The Cobb Douglass Cost Minimizing Inputs calculator computes the Cobb Douglas cost minimizing factors.
INSTRUCTION: Choose units and enter the following:
- (α) Production Exponent of Labor
- (β) Production Exponent of Capital
- (w) Per unit cost of labor
- (r) Per unit cost of capital
- (q) Quantity to be produced.
Cobb Douglass CMI: The calculator returns the factors (see below). The total cost C*(q) is returned in U.S. dollars. However, this can be automatically converted to other currency units via the pull-down menu.
- L*(q)
- K*(q)
- C*(q) This is the total cost.
The Math / Science
The Cobb Douglas Cost Minimizing Input formula is a function of labor (L), capital (K), output elasticity (α), output elasticity of capital (β). The goal is to set factors such that as production increases, cost increase in the minimum way. The formulas for Cobb Douglass Cost Minimizing Input are:
`L*(q) = ((w/r)*(β/α))^(-β/(α+β))*q^(1/(α+β))`
`K*(q) = ((w/r)*(β/α))^(α/(α+β))*q^(1/(α+β))`
`C*(q) = w * ( ( w/r * b/a )^(-b/(a+b)) * q^(1/(a+b))) + r*( ( w/r * b/a )^(a/(a+b))*q^(1/(a+b)) )`
where:
- α = Production Exponent of Labor
- β = Production Exponent of Capital
- w = per unit Cost of Labor
- r = per unit Cost of Capital
- q = Quantity to be Produced
