Copyright (c) Christopher Makler / econgraphs.org

# Cost Minimization along an Isoquant: {{ model.title }}

production technology
F(L,K) = AL^\alpha K^\beta
\alpha = {{params.alpha | number: 2}}:
\beta = {{params.beta | number: 2}}:
A = {{params.A | number: 2}}:
input prices and quantity
{{ notation.wLabel }} = {{params.w | number: 2}}:
{{ notation.rLabel }} = {{params.r | number: 2}}:
{{ notation.outputLabel }} = {{params.q | number}}:
Cost-Minimizing Bundle
{{ notation.LRCostLabel }}({{ notation.lLabel }},{{ notation.kLabel }}) = {{ notation.wLabel }}{{ notation.lLabel }} + {{ notation.rLabel }}{{ notation.kLabel }} {{ notation.LRCostLabel }}({{ model.shortRunLaborRequirement() | number:0 }},{{ params.K | number:0 }}) = {{ params.w | number:2 }} \times {{ model.shortRunLaborRequirement() | number:0 }} + {{ params.r | number:2 }} \times {{ params.K | number:0 }} || = {{ model.shortRunTotalCost() | number:2 }} TC({{ model.conditionalLaborDemand() | number:0 }},{{ model.conditionalCapitalDemand() | number:0 }}) = {{ params.w | number:2 }} \times {{ model.conditionalLaborDemand() | number:0 }} + {{ params.r | number:2 }} \times {{ model.conditionalCapitalDemand() | number:0 }} || = {{ model.longRunTotalCost() | number:2 }}

Note: there may be some rounding!