ECON211 Chapter Notes - Chapter 9: Production Function, Envelope Theorem, Horse Length

• School: University of Waterloo
• Department: Economics
• Course: ECON211
• Professor: John Burbidge

Document Summary

An example of a pro t-maximizing rm and an example of a cost-minimizing rm: consider a price-taking, pro t-maximizing rm in a one-output, two-input world. Denote the price of output by p and input prices by w1, w2, and suppose its production function is q = 2z1/2. Answer (a) if the hessian of the production function is negative de nite, then it is strictly concave. Calculate f1 (z1, z2) = 2 f2 (z1, z2) = 4. 2 f12 (z1, z2) = 0 f22 (z1, z2) = . The hessian is: f12 (z1, z2) f22 (z1, z2) (cid:19) = 1 (cid:18) f11 (z1, z2) f12 (z1, z2) For z1, z2 positive f11 < 0 and f11f22 f 2 are satis ed, so the production function is strictly concave in z1, z2. The rm"s pro ts are: pf (z1, z2) w1z1 w2z2. Note that the hessian of pro ts is p times the hessian of the production function.