Econ 301Intermediate MicroeconomicsProf. Marek WeretkaProblem set 5(due Thursday, March 4th, before class)Problem 1 (Intertemporal Choice)Gerald is a CEO at Brainies Consulting Inc. Hi s income in the …rst year is m1= $200 and in the seco ndm2= $200. Assume that the interest rate is r = 100%: (His time horizon is limited to thes e two years.)a) Find P V and F V of Gerald’s inc om e.b) show on the graph (C1; C2) Gerald’s budget set. Ma rk P V , F V and the slope of his budget linec) explain what borrowing/lending strategy gives Gerald each of the two "extreme" consumpti on points.(how much does he borr ow/lend in the …rst period, how much does he pay back/ receive in the second per iod?)c) suppose his utility fun ction isU(C1; C2) = ln C1+ ln C2Find analytically Gerald’s optimal choice and show it on the graph. Does the optimal consumption involvesaving or borrowing?Problem 2 (Intertemporal Choice)The preferences of a manager and a sportsman are given byU(C1; C2) = ln C1+11 + ln C2Suppose r =  = 100%.a) Give economic interpre tation to coe¢ cient :b) Derive optimal consumption plan of a manager (C1; C1) if his income in two periods is given bym = (0; 3000): Find optimal level o f savings S in the …rst period.c) Derive optimal consumpt ion plan of a sportsman, (C1; C1) if his income in two periods is given bym = (1500; 0): Find optimal level o f savings in the …rst p eriod.d) A re the manager and the sportsman smoothin g their consumption pro…les?f) Show, using one of the secrets of happiness, that the optimal consumption of the manager is decreasingover time when r < :Problem 3 (Annuity and Perpetuity)a) Derive PV formula for pe rpetuity with payment x and interest equal to r,b) D erive PV formu la for annuity that pays x; maturity is T and interest rate is r:Problem 4 (Present Value, use a calculator)a) Buying or renting You are moving in to Madison (you are going to stay her e forever!) and you wouldlike to …nd an a partm ent. You can ei ther buy it or rent it. The monthly rent is $500 and the monthly interestrate is 0:1%. Alternatively, you can purchase the apartment, paying $600; 000: How are you going to …nanceyou new accommodation? Argue us ing the P V formula. Showb) You take a loan to buy a car that costs $4000. Wha t is your monthly p ayment if your want t o payback the l oan a fter 3 year s, (36 payments) and the monthly interest rate 0.5%: (Hint: Loan with con stantpayments is like annuity!)c) You are hired by Merrill L ynch –a …nancial management and advisory …rm – to help asses the valueof a T-bond (T-bond is a bond issued by the Department of the Treasury) with the face value F = $1000;coupon c = $100 (paid annually till T  1 (included) and face value F paid in T ) and time to maturity equalto T = 10 years. The interest rate is equal to r = 10%. Fi nd the PV of such bond. Is it a good or bad dealto buy such bond for $900?: Explaind) You want to receive $40; 000 per year when retired (61 and 80). How much do you have to save between21 -60 years. (Interest rate is 5%)e) You save $20; 000 per year when working (21 and 60). How much will you consume per year when youretire (age 61–80) (Interest rate is 5%)1Problem 5 (Life cycle problems, use Excel program)a) You are going to e arn mt= $200; 000 when working (age 21 and 60), and then you are going to livefor the next 20 years with mt= $0. Fin d the constant level of consumption C during years (21-80) that canbe …nance d from you r income. (Interest rate is 5%). Fi nd the level of savings St= mtC f or peri ods t < 60and for t > 60b) Consider the pro blem as in a). Assume that apart from your regular income, at the age of 20 youinherit $1000; 000 (one mil lion $). Find C and St?c) Consider the problem as in b). Assume that you also leave a your o¤spring a bequest of $1000; 000(one millio n $). Find C and Std) Optional: Accumulated wealth in period t i s given by Wt= Wt1(1 + r) + stthat is it coincides withwealth from the previous pe riod plus interest and savings in t:.The initial we alth of agent W20= 0: UsingExcel sheet, plot the behavior of wealth Wtover you life time for points a-c. When the wealth of our agentattains ma ximum? What can you say about the level of wealth at the end of life W80?2Questionnaire Econ 301This is an anonymous questionnaire. Answer the questions but do not sign it. Thequestionnaire will be collected on TuesdayWhich year are you in and what is your major?I. Problem sets:1. How much time (on average) do you spend solving PS?2. Are PS: supereasy, easy, OK, di¢ cult, very di¢ cult.3. Are PS helpful in understanding the material?4. How di¢ cult is math needed to solve problems? supereasy, easy, OK, di¢ cult, very di¢ cult.II. Class1. Do you …nd solving problem in class useful?2. Do you prefer more intuitive or formal exposition of the material?3. How about the pace of the course: too slow, slow, OK, fast, to o fast.4. What fraction of the theory presented in the class can you follow 20%, 40%, 60%, 80%, 100%5. How would you improve the course?III. M idterm1. Do you think the midterm was fair ?2. The level of di¢ culty: Was it supereasy, easy, OK, di¢ cult, very di¢ cult?3. The contents: where you surprised by any of the questions?4. Length: what the midterm very short, short, OK, long , too long?IV. TA sections1. Do you …nd them helpful in understanding the material?2. Do you …nd them helpful in solving your