Derive Lucy’s inverse demand for current and future consumption, C0 * = fH… L and C1 * = fH… L in an exchange-only Fisher-type economy. Plot both demand functions on the same graph with the interest rate on the horizontal axis and consumption on the vertical. Give a two- or three-sentence interpretation
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Assignment 2 INTERTEMPORAL CHOICE FINA 385 • Winter 2012 Professor Gregory Lypny Monday, January 30, 2012 10:25:39 About this assignment The assignments are your opportunity to explore the topics that we discuss in class. For this one, you will derive Lucy’s consumption optimum in a riskless, two-period Fisher-type economy. Lucy’s utility function is uHC0, C1L = C0a C1g where 0 <><><><>
Assignment 2.cdf Assignment 2 INTERTEMPORAL CHOICE FINA 385 • Winter 2012 Professor Gregory Lypny Monday, January 30, 2012 10:25:39 About this assignment The assignments are your opportunity to explore the topics that we discuss in class. For this one, you will derive Lucy’s consumption optimum in a riskless, two-period Fisher-type economy. Lucy’s utility function is uHC0, C1L = C0 Α C1 Γ where 0 < α="">< 1="" and="" 0="">< γ="">< 1. her investment opportunities are described by c1 = a lnhb - c0l + c choose your student id in the pull-down menu to find the values of the various parameters that you will need to do your work. student id choose your parameters... exercise 1 15 marks. derive lucy’s inverse demand for current and future consumption, c0 * = f h… l and c1 * = f h… l in an exchange-only fisher-type economy. plot both demand functions on the same graph with the interest rate on the horizontal axis and consumption on the vertical. give a two- or three-sentence interpretation. exercise 2 printed by mathematica for students exercise 2 10 marks. plot and interpret the relationship between lucy’s optimal consumption and her preference parameter, α. (in other words, let α vary.) exercise 3 60 marks. work out the equilibrium for a production-and-exchange economy. a. calculations 30 marks. fill in the table. some of the numbers may appear in more than one place in the table. endowment optimum wealth utility mrs marginal roi hmrtl optimal investment hi*l - npvhi*l - production hp 0 *, p 1 *l - consumption hc 0 *, c 1 *l - amount @lentborrowedd - b. explanation 15 marks. explain lucy’s situation and the results intuitively, using as little jargon as possible. pretend that you are writing a one-paragraph piece for the economist. see if you can do it in under 15 sentences. c. graph 10 marks. illustrate your results in a well-labelled and absolutely gorgeous graph. d. issuing shares 5 marks. suppose that lucy decides to issue shares to raise the investment money she needs. assume that there are currently 1,000 shares outstanding, and that lucy owns them all. the company has no debt. how many shares will she have to issue? explain briefly how you arrived at your answer. exercise 4 15 marks. read loewstein, g., and d. prelec, 1992, “anomalies in intertemporal choice: evidence and interpretation,” the quarterly journal of economics, 107(2): 573-597. choose one of the observations relating inferred discount rates to gain or loss, briefly describe it by providing an example of your own, and explain why it is an economic anomaly. 2 assignment 2.cdf printed by mathematica for students 1.="" her="" investment="" opportunities="" are="" described="" by="" c1="a" lnhb="" -="" c0l="" +="" c="" choose="" your="" student="" id="" in="" the="" pull-down="" menu="" to="" find="" the="" values="" of="" the="" various="" parameters="" that="" you="" will="" need="" to="" do="" your="" work.="" student="" id="" choose="" your="" parameters...="" exercise="" 1="" 15="" marks.="" derive="" lucy’s="" inverse="" demand="" for="" current="" and="" future="" consumption,="" c0="" *="f" h…="" l="" and="" c1="" *="f" h…="" l="" in="" an="" exchange-only="" fisher-type="" economy.="" plot="" both="" demand="" functions="" on="" the="" same="" graph="" with="" the="" interest="" rate="" on="" the="" horizontal="" axis="" and="" consumption="" on="" the="" vertical.="" give="" a="" two-="" or="" three-sentence="" interpretation.="" exercise="" 2="" printed="" by="" mathematica="" for="" students="" exercise="" 2="" 10="" marks.="" plot="" and="" interpret="" the="" relationship="" between="" lucy’s="" optimal="" consumption="" and="" her="" preference="" parameter,="" α.="" (in="" other="" words,="" let="" α="" vary.)="" exercise="" 3="" 60="" marks.="" work="" out="" the="" equilibrium="" for="" a="" production-and-exchange="" economy.="" ="" a.="" calculations="" 30="" marks.="" fill="" in="" the="" table.="" some="" of="" the="" numbers="" may="" appear="" in="" more="" than="" one="" place="" in="" the="" table.="" endowment="" optimum="" wealth="" utility="" mrs="" marginal="" roi="" hmrtl="" optimal="" investment="" hi*l="" -="" npvhi*l="" -="" production="" hp="" 0="" *,="" p="" 1="" *l="" -="" consumption="" hc="" 0="" *,="" c="" 1="" *l="" -="" amount="" @lentborrowedd="" -="" ="" b.="" explanation="" 15="" marks.="" explain="" lucy’s="" situation="" and="" the="" results="" intuitively,="" using="" as="" little="" jargon="" as="" possible.="" pretend="" that="" you="" are="" writing="" a="" one-paragraph="" piece="" for="" the="" economist.="" see="" if="" you="" can="" do="" it="" in="" under="" 15="" sentences.="" ="" c.="" graph="" 10="" marks.="" illustrate="" your="" results="" in="" a="" well-labelled="" and="" absolutely="" gorgeous="" graph.="" ="" d.="" issuing="" shares="" 5="" marks.="" suppose="" that="" lucy="" decides="" to="" issue="" shares="" to="" raise="" the="" investment="" money="" she="" needs.="" assume="" that="" there="" are="" currently="" 1,000="" shares="" outstanding,="" and="" that="" lucy="" owns="" them="" all.="" the="" company="" has="" no="" debt.="" how="" many="" shares="" will="" she="" have="" to="" issue?="" explain="" briefly="" how="" you="" arrived="" at="" your="" answer.="" exercise="" 4="" 15="" marks.="" read="" loewstein,="" g.,="" and="" d.="" prelec,="" 1992,="" “anomalies="" in="" intertemporal="" choice:="" evidence="" and="" interpretation,”="" the="" quarterly="" journal="" of="" economics,="" 107(2):="" 573-597.="" choose="" one="" of="" the="" observations="" relating="" inferred="" discount="" rates="" to="" gain="" or="" loss,="" briefly="" describe="" it="" by="" providing="" an="" example="" of="" your="" own,="" and="" explain="" why="" it="" is="" an="" economic="" anomaly.="" 2="" assignment="" 2.cdf="" printed="" by="" mathematica="" for="">