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Minimizing Cost

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K = Capital. Isocost Isocost: The set of combinations of labor and capital that yield the same total cost for the firm. Figure 7.1. Page 232 ... – PowerPoint PPT presentation

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Title: Minimizing Cost


1
Minimizing Cost
2
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 firms input quantities cannot be
  • changed.

3
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.

4
Isocost
  • Isocost
  • The set of combinations of labor and capital
    that yield the same total cost for the firm.
  • Figure 7.1. Page 232

5
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)

6
  • 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?

7
  • 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 ?

8
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)

9
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)

10
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)

11
Tabel 7.1. Page 245Price Elasticities Of Input
Demand For Manufacturing Industries In Alabama
Input Industry Capital Production Labor Non Production Labor Electricity
Textiles -0.41 -0.50 -1.04 -0.11
Paper -0.29 -0.62 -0.97 -0.16
Chemicals -0.12 -0.75 -0.69 -0.25
Metals -0.91 -0.41 -0.44 -0.69
12
Short Run Cost Minimization
  • TC TVC TFC
  • TC Total Cost.
  • TVC Total Variable Cost.
  • TFC Total Fixed Cost.

13
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.

14
Figure 7.14 Page 248Short Run Cost Minimization
With One Fixed Input.
15
  • Figure 7.15. Page 249
  • Short Run Input Demand Versus Long Run Input
    Demand.
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