Test #1: Take-Home Questions Note: You must show all of your work to receive full or partial credit. Because of superb education at The University of Tampa, you have been handpicked by The President to serve as his special advisor on macroeconomic issues, with an ofce in the South Wing of the White House. On the rst day on your new job, you are entrusted with the following tasks: 1. Consider a Cobb-Douglas production function given by: Y = srrifzrz where l' is output, K is capital, L is labor. (The parameter values were provided by the FBI.) Show that this function has all four of the desired properties of production functions (as outlined in W0909 Class Notes [posted on Blackboard)). Briey explain the signicance of each of the four properties. Additionally, nd the cross partial derivatives (\"5% and 32%). Briey explain their signs (positive, negative, or zero) and the signicance of your findings. 2. The President believes that the production function above is missing a very important variable, the entrepreneurial factor, so you set up your Cobb-Douglas equation as follows: if = Army\"'3, Where l' is output, A is total factor productivity, K is capital, L is labor, E is the entrepreneurial factor, 0