14. Let's play "Where's Waldo?" You will have to find some mistakes (if there is any) in the definition and solution of a social planning problem. Hopefully it is as easy for you as the "social distancing" edition of Where is Waldo? in the next page! a. (5 points) When I was about your age, a professor asked me to define a social planner's problem. In the economy there was an infinitely-lived representative household, with a per-period utility u(ct, ), discount was B and the production function was yt = A kall . This is what I wrote. max [ct, It, kt+1 ) 1=0 +=0 [ Bu(ct, le) subject to C+ + Kt+1 S welt + ( 1 + re ) kt Point at my mistakes (how was I confused?) and write the correct definition. b. (5 points) Then the professor asked me what is the minimum number of FOC's that I can compute from the Lagrangian to characterize the solution fully. I took FOCs with respect to ct, It, Ct+1, It+1 and kt+1. Was this correct? Were all of them necessary? c. (5 points) After some frustrating time, I fixed the previous mistakes and came up with the equations that solve the problem. Were they right? Point at the potential mistakes and write the right version if they are incorrect. (I denoted u. and up the derivatives of u with respect to consumption and labor respectively). Uc(Ct, It) = Buc(C++1, 1+1) aut+1- Key +1 - 8 2 ( ct, 4t) = Wc(ct, It) (1 - a) y Ct + Kt+1 - (1 - 8) kt