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.

 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:

(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

 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 - LB =  10 - 3 = 7 In 7 hours we can WEAVE at most 7 yards of CLOTH QC  =  LC/c  =  7/1  = 7

 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.

 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)