Problem 3 (Cost minimization, Cobb Douglas production function) In Florida, in Spring 2020, Doctors without Borders (MSF) organized a mobile clinic to offer Covid19 testing services to migrant farm hands. The clinic production function was Q = ELD'SK where Q is the number of migrant workers tested each day, L is the daily number of people working at the clinic, and K is the number of pieces of equipment the clinic uses each day. The clinic's MP, = % and the clinic' s MPH = EU\". a. Does technology at the MSF mobile testing clinic display diminishing marginal returns to labor and/ or capital? Explain, clearly. b. What is the expression of the clinic's Marginal Rate of Technical Substitution? Are the clinic's isoquants bowed in towards the origin (convex)? How do you interpret this finding? c. Does technology at the clinic display increasing, constant, or decreasing returns to scale? Clearly explain. MSF had an average daily cost of labor of $200 and an average rental cost of equipment of $100. The clinic tested 125 workers each day. d. By using the feasibility condition (output target) and the tangency condition (cost minimizing mix) find the combination of labor and equipment that minimized the clinic' 5 cost of testing 125 migrant workers. (Keep in mind that the cube root of 125 is 5.) e. What was the clinic' 5 daily total cost of production? What was the clinic' 5 unit cost of testing one migrant worker? f. In a diagram measuring labor (L) along the horizontal axis and equipment (K) along the vertical axis draw an isoquant curve and an iso-cost line to illustrate the clinic's cost minimizing technique. g. With the aid of your diagram, explain qualitatively how MSF would have changed the combination of workers and pieces of equipment used at the mobile clinic if the rental cost of a piece of equipment increased to $400. In the same Spring, other health organizations set up drivethrough testing sites with the same production function as the MSF's clinic that tested 1,000 people per day. Assume that these health organizations paid the same wages and rental cost of equipment as MSF. h. How many workers were used each day at a drivethrough testing site? How many pieces of equipment? i. What was the daily cost of testing at a drivethrough testing site? What was the unit cost of testing one person? Why were the drive~through testing sites more efficient than MSF's mobile clinic