This assignment comprises 10% of the assessment for ETF2700/ETF5970. You must submit a “hard copy” of your written work (with an Assignment Cover Sheet from the “ASSIGNMENTS” sectionofMoodle)by6pmonMonday17September2018.Submitittoyourtutorinyourtutorial (or to your tutor’s mailbox, 5th floor HBlock).ENSURE that you•Submit a printed “hard copy” of your assignment to your tutor. Your assignment must be typed.•Name your assignment: Surname-Initials A2.docx, e.g., Einstein-AA2.docx.•Upload this file to Moodle asfollows:Go to the “ASSIGNMENTS” section. Click on the “Submit your Assignment 2 here Due on 17 Sep” link to upload. The following message will appear momentarily, “File uploaded successfully.”[To later confirm your upload was successful, go to the “ASSIGNMENTS” section and click on the Assignment 2 uploading link. The uploaded files name will be shown.]NB, DO NOT submit any Excel files. You may upload only ONE file.•Submit both hard copy and electronic copy before the due, otherwise your submission will NOT beaccepted.•Retain your marked assignment until after the publication of final results for thisunit.Further Information•A maximum penalty of 10% of the total mark allocated to this assessment will be deducted for each day that it is late, up to 4 days. An assignment may not be submitted if it is late by more than 4days.•Extensionsbeyondtheduedatewillonlybeallowedinspecialcircumstances.Youmayvisithttps://www.monash.edu/exams/changes/special-considerationfor the university policy and application procedure for special consideration.•Do not submit your assignment in a folder: stapled pages are easier for themarker.•Save trees! Double-sided printing isencouraged.•If you don’t understand what the questions areasking,–studytheunit’scontentpriortoattemptingthetutorialandassignmentquestions.This should enhance your ability to understand thequestions.–ask a staff member to clarify the questions for you. A staff consultation roster is on Moodle.Avoid Plagiarism!Intentional plagiarism amounts to cheating. See the Monash Policy.Plagiarism: Plagiarism means to take and use another person’s ideas and or manner of ex- pressing them and to pass these off as one’s own by failing to give appropriate acknowledgement. Thisincludesmaterialfromanysource,staff,studentsortheinternet-publishedandunpublished works.Collusion: Collusion is unauthorised collaboration with another person or persons. Where there are reasonable grounds for believing that intentional plagiarism or collusion has occurred, this will be reported to the Chief Examiner, who may disallow the work concerned byprohibiting assessment or refer the matter to the FacultyManager.QuestionsImportant: There are six questions. Please attempt all the questions, show all the stepsofyourcalculations,andprovideexplanationstojustifyyouranswers.Toobtain full marks, it is important to provide complete answers supported by logically sound explanations, unless the question explicitly states that no explanation is needed. Itis not sufficient to simply provide calculatorinstructions.Total marks: 100[This assignment is worth 10% towards the final mark of this unit].Question 1 (20 marks)An ice-cream lover has a total of $10 to spend one evening. The price of ice-cream is $p per litre. Theperson’spreferencesforbuyingq litresofice-cream,leavinganonnegativeamount$(10−pq) to spend on other items, are represented by the utilityfunction:(a)Findthefirst-orderconditionforautilitymaximizingquantityofice-cream.[Hint:thesquare root function is a power function with exponent1.](b)Solve the first-order condition derived in (a) in order to express the utility maximizing quan- tity q∗as a function of p.(c)What guarantees that your quantity q∗is really amaximum?(d)Express the elasticity of demand for ice-cream as a function of the price $p per litre. When the price is $2.50 per litre, calculate the price elasticity of the person’s demand forice-cream.Question 2 (20 marks)Suppose that a representative Norwegian family’s demand for milk depends on the price p 0and the family’s income r 0 according to the function:where A, a and b are positive constants.(a)Find a constant k (in terms of the constants a and b) suchthat(b)Based on data for the period 1925–1935, it is estimated that Norwegian milk demand could be represented by equation (1) with a = 1.5 and b = 2.08. Calculate the value of kin this case.(c)Forthevaluesofaandbinpart(b),supposemoreoverthatp=p(t)=p0(1.06)tandr=r(t)= r0(1.08)tin(1)arebothfunctionsoftimetwherep0isthepriceandr0istheincomeattime t = 0. Hence, E(p(t), r(t)) = E(t) is also a function of time t. Calculate the proportional rate of growth, that is, the derivative of function ln(E(t)).Question 3 (20 marks)The profit obtained by a firm from producing and selling x and y units of two brands of a com- modity is given byP (x, y) = −0.1x2− 0.2xy − 0.2y2+ 47x + 48y − 600.(a)AssumeP(x,y)hasamaximumpoint.Find,stepbystep,theproductionlevelsthatmaximize profitbysolvingthefirst-orderconditions.Ifyouneedtosolveanysystemoflinearequations, use Cramer’s rule and provide all calculationdetails.(b)Due to technology constraints, the total production must be restricted to be 200 units. Find, stepbystep,theproductionlevelsthatnowmaximizeprofits–usingtheLagrangeMethod.If youneedtosolveanysystemoflinearequations,useCramer’sruleandprovideallcalculation details. You may assume that the optimal point exists in thiscase.(c)Report the Lagrange multiplier value at the maximum point and the maximal profit value from question (b). No explanation isneeded.(d)Using new technology, the total production can now be up to 250 units. Use the values from question (c) to approximate the new maximalprofit.(e)Compare the true new maximal profit for question (d) with its approximate value you ob- tained.Bywhatpercentageisthetruemaximalprofitlargerthantheapproximatevaluefrom question(c)?Question 4 (10 marks)The following table contains the return on equity (in percentage) of four firms and the salary (in thousand of dollars) of their CEOs.

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