Question 1

Question 1. Consider a firm that can produce its output q using a Cobb- Douglas production function f: R} 9 R where q = f(z1,22) = A212/522V5 where Z1, 22 are net inputs in the production process. a) Write the expression of the firm's Production Set Y b) Check if technology is characterized by increasing, decreasing, or constant returns to scale. c) For input prices W1: 2 and wz =1 find the cost minimizing technique that allows the firm to produce q = 64 units of output. d) Now, let (W7,W2) E R2++ denote the generic vector of input prices and find the conditional factors demand z(w,q) then substitute z(w,q) in the expression w1z1+w222 to find the cost function c(w,q). Now consider the general case of a firm that can transform two inputs zJ with j = l, 2 into an output q according to the technology CKZi, Zz .23) = 21'25 e) Find the conditions on parameters a and B for the firm's technology 1) Exhibits diminishing marginal returns to factor 1 and/or diminishing marginal returns to factor 2. 2) Exhibits non-increasing, or non-decreasing, or constant returns to scale f) Find the expression of the firm's conditional factors demand 2 = z(w,q)