Consider the Cobb-Douglas production function with X=l 1 l 2 where +l 1 ,

Consider the Cobb-Douglas production function with   X=l^α₁l^β₂ where α+β•l₁, where d>0. 

(a) Denoting the input prices by w₁ and w₂, derive the cost function as it depends on x and e. Show that it satisfies assumption 5.1.

(b) What happens when α+β=1?

Data from assumption 5.1

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Assumption 5.1 The cost function C(x,e) is twice continuously differentiable with C. ()>0, and for any production level x there is an emission level er such that C(x,e) = 0. Furthermore C(x,e) <0 Ve