economics mathematics

BONUS (2 points): What must be true about a function in order for Young's Theorem to hold? (hint: Young's Theorem is f, - f,,) .Using the chain rule, find the partial derivative " (10 points. 2 points only d's if you find the derivative through substitution.)\f3. Find the partial derivative oz of the implicit function dy Inx + Iny - Inz = e" (10 points). Hint: Remember that z is assumed to be a function of y.2. Consider two products, A and B, whose demand is a function of the prices of both A and B; . 200 9A PAPAZ 1000 1 PAPE Find " and " (8 points) and determine whether A and Bare ap A complements, substitutes (competitive goods), or neither (2 points). APlease answer each question fully. You are allowed a non-programrnahie calculator for the exam. There are 5 questions each worth 10 points. There is- also a 2 point bonus question. lHDIEATE YOUR FINAL ANSWER. 1WITH A. BOX ARDUND IT. ' 1. Cobb Douglas production functions are typically written in the form r- - acts\" on Show that 5% 4%. (6 points for finding the correct derivative. 4 points for proving the equality.)