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Simple Opportunity  Set

This is an example of a most simple economic decision under constraint of limited resource. It involves:

single factor of production

LABOR

two products

BREAD and CLOTH

two technologies

BAKING and WEAVING

Note that for each product, there is only one technology,  and both products require the input of the same factor of production. The technologies are assumed to be 'fixed coefficients',  i.e. requiring the constant quantity of input per each unit of output.

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  Notation:

variables

parameters

quantities

units:

technical coefficients:

units:

L  ... LABOR

man-hours

b ...LABOR/BREAD

hours per  one loaf

QB... BREAD

loaves

c ... LABOR/CLOTH

hours per one yard

QC...CLOTH

yards

 

 

  Equations:

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(1)

LB  =   b QB

LABOR needed for BAKING QB loaves of BREAD.

(2)

LC   =   c QC

LABOR needed for WEAVING QC yards of CLOTH.

(3)

L >=  LB  +  LC

Sum of LABOR needed for BAKING and WEAVING

cannot exceed available man-hours of LABOR.

 

 

  Numerical Example

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L  = 10

Total available LABOR is 10 man-hours.

b  =  .5

half an hour of LABOR is needed to BAKE one loaf of BREAD

c  =  1

one hour of LABOR is needed to WEAVE one yard of CLOTH

Suppose we want 6 loaves of BREAD.

QB   =  6

How much CLOTH can we produce?

QC  =   ?

BAKING 6 loaves of BREAD takes 3 hours of LABOR.

LB  =   b QB =  (.5) 6 = 3

7 hours remain for WEAVING CLOTH

LC =< L - LB10 - 3 = 7

In 7 hours we can WEAVE at most 7 yards of CLOTH

QC  LC/7/1  = 7

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If we want 6 loaves of BREAD we can produce at most 7 yards of CLOTH, given the limited amount of LABOR and existing technology of BAKING and WEAVING.  

 

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If we want 14 loaves of BREAD we can produce at most 3 yards of CLOTH, given the limited amount of LABOR  and existing technology of BAKING and WEAVING

.

  PRODUCTION   POSSIBILITY FRONTIER
 (PPF)

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PPF algebraic derivation

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Designed and maintained by Oldrich Kyn - Copyright 1997-2005.  All rights reserved. Copyrights of signed articles, graphics, sounds and programs is held by the original authors.


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