Problem set 4 Instructor: Serguei Maliar 1. Consider cost minimization problem minc (1, 21) = w121 + W2x2 x1,X2 y = f(21, 202) Consider the production functions: a) f(x1, 2) = 2 1 + 22 b) f(21, 2) = 221 + 22; c) f(21, 202) = min {2x1, 22 } ; d) f(21, 2) = 21 2 , 1/2x1/2 where the production factor 2 is fixed in the short run at the level x2 = X2. e) f(21, 2) = 1' 2 , 1/2x1/2 where the production factor 21, 22 are fixed in the short run at the level x1 = 1 and 22 = X2. For each of these production functions, show the solution graphically (draw isoquants and isocosts and show the point or points that minimize the cost). Also, derive a solution analytically including conditional factor demand at and xt and cost function c (w1, w2, y)