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Optical Networks - _References_20

Course: ECE 6543, Spring 2010
School: Georgia Tech
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to 40 Introduction Optical Networks of the early undersea optical ber transmission systems. See also [KM98] for a more recent overview. Experiments reporting more than 1 Tb/s transmission over a single ber were rst reported at the Optical Fiber Communication Conference in 1996, and the numbers are being improved upon constantly. See, for example, [CT98, Ona96, Gna96, Mor96, Yan96]. Related work has focused on...

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to 40 Introduction Optical Networks of the early undersea optical ber transmission systems. See also [KM98] for a more recent overview. Experiments reporting more than 1 Tb/s transmission over a single ber were rst reported at the Optical Fiber Communication Conference in 1996, and the numbers are being improved upon constantly. See, for example, [CT98, Ona96, Gna96, Mor96, Yan96]. Related work has focused on (1) transmitting terabits-persecond aggregate trafc across transoceanic distances with individual channel data rates at 10 or 20 Gb/s [Cai01, Bak01, VPM01], or 40 Gb/s channel rates over shorter distances [Zhu01], or (2) obtaining over 10 Tb/s transmission capacity using 40 Gb/s channel rates over a few hundred kilometers [Fuk01, Big01]. The rate of network trafc growth has been reported by a number of sources over the years. A Web site that has estimates as well as references to other sources is the Minnesota Internet Trafc Studies (MINTS), which can be found at www.dtc.umn.edu/mints/. Finally, we did not cover standards in this chapter but we will do so in Chapters 6, 8, and 9. The various standards bodies working on optical networking include the International Telecommunications Union (ITU), the American National Standards Institute (ANSI), the Optical Internetworking Forum (OIF), Internet Engineering Task Force (IETF), the Institute of Electrical and Electronic Engineers (IEEE) and Telcordia Technologies. Appendix C provides a list of relevant standards documents. References [ACHG+ 08] R. Alferness, C. Chang-Hasnain, C. Giallorenzi, D. Keck, and A. Willner, editors. IEEE/OSA Journal of Lightwave Technology: Special Issue on Celebrating 25 Years of the IEEE/OSA, volume 26, May 2008. [Agr95] G. P. Agrawal. Nonlinear Fiber Optics, 2nd edition. Academic Press, San Diego, CA, 1995. [Agr97] G. P. Agrawal. Fiber-Optic Communication Systems. John Wiley, New York, 1997. [AKW00] R. C. Alferness, H. Kogelnik, and T. H. Wood. The evolution of optical systems: Optics everywhere. Bell Labs Technical Journal, 5(1):188202, Jan.Mar. 2000. [Alf99] R. Alferness, editor. Bell Labs Technical Journal: Optical Networking, volume 4, Jan.Mar. 1999. [Bak01] B. Bakhshi et al. 1 Tb/s (101 10 Gb/s) transmission over transpacic distance using 28 nm C-band EDFAs. In OFC 2001 Technical Digest, pages PD21/13, 2001. [Bar96] R. A. Barry, editor. IEEE Network: Special Issue on Optical Networks, volume 10, Nov. 1996. References 41 [Big01] S. Bigo et al. 10.2 Tb/s (256 42.7 Gbit/s PDM/WDM) transmission over 100 km TeraLight ber with 1.28bit/s/Hz spectral efciency. In OFC 2001 Technical Digest, pages PD25/13, 2001. [BKLW00] W. F. Brinkman, T. L. Koch, D. V. Lang, and D. W. Wilt. The lasers behind the communications revolution. Bell Labs Technical Journal, 5(1):150167, Jan.Mar. 2000. [Bra89] C. A. Brackett, editor. IEEE Communications Magazine: Special Issue on Lightwave Systems and Components, volume 27, Oct. 1989. [Cai01] J.-X. Cai et al. 2.4 Tb/s (120 20 Gb/s) transmission over transoceanic distance with optimum FEC overhead and 48% spectral efciency. In OFC 2001 Technical Digest, pages PD20/13, 2001. [CHK+ 96] R. L. Cruz, G. R. Hill, A. L. Kellner, R. Ramaswami, and G. H. Sasaki, editors. IEEE JSAC/JLT Special Issue on Optical Networks, volume 14, June 1996. [CNW90] N. K. Cheung, G. Nosu, and G. Winzer, editors. IEEE JSAC: Special Issue on Dense WDM Networks, volume 8, Aug. 1990. [CS83] J. S. Cook and O. I. Szentisi. North American eld trials and early applications in telephony. IEEE JSAC, 1:393397, 1983. [CSH00] G. K. Chang, K. I. Sato, and D. K. Hunter, editors. IEEE/OSA Journal of Lightwave Technology: Special Issue on Optical Networks, volume 18, 2000. [CT98] A. R. Chraplyvy and R. W. Tkach. Terabit/second transmission experiments. IEEE Journal of Quantum Electronics, 34(11):21032108, 1998. [DL00] S. S. Dixit and P. J. Lin, editors. IEEE Communications Magazine: Optical Networks Come of Age, volume 38, Feb. 2000. [DYJ00] S. S. Dixit and A. Yla-Jaaski, editors. IEEE Communications Magazine: WDM Optical Networks: A Reality Check, volume 38, Mar. 2000. [FGO+ 96] M. Fujiwara, M. S. Goodman, M. J. OMahony, O. K. Tonguez, and A. E. Willner, editors. IEEE/OSA JLT/JSAC Special Issue on Multiwavelength Optical Technology and Networks, volume 14, June 1996. [Fuk01] K. Fukuchi et al. 10.92 Tb/s (273 40 Gb/s) triple-band/ultra-dense WDM optical-repeatered transmission experiment. In OFC 2001 Technical Digest, pages PD24/13, 2001. [GJR96] P. E. Green, F. J. Janniello, and R. Ramaswami. Multichannel protocol-transparent WDM distance extension using remodulation. JSAC/JLT IEEE Special Issue on Optical Networks, 14(6):962967, June 1996. [Gla00] A. M. Glass et al. Advances in ber optics. Bell Labs Technical Journal, 5(1):168187, Jan.Mar. 2000. 42 Introduction to Optical Networks [GLM+ 00] O. Gerstel, B. Li, A. McGuire, G. Rouskas, K. Sivalingam, and Z. Zhang, editors. IEEE JSAC: Special Issue on Protocols and Architectures for Next-Generation Optical Networks, Oct. 2000. [Gna96] A. H. Gnauck et al. One terabit/s transmission experiment. In OFC96 Technical Digest, 1996. Postdeadline paper PD20. [Gre93] P. E. Green. Fiber-Optic Networks. Prentice Hall, Englewood Cliffs, NJ, 1993. [HD97] G. R. Hill and P. Demeester, editors. IEEE Communications Magazine: Special Issue on Photonic Networks in Europe, volume 35, Apr. 1997. [Hec98] J. Hecht. Understanding Fiber Optics. Prentice Hall, Englewood Cliffs, NJ, 1998. [Hec99] J. Hecht. City of Light: The Story of Fiber Optics. Oxford University Press, New York, 1999. [HSS98] A. M. Hill, A. A. M. Saleh, and K. Sato, editors. IEEE JSAC: Special Issue on High-Capacity Optical Transport Networks, volume 16, Sept. 1998. [Ish83] H. Ishio. Japanese eld trials and applications in telephony. IEEE JSAC, 1:404412, 1983. [KH66] K. C. Kao and G. A. Hockham. Dielectric-ber surface waveguides for optical frequencies. Proceedings of IEE, 133(3):11511158, July 1966. [KK97a] I. P. Kaminow and T. L. Koch, editors. Optical Fiber Telecommunications IIIA. Academic Press, San Diego, CA, 1997. [KK97b] I. P. Kaminow and T. L. Koch, editors. Optical Fiber Telecommunications IIIB. Academic Press, San Diego, CA, 1997. [KKM70] F. P. Kapron, D. B. Keck, and R. D. Maurer. Radiation losses in glass optical waveguides. Applied Physics Letters, 17(10):423425, Nov. 1970. [KLHN93] M. J. Karol, C. Lin, G. Hill, and K. Nosu, editors. IEEE/OSA Journal of Lightwave Technology: Special Issue on Broadband Optical Networks, May/June 1993. [KLW06] I. Kaminow, T. Li, and A. E. Willner, editors. IEEE/OSA Journal of Lightwave Technology: Special 40th Anniversary Issue on Optoelectronics, volume 24, Dec. 2006. [KM98] F. W. Kerfoot and W. C. Marra. Undersea ber optic networks: Past, present and future. IEEE JSAC: Special Issue on High-Capacity Optical Transport Networks, 16(7):12201225, Sept. 1998. [Lin89] C. Lin, editor. Optoelectronic Technology and Lightwave Communications Systems. Van Nostrand Reinhold, New York, 1989. [Mac74] J. B. MacChesney et al. Preparation of low-loss optical bers using simultaneous vapor deposition and fusion. In Proceedings of 10th International Congress on Glass, volume 6, pages 4044, Kyoto, Japan, 1974. References 43 [MK88] S. D. Miller and I. P. Kaminow, editors. Optical Fiber Telecommunications II. Academic Press, San Diego, CA, 1988. [Mor96] T. Morioka et al. 100 Gb/s 10 channel OTDM/WDM transmission using a single supercontinuum WDM source. In OFC96 Technical Digest, 1996. Postdeadline paper PD21. [MT83] A. Moncalvo and F. Tosco. European eld trials and early applications in telephony. IEEE JSAC, 1:398403, 1983. [NO94] K. Nosu and M. J. OMahony, editors. IEEE Communications Magazine: Special Issue on Optically Multiplexed Networks, volume 32, Dec. 1994. [Ona96] H. Onaka et al. 1.1 Tb/s WDM transmission over a 150 km 1.3 m zero-dispersion single-mode ber. In OFC96 Technical Digest, 1996. Postdeadline paper PD19. [Pru89] P. R. Prucnal, editor. IEEE Network: Special Issue on Optical Multiaccess Networks, volume 3, Mar. 1989. [RT84] P. K. Runge and P. R. Trischitta. The SL undersea lightwave system. IEEE/OSA Journal on Lightwave Technology, 2:744753, 1984. [ST91] B. E. A. Saleh and M. C. Teich. Fundamentals of Photonics. John Wiley, New York, 1991. [Sta83] J. R. Stauffer. FT3Ca lightwave system for metropolitan and intercity applications. IEEE JSAC, 1:413419, 1983. [VPM01] G. Vareille, F. Pitel, and J. F. Marcerou. 3 Tb/s (300 11.6 Gbit/s) transmission over 7380 km using 28 nm C+L-band with 25 GHz channel spacing and NRZ format. In OFC 2001 Technical Digest, pages PD22/13, 2001. [Wil00] A. E. Willner, editor. IEEE Journal of Selected Topics in Quantum Electronics: Millennium Issue, volume 6, Nov.Dec. 2000. [Yan96] Y. Yano et al. 2.6 Tb/s WDM transmission experiment using optical duobinary coding. In Proceedings of European Conference on Optical Communication, 1996. Postdeadline paper Th.B.3.1. [Zhu01] B. Zhu et al. 3.08 Tb/s (77 42.7 Gb/s) transmission over 1200 km of non-zero dispersion-shifted ber with 100-km spans using C- L-band distributed Raman amplication. In OFC 2001 Technical Digest, pages PD23/13, 2001. This page intentionally left blank
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Georgia Tech - ECE - 6543
110Propagation of Signals in Optical Fiber(b) For what value of z is the width of the pulse equal to that of an unchirped pulse, for the same value of z? (Assume the chirped and unchirped pulses have the same initial pulse width.) 2.12 2.13 Show that in
Georgia Tech - ECE - 6543
References237show that the resulting ltering function is periodic, with a period given by the least common multiple of f1 and f2 . For example, if periods of the two lters are 500 GHz and 600 GHz, then the cascaded structure will be periodic with a peri
Georgia Tech - ECE - 6543
References2854.17If the BER of an uncoded system is p, show that the same system has a BER of 3p2 + p3 when the repetition code (each bit is repeated three times) is used. Note that the receiver makes its decision on the value of the transmitted bit by
Georgia Tech - ECE - 6543
362Transmission System EngineeringReferences[Agr95] G. P. Agrawal. Nonlinear Fiber Optics, 2nd edition. Academic Press, San Diego, CA, 1995. [BA94] F. Bruy` re and O. Audouin. Assessment of system penalties induced by polarization e mode dispersion in
Georgia Tech - ECE - 6543
430Client Layers of the Optical LayerTable 6.6 Specications for STM-16 intraofce and shorthaul interfaces (from ITU G.957).Parameter Transmitter Wavelength range Transmit power (max) Transmit power (min) Receive sensitivity (min) Receive overload (min)
Georgia Tech - ECE - 6543
466WDM Network Elements(b) Next suppose that 25% of the lightpaths passing through need to be converted from one wavelength to another. This is done by sending the lightpath to one of a pool of regenerators/wavelength converters attached to the OXC. Eac
Georgia Tech - ECE - 6543
508Control and ManagementABCDEFGOLTAmplifierFigure 8.14 Example for Problem 8.3.Draw a time line indicating the behavior of each node in the network after the failure, including the transmission of OCh-FDI and OMS-FDI signals. (b) Now assume t
Georgia Tech - ECE - 6543
References5699.10Consider a four-ber BLSR that uses both span and ring switching. What are the functions required in network management to (a) coordinate span and ring switching mechanisms and (b) allow multiple failures to be restored? Consider the ex
Georgia Tech - ECE - 6543
References623B A CEDFigure 10.22 Network topology for Problem 10.26.Gb/s A B C DB 15C 25 5D 5 35 15E 15 15 25 5(a) Assuming OC-192c (10 Gb/s) trunks are used, complete an equivalent table for the required number of lightpaths (that is, waveleng
Georgia Tech - ECE - 6543
References651transmitted out of each port on the wavelength router. Assume that in addition to the standard loss, we get only 1/2N of the transmitted power in each channel, where N is the number of ONUs. 11.2 Consider the RITENET architecture shown in F
Georgia Tech - ECE - 6543
References699to the header and payload. Again, if we want to maintain the payload at 90% of the overall packet, and the header at 10 bytes at 1 Gb/s, what size does the payload need to be?References[Ams83] S. Amstutz. Burst switchingan introduction. I
Georgia Tech - ECE - 6543
744Deployment Considerationswhere the crossconnect uses short-reach interfaces connected to transponders in the OLTs and to short-reach interfaces in the routers; (2) an opaque photonic crossconnect solution, where the photonic crossconnect (PXC) is con
Georgia Tech - ECE - 6543
788Multilayer Thin-Film FiltersThe three-cavity lter is described by the sequence G(H L)5 H LL(H L)11H LL(H L)11 H LL(H L)5 H G. Again, the values nG = 1.52, nL = 1.46, and nH = 2.3 were used.References[Kni76] Z. Knittl. Optics of Thin Films. John Wil
Georgia Tech - ECE - 6543
800Receiver Noise StatisticsNote that the photocurrent is passed through a low-pass lter with bandwidth Be . The noise power at the output of the lter is given by 2 = where2 shot = 2e [GPi + Pn (G 1)Bo ]Be , 2 sig-spont = 4 Be Be 2 2 2 SI (f )df = shot
Georgia Tech - ECE - 6543
38Introduction to Optical Networksthan in the electrical layer. At the same time, the optical layer is evolving to provide additional functionality, including the ability to set up and take down lightpaths across the network in a dynamic fashion, and th
Georgia Tech - ECE - 6543
106Propagation of Signals in Optical Fiberlong times) to relieve strain and hence does not suffer the chemical surface changes that afict strained glass. Plastic optical ber has been in the home for decades. For example, the Sony/Philips Digital Interco
Georgia Tech - ECE - 6543
Summary2292fp - fs fs fp 2fs - fp fs fp 2fp - fs 2fp - fs FilterSOAFigure 3.79 Wavelength conversion by four-wave mixing in a semiconductor opticalamplier.efciency goes down signicantly as the wavelength separation between the signal and probe is in
Georgia Tech - ECE - 6543
278Modulation and Demodulation4.5.2InterleavingFrequently, when errors occur, they occur in bursts; that is, a large number of successive bits are in error. The Reed-Solomon codes we studied in the previous section are capable of correcting bursts of
Georgia Tech - ECE - 6543
Summary353ITU allows such systems to have some wavelengths that are on a 25 GHz grid; see ITU G.692 for details. That being said, a much more difcult decision is to pick a standard set of wavelengths for use in 4-, 8-, 16-, and 32-wavelength systems to
Georgia Tech - ECE - 6543
Summary427Table 6.5 Fibre Channel storage-area network.Name 1GFC 2GFC 4GFC 8GFC 10GFC Data Rate (MBytes/s) 100 200 400 800 1000 Transmission Rate (Gb/s) 1.063 2.125 4.252 8.504 10.519lasers at 850 nm are used with multimode bers with a reach of up to
Georgia Tech - ECE - 6543
Summary461Based on the discussion above, it would appear that the wavelength plane approach offers a cheaper alternative to large-scale nonblocking optical switches. However, we did not consider how to optimize the number of add/drop terminations (which
Georgia Tech - ECE - 6543
Summary505Since the Class I safety standard also species that emission limits must be maintained during single-fault conditions, the open ber control circuitry at each node is duplicated for redundancy.SummaryNetwork management is essential to operate
Georgia Tech - ECE - 6543
Summary565If any of the conditions above are not met, then the protection scheme may not converge. For example, if the client layer protection is nonrevertive, it may switch over once to the protection path, discover that path is not available, and not
Georgia Tech - ECE - 6543
618WDM Network DesignSummaryWe studied the design of wavelength-routing networks in this chapter. We saw that there is a clear benet to building wavelength-routing networks, as opposed to simple point-to-point WDM links. The main benet is that trafc th
Georgia Tech - ECE - 6543
Summary649broadcast network with dedicated bandwidth and eventually to a switched network with dedicated bandwidth.SummaryService providers, both telephone operators and cable companies, are actively looking to deploy broadband access networks to prov
Georgia Tech - ECE - 6543
696Photonic Packet SwitchingSummaryPhotonic packet-switched networks offer the potential of realizing packet-switched networks with much higher capacities than may be possible with electronic packet-switched networks. However, signicant advances in tec
Georgia Tech - ECE - 6543
Summary739(O/E) conversions, particularly at the higher bit rates, it makes sense to minimize the number of these converters in the network. The rst step in this direction was the development of ultra-long-haul systems, which provided longer reach betwe
Georgia Tech - ECE - 6543
The horizons of optical networks are much more than high speed physical layer transport. An intelligent optical network design must include higher network layer considerations. This is the only book currently on the market that addresses optical networks
Georgia Tech - ECE - 6543
1.2Services, Circuit Switching, and Packet Switching5Central officeHomeBusinessLong haul Interexchange networkMetropolitan Interoffice networkMetropolitan Access networkFigure 1.1 Different parts of a public network.The network shown in Figure 1
Georgia Tech - ECE - 6543
10Introduction to Optical Networks1.3Optical NetworksOptical networks offer the promise to solve many of the problems we have discussed. In addition to providing enormous capacities in the network, an optical network provides a common infrastructure o
Georgia Tech - ECE - 8833
MATLABThe Language of Technical ComputingComputation Visualization ProgrammingGetting Started with MATLABVersion 5How to Contact The MathWorks:508-647-7000 508-647-7001 The MathWorks, Inc. 24 Prime Park Way Natick, MA 01760-1500http:/www.mathworks.
Princeton - ECO - 310
ECO 310, Fall 2008 Problem Set 2: Consumer Theory Due in class on October 7Question 1You have just emerged from medical school with a debt service burden of $25,000 per year, and have set up practice. You have to decide how hard to work. For each hour o
Princeton - ECO - 310
ECO 310, Fall 2008 Problem Set 5: Equilibrium Analysis Due in class on November 18 Question 1In this problem we will consider the sh industry on the island of San Serife. For this purpose we will aggregate all the other goods into one composite, and meas
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ECO 310, Fall 2008 Problem Set 6: General Equilibrium, Monopoly Due in class on November 25 Question 1Consider a small country with two rms. Firm 1 produces x = min(kx , lx ) units of good x; rm 2 produces y = ky ly units of good y . This country has 24
Princeton - ECO - 310
ECO 310, Fall 2008 Problem Set 7: Oligopoly Due in class on December 2 Question 1Consider a Cournot duopoly with homogeneous products. The inverse demand function is given by P = (q1 + q2 )3/2 . Each rms marginal cost is constant and equal to c > 0. (a)
Princeton - ECO - 310
ECO 310, Fall 2008 Problem Set 8: Uncertainty Due in class on December 9 Question 1Satoru is an expected utility maximizer with von Neumann-Morgenstern index U (W ). He is oered the following gamble: gain $h with probability 1/2+ , and lose $h with proba
Princeton - ECO - 310
Econ 310 Problem Set 1Lucas Manuelli (rst question being slightly altered) October 13, 2008Question 1 (b) For x > 0 we have f 0 (x) = 80 20x so f 0 (4) = 0: In addition for x > 0 we have f 00 (x) = 20 so the function is concave for positive x so that x
Princeton - ECO - 310
Econ 310 Problem Set 2Lucas Manuelli October 5, 2008Exercise 1 (a) I = 50H (b) We simply need to maximize U (I; H ) = U (50H = ln(50H 25000; H ) 25000) + 2 ln(5000 H) 25000taking the derivative and setting equal to zero we see that U0 = 50 50H 25000 2
Princeton - ECO - 310
Economics 310 Microeconomic Theory: A Mathematical Approach Fall 2008 Solution to Problem Set 3 Question 1:For each of the following utility functions over two goods, nd the Marshallian demand, the Hicksian demand and expenditure function The Marshallian
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ECO 310 - Fall 2007 Microeconomic Theory - A Mathematical Approach Problem Set 4 - Answer KeyQuestion 1:(a) By Shepherds Lema E/px = X C so X C =M1 py/2 U2px1/2and Y C =1 px/2 U2py1/2.By Roys Identity X = X = (V /px )/(V /I ). Inverting the ex
Princeton - ECO - 310
ECO 310 Fall 2007 Microeconomic Theory A Mathematical Approach Problem Set 5 Answer KeyQuestion 1:(a) Each consumer maximizes U (x; y ) = y + 10 x subject to the budget constraint px + y = M : Substituting out y , the objective is F (x) Now F 0 (x) = 10
Princeton - ECO - 310
Economics 310 Microeconomic Theory: A Mathematical Approach Fall 2008 Solutions to Problem Set 6Question 1(a) The production possibility frontier shows the ecient combination of goods x and y with this countrys endowment of labor and capital. By drawing
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ECO 310 - Fall 2008 Microeconomic Theory - A Mathematical Approach Problem Set 7 - Answer KeyQuestion 1:(a) There were two hard parts to this question: nasty algebra, and the intuition. Firm 1 prot is s1= (pc) q1 = f [q1 + q2 ]3 =2c g q1 :So its C
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ECO 310 - Fall 2008 Microeconomic Theory - A Mathematical Approach Problem Set 8 - Answer KeyQuestion 1:1 1 U (W0 ) = ( + )U (W0 + h) + ( )U (W0 h) 2 2 1 1 1 1 U (W0 ) ( + )(U (W0 ) + hU (W0 ) + h2 U (W0 ) + ( )(U (W0 ) hU (W0 ) + h2 U (W0 ) 2 2 2 2 h 2
Princeton - ECO - 310
Examination Cover SheetPrinceton University Undergraduate Honor Committee May 2008Course Number: ECONOMICS 310 Course Name: Microeconomic Theory cfw_ A Mathematical Approach Professor: Stephen Morris Date: May 19 Time: 1:30pm This examination is adminis
Princeton - ECO - 310
ECO 310 Microeconomic Theory: A Mathematical Approach Spring 2008 Solutions to the Final ExaminationSection BQuestion 4(i.a) The cost of producing Q units is minimized by setting 10K = L = Q so LRT C (Q) = r(Q/10)+ wQ, LRAC (Q) = LRT C (Q)/Q = r/10+ w
Princeton - ECO - 310
ECO 310 - Fall 2008 Microeconomic Theory - A Mathematical Approach Final Exam 01/14/09 - Answer Key0.1Question 1: P 1, eI/P I + P (ln(1/P ) 1); : P 1, eI/P I + P (ln(1/P ) 1); : P 1, : P 1, eI/P I + P (ln(1/P ) 1); : P 1, eI/P I + P (ln(1/P ) 1); : P 1
Princeton - ECO - 310
1Question 5Suppose Dd and Rd are asset positions for Daisy of democratic and republican assets, while Dr and Rr are those of Robert. Then, a) U d = 0.6 ln Dd + 0.4 ln Rd and U r = 0.2 ln Dr + 0.8 ln Rr 5 points were assigned for a completely correct ans
Princeton - ECO - 310
Examination Cover SheetPrinceton University Undergraduate Honor CommitteeCourse Number: ECO 310 Course Name: Microeconomic Theory: A Mathematical Approach Professor: Satoru Takahashi Date: January 22, 2008 Time: 1:30pmThis examination is administered u
Princeton - ECO - 310
Examination Cover SheetPrinceton University Undergraduate Honor CommitteeCourse Number: ECO 310 Course Name: Microeconomic Theory: A Mathematical Approach Professor: Satoru Takahashi Date: January 22, 2008 Time: 1:30pm This examination is administered
Princeton - ECO - 310
Examination Cover SheetPrinceton University Undergraduate Honor CommitteeCourse Number: ECO 310 Course Name: Microeconomic Theory: A Mathematical Approach Professor: Satoru Takahashi Date: Wednesday, January 14, 2009 Time: 1:30 p.m. This examination is
Princeton - ECO - 310
ECO 310, Fall 2007 Midterm Examination Solutions October 25Question 1 [50 points]If necessary, you may use log 2 0.69, log 3 1.10, log 4 1.39, log 5 1.61, log 6 1.79, and log(1 + z ) z when z is close to 0. Consider the following quasi-linear utility fu
Princeton - ECO - 310
ECO 310 cfw_ Spring 2008 Microeconomic Theory cfw_ A Mathematical Approach Stephen MorrisMidterm Examination Important instructions:1. This is a closed-book examination. Put away your books, handouts, notes, calculators, palmtops, cellular phones, : : :
Princeton - ECO - 310
ECO 310, Fall 2008 Midterm Examination October 24 Important instructions1. This is a closed-book examination. Put away your books, handouts, notes, calculators, palmtops, cellular phones, . . . now. 2. Print your name and your preceptors name clearly on
Princeton - ECO - 310
ECO 310, Fall 2008 Midterm Examination October 23 Important instructions1. This is a closed-book examination. Put away your books, handouts, notes, calculators, palmtops, cellular phones, . . . now. 2. Print your name and your preceptors name clearly on
Princeton - ECO - 310
ECO 310 - Fall 2008 Microeconomic Theory - A Mathematical Approach midterm 10/23 - Answer KeyQuestion 1:(a)(10 points) FONCS: L(x; y; ) = (x x0 )(y y x This implies thaty y0 x x0y0 ) + (IPx xPy y )y0 = P x x0 = Px Py (x Py x0 ) into the budget cons
Princeton - ECO - 310
ECO 310 - Fall 2008 Microeconomic Theory - A Mathematical Approach Midterm 10/24/08 - Answer KeyQuestion 1:(a)(10 points) L(x, y, ) = xy + y + (I Px x Py y ) FONCS: y = Px x + 1 = Py This implies y =Px Py ( x+ 1). Substitute y into the budget constrai
Princeton - ECO - 310
ECO 310 - Fall 2008 Microeconomic Theory - A Mathematical Approach midterm 10/23 - Answer KeyQuestion 1:(a)(10 points) L(x, y, ) = (x x0 )(y y0 ) + (I Px x Py y ) FONCS: y y0 = Px x x0 = Py This implies thaty y0 xx0=Px Py .Substitute y = y0 + x=Px
Princeton - ECO - 310
Princeton University - Department of Economics Fall Term 2008 ECO 310 - MICROECONOMIC THEORY: A MATHEMATICAL APPROACH Lectures: Tuesdays and Thursdays 11am-12:20pm, Friend Center 101 Professor: Satoru Takahashi, 201 Fisher Hall, 8-7919, satorut@princeton.
Princeton - ECO - 362
Princeton University Department of EconomicsEconomics 362 Problem Set 8 Multi-Factor ModelsFall Term 2009-2010Use the following to answer questions 1-2: Consider the multifactor APT. There are two independent economic factors, F1 and F2. The risk-free
Princeton - ECO - 362
Princeton University Department of Economics Economics 362 Answers to Problem Set 9 1. The percentage bond price change will be: Duration y .005 = 7.194 = .0327 or a 3.27% decline. 1+ y 1.10 Fall Term 20092. Computation of duration: a) YTM = 6% (1) Time