    independent of the characteristics of the other
    inputs employed.
  • The Cobb-Douglas (Multiplicative, Double log,
    Power Production) Function
  • Returns to Scale can vary
  • The Marginal Product of any one input is
    dependent on the characteristics of the other
    inputs employed.
  • How do you choose? Remember the Box-Cox Test.
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