microeconomics...

\flQuestion 11 Because of superb graduate education at our Department, you have been handpicked by The President to serve as his special assistant to his hotel business that operates informally out of the South 1|Wing of the White House.5| Your rst task is to derive the prot maximizing inputs and output of his hotel business. You quily learn that this president strictly prefers silnple answers So you consider a lDoblo-[llt'iuglas production function with labor and capital as inputs In terms of notation, output q is given by q = 442?:235 where A,o1,o5,21,2g E III. We denote by 21 and 15 the amount of labor and capital, respectively. a.} UnfortunatelyI the parameters A, on and org are only known to the IRS and the Russians Ieclijng the right connections to either of them, you set out to estimate the parameters of the production function. How would you estimate it using IDLE? Set up the \"eronometric mode \" and state the estimator. b.} Afta ring up your {illegal} copy of Stata, you estimate parameters Am, and o; and nd that islet :- U with in + as -:: 1. Armed with these estimates, you set out to calculate prot maximising inputs and output. The President has lamented about the competitiveness of the hotel businem. Thus you feel safe to assume that his businem is a price taker both in the factor and output markets. Denote by p the price of the output and by on and urn the prices of the inputs, respectively. Set up the prot maximisation problem and derive step-by-step the conditional factor demand functions (in, factor demand conditional on optimal output] and the supply function. c.} Derive also the profit function [as a function of factor prices and output price}. {The President is really interested in prots Moreover, it will be relevant in the latter parts of the question] d.} Very proud of your achievement, you quickly run back to the oval ofce to cheer fully present your results. After 140 seconds1 The President dismisses your results as fake news He sternly declares that you omitted a very very important variable. He won't tell you what it is, but he knows it is there, and you better get it right otherwise you are red. In your despair, you ask around what it could be. Not sur prisingly, Jean Speiser is miw'illing to tell you. In this high-stress environment, you experience nightmares the moment you try to sleep. As always, Professor Schjpper '1 \"""1 \"'2' \"I! I lt'.' where ea denotes the entrepreneurial factor. Initially you suspect that only the FBI and the Russian have data on 23. Since you don't nd it politically opportune to contact either of them at this point of time, you need some other way to gure out as. 1|ii'ith the entrepreneurial [actor in mind, what number should you assume for oat? Explain in as much details as possible. Verify that the conditions under which one can apply McKenzie's proposition [see part g} are satised in our case. a} Having set a; to what McKenzie would have probably set it1 you seem to struggle to gure out the supply 1; because you don't know the price of the entrepreneurial factor, W3. Argue that we can set _-i._ _"s_ _ _ _ Lniug i l-u-e i l-t-n: tuti1 te calm (aim) (aw) {You should recognize this expression from earlitu' parts of the question. You are also allowed to make an assumption on 23 but this assumption should be verbally justied-i nned with this insight, you rush back to the oval ofce and argue that both The President and you got it light. That is, it is true that you olnitted the en trepreneurial factor but your earlier results on the optima] input of labor and capital and optimal supply are still correct. Verify this claim. f.} The President turns to his trusted trade adviser, Piotr Noyato, to verify your anal- ysis. Being educated both in l[BabbDouglas production functions and constant returns to scale, he rejects your analysis claiming that it implies that The Presi dent's hotel business malces zero prom. This ies in the ane ofempirical evidence of strictly positive prots made by The President. As often, he is just confused but The President is already furious over allqed zero profits. How can you clear up the confusion? Explain. g.} The President seems pleased to hear that after all he makes positive prots He invites you to teach his staff about your analysis. 1t"ou start by stating McKenzie's insight in general terms: \"Fbr any content production set 1" g IL with I] E 1", there is a constant returns, convex production set 1\" g R\"! such that Y = {y E If\" : {1.51} E 1\"}.\" Provide a proof of this proposition {There is a Twitterlike proof in lem than 14D characters.) (Hint: Think about the dening property of a production set with constant returns}