help needed
Uncertainty 1. (6 points) von Neumann-Morgenstern Expected Utility There is uncertainty inherent in our experience of this existence. You have utility over housing xh and leisure consumption xi, and you are aware that your choice of a partner impacts your utility over these goods. There is a pm,\" chance of nding happiness with a partner who is an equal (smart and wonderful like you, and willing to do all the work required of a human relationship), and there is a stgn chance you settle for someone out of fear of dying alone (because humans fear things I guess]. If you nd a great partner, utility is given by 12xh7xl, and 3cth if you don't. You face budget constraint m = phxh + plxl. Professor John von Neumann Professor Oskar Morgenstern Professor Gonzo a. (1 point) Establish the von Neumann-Morgenstem utility mction. b. (1 point) How do changes in pyahs and psggh affect Marshallian demand for xh and x;? c. (1 point) What is expected utility if Pyaas= 0.03, psigh=0.97, xh = 21, and xl=l4 when you immediately settle for the rst person who talks to you? (1. (1 point) Let utility for perpetually being single be given by 3xh3xl. How many utils would this give you given the parameters listed in part c.'? Would you choose this or would you play the lottery for a partner? e. (1 point) What pyahs would you need to play the lottery for a partner (I totally gave away part of the answer to part (L, didn't 1?)? f. (1 point) pyahs and pgh are exogenous in this model, but what could you do as a person to achieve the pm,\" you calculated in part e? (Note: of course I'm not endorsing solitude or playing the life partner lottery; I'm prompting introspection through applying this material to every aspect of the human experience and highlighting the beauty of the elegant applied philosophy that is economics. .. or something)