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Derive cost function for the Cobb-Douglas technology and prove the following properties of cost function c(w,y). (1) Nondecreasing in input price. (2) Homogeneous of degree

Derive cost function for the Cobb-Douglas technology and prove the following properties of cost functionc(w,y).

(1) Nondecreasing in input price.

(2) Homogeneous of degree one in input price.

(3) Concave function in input price.

(4) Shephard's lemma.

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