productionI do not have any problem solving maximization problems using the Lagrangian function. However, I came across an “unusual” implicit production function and I do not know how to find the cost function from it.
Y = min(aL, bK)
Where Y is the output level, K is the number of units of capital, L is the number of units of labour and a and b are both strictly greater than 0.
Your help will be much appreciated.
It is the Leontief technology production function. Thereore, the producer operates at a point where y=aL=bK. This implies that if the firm want to produce y units of output, it must use y/a units of L and y/b units of K, irrespective of input prices. That means, the cost function must be c(w,l,y)=wL+rK=w(y/a)+r(y/b)=y{(w/a)+(r/b)}.
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