Simple Opportunity Set
This is an example of a most simple economic decision under constraint of limited resource. It involves:
single factor of production
BREAD and CLOTH
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.
L ... LABOR
hours per one loaf
c ... LABOR/CLOTH
hours per one yard
LB = b QB
LABOR needed for BAKING QB loaves of BREAD.
LC = c QC
LABOR needed for WEAVING QC yards of CLOTH.
L >= LB + LC
Sum of LABOR needed for BAKING and WEAVING
cannot exceed available man-hours of LABOR.
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
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