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Minimizing Cost. The Long Run Cost Minimization Problem. Long run: The period of time that is long enough for the firm to vary the quantities of all of its inputs as much as it desires. Short run: The period of time in which at least one of the firm’s input quantities cannot be

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The long run cost minimization problem
The Long Run Cost Minimization Problem

  • Long run:

    The period of time that is long enough for the firm to vary the quantities of all of its inputs as much as it desires.

  • Short run:

    The period of time in which at least one of

    the firm’s input quantities cannot be

    changed.


The long run cost minimization problem continued
The Long Run Cost Minimization Problem (continued)

  • Min TC = wL + rK

    of producing Q units of output.

    Min = minimize.

    TC = Total Cost.

    w = the price of a unit of labor service.

    r = the price per unit of capital services.

    L = Labor.

    K = Capital.


Isocost
Isocost

  • Isocost:

    The set of combinations of labor and capital that yield the same total cost for the firm.

    Figure 7.1. Page 232


The solution to the long run cost minimization problem
The Solution To The Long Run Cost Minimization Problem

  • When the isoquant is just tangen to an isocost line

    Figure 7.2. Page 233

    Cost minimizing input combination

    Slope Isoquant = Slope Isocost

    (MPl / w) = (MPk / r)


  • Problem:

    Production function Q = 50 (LK)1/2

    w = 5; r = 20

    What is the cost minimizing if the firm want to produce Q = 1000?


  • Answer:

    MPl = 25 (K/L)1/2

    MPk = 25 (L/K)1/2

    ( MPl / w ) = (MPk / r)

    [ 25 (K/L)1/2 / 5 ] = [ 25 (L/K)1/2 / 20 ]

    L = 4K

    K = 10

    L = 40

    TC = ?


Deriving the input demand curves from a production function
Deriving The Input Demand Curves From A Production Function

  • Problem:

    The production function Q = 50 (LK)1/2

    What are the demand curves for Labor and Capital?

    (MPl / w) = (MPk / r)

    K = f (r, w, Q)

    L = f (r, w, Q)


The price elasticity of demand for inputs
The Price Elasticity Of Demand For Inputs

  • Price Elasticity Of Demand For Labor:

    The percentage change in the cost minimizing quantity of labor with respect to a 1 percent change in the price of labor.

    e L,w = (DL / Dw) / (w / L)


The price elasticity of demand for inputs continued
The Price Elasticity Of Demand For Inputs (continued)

  • Price Elasticity Of Demand For Capital:

    The percentage change in the cost minimizing quantity of labor with respect to a 1 percent change in the price of capital.

    e L,w = (DK / Dr) / (r / K)


Tabel 7 1 page 245 price elasticities of input demand for manufacturing industries in alabama
Tabel 7.1. Page 245Price Elasticities Of Input Demand For Manufacturing Industries In Alabama


Short run cost minimization
Short Run Cost Minimization

  • TC = TVC + TFC

    TC = Total Cost.

    TVC = Total Variable Cost.

    TFC = Total Fixed Cost.


Short run cost minimization continued
Short Run Cost Minimization (continued)

  • TVC:

    the sum of expenditures on variable inputs, such as labor and materials, at the short run cost minimizing input combination.

  • TFC:

    the cost of fixed inputs, it does not vary with output.


Figure 7 14 page 248 short run cost minimization with one fixed input
Figure 7.14 Page 248Short Run Cost Minimization With One Fixed Input.



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