Econ 11B - Mathematics for Economics - Exam One Grading & Answer Key

Grading  Five Questions - fifty points total, ten points each question  Questions, Answers & Grading Key [PDF]    Step-by-Step Solutions  Question 1 - The Cobb-Douglas Production Function is typically written in a form something like, . Show that:                                 (show that the partial of a Cobb-Douglas Production function can be simplified in terms of P and the term the partial is in respect to)    Solution  Question 2 - Consider two products, A & B. The demand for goods A & B is a function of the price of both good A & B, and described by the following two quantity-demanded equations:                        Now, find . Given your result, explain why A & B are either compliments, substitutes (competitive goods) or neither.  (given terms describing quantity demanded, find their cross partials (their cross-price elasticities) and determined and explain what type of goods they are)   Solution Question 3 - Find the partial derivative  of the implicit function,                        Solution Question 4 - For the following function,                                                 Show that   (although by Young's Theorem we know this to be true, we are proving it with this functional form)       Solution Question 5 -  Let   ,  where;                          Using the Chain Rule, find the partial derivative . And, for good measure, find the partial via the substitution method as well.    Solution