MRS: Application to Broadband Pricing Insights: Cobb-Douglas Utility Model ,PSHUIHFW6XEVWLWXWHV 3UHIHUHQFHV Insights: Linear Utility Model Perfect 6XEVWLWXWHV Preferences 5HODWLYH,QWHQVLW RIPreferences Convex Combinations (Strictly) Convex Preferences Budget Set with Uniform Prices and Exogenous Income Utility Maximization Problem (Intro & Types of Utility Models in this course) (On your own) UMP Math: Watch 2020-2021 Videos and Read Consumer Theory Chapter UMP Summary 1 Today: Ajaz Hussain, Economics, University of Toronto (STG) ‘SRWYQIV8LISV] Part 6 Micro-Case: Broadband Service Household Demand for Broadband Internet in 2010 BE Journal of Public Economics 3 9XMPMX]SJ&VSEHFERH7IVZMGI!0MRIEV*YRGXMSRSJXLIJSPPS[MRK ‘LEVEGXIVMWXMGW &VSEHFERH7IVZMGI’LEVEGXIVMWXMGW Coefficient(Marginal Utility) Cost to Broadband Users 0.021 1 1 Fast speed internet service 0.945 0.022 45 Very fast speed internet service 1.009 0.021 48.05 Reliable internet service 0.417 0.05 19.86 Priority of download service 0.134 0.157 6.39 Tele-health connectivity 0.092 0.229 4.38 Mobile laptop connectivity 0.00001 2,100 0.000476 Video phone capabilities 0.106 0.198 5.05 movie rentals 0.069 0.304 3.29 How can a Broadband service provider use these numbers (say, for cost and to make more money Micro-Case: Broadband Service 6XSSRVHDFDEOHFRPSDQUDLVHVWKH FRVWRIEURDGEDQG VHUYLFHV What can/should this company do to prevent customers from VZLWFKLQJGHIHFWLQJ WRRWKHUEURDGEDQGSURYLGHUV” Suppose a cable company LPSURYHV EURDGEDQGVHUYLFH How much can the company raise cost without risking customers VZLWFKLQJGHIHFWLQJ WRRWKHUEURDGEDQGSURYLGHUV” 4 How can a Broadband service provider use these numbers (say, for cost and to make more money Cost 以 AttributeTUT 00 0 AttributeTUX lostA lil out 以 Micro-Case: Broadband Service Use the following table and graphs to answer the questions on the previous slide 5 &VSEHFERH7IVZMGI’LEVEGXIVMWXMGW Coefficient(Marginal Utility) Cost to Broadband Users 0.021 1 1 Very fast speed internet service 1.009 0.021 48.05 How can a Broadband service provider use these numbers (say, for cost and to make more money dans acostu MRS 咒器 on MRS qq.cn mu 不 21muz Micro-Case: Broadband Service Use the following table and graphs to answer the questions on the previous slide 6 &VSEHFERH7IVZMGI’LEVEGXIVMWXMGW Coefficient(Marginal Utility) Cost to Broadband Users 0.021 1 1 Very fast speed internet service 1.009 0.021 48.05 How can a Broadband service provider use these numbers (say, for cost and to make more money V1我 lost不以 想占1MRSkmi 4805 costni _SEiiiii.n.ci 148.05 independent Ajaz Hussain, Economics, University of Toronto (STG) ‘SRWYQIV8LISV] Part 7 I lkfcq.iq Interior VsBoundary goodbadlneutral intensityofpreference &REE-‘RXJODV Insights from Utility Model & Indifference Curves λ λ 8 A B C Notice Suppose @ this High ratio ‘SRWYQIVLEWKVIEXIVMRXIRWMX]SJTVIJIVIRGIJSV # Suppose @ this Low ratio ‘SRWYQIVLEWKVIEXIVMRXIRWMX]SJTVIJIVIRGIJSV # Bso Lax.y intercept PositiveinteriorBoundk pos.tw NegativeTradeoff mnvur notaconstant 出品 tnanqgungupiotq.tnin togeta gmnguplessqtogetquwq.ouk.az more thana /LQHDU Insights from Utility Model & Indifference Curves 9 A B C Notice @ This High ratio ‘SRWYQIVLEWKVIEXIVMRXIRWMX]SJTVIJIVIRGIJSV # @ This Low ratio ‘SRWYQIVLEWKVIEXIVMRXIRWMX]SJTVIJIVIRGIJSV # p 70 gunmore givealess MN 缃景 台 i likegoodmorethangood2卡4 Likegood2morethangoodI Cobb-Douglas Utility Model: Characterizing Preferences Indifference Curves λ λ Indifference curves are FXUYHGtowards origin 10 At interior bundles, consumer goods At interior bundles, consumer perceives goods as substitutes NOT in the ECO 101 sense) At interior bundles, consumer has (strictly convex preferences) Consumer would rather consume both goods together than each good separately ( ) n 9 1 go Cobb-Douglas Utility Model: Characterizing Preferences Indifference Curves λ λ Indifference curves are FXUYHGtowards origin 11 At interior bundles, consumer goods At interior bundles, consumer perceives goods as substitutes NOT in the ECO 101 sense) At interior bundles, consumer has (strictly convex preferences) Consumer would rather consume both goods together than each good separately ( ) Ajaz Hussain, Economics, University of Toronto (STG) ‘SRWYQIV8LISV] Part 8 Suppose and At an interior bundle in the consumption set: then 7KLVLVDSRZHUIXOPHFKDQLVPIRULGHQWLILQJWHVWDEOH PDUNHWVHJPHQWV 13 Intensity of Preferences IRU *RRG *RRGV n NE Likegoodmove goodI likegoodmove good2 A denttradeoff B ifanswersarethesame Bothgoodsinthesamesegment 交换的数量相同 Example: and the Intensity of Preferences 6HJPHQWDWLRQ 14 Horsepower Interior Space Extra 50 hp Source: A. Petrin Quantifying the Benefits of New Products: The Case of the Minivan Journal of Political Economy (2002) How much interior space would parents vs. teenagers KMZIYT substitute/tradeoff) in exchange for 50 more horsepower engine and remain indifferent to the initial bundle 4YVTPI 7IKQIRX &PYI 7IKQIRX Parents ǔteenagers teenagerswnnngtoqueupmorensm.eu inexchangeforpower Ajaz Hussain, Economics, University of Toronto (STG) ‘SRWYQIV8LISV] Part 9 Tasteforvariety 16 :HLJKWHG$YHUDJH &RQYH[&RPELQDWLRQV mmslope icon7525 A ò Avg ixinot wavgwixigaom.ua cini a 收 innit偕 灬偕时以加 un B 1 1点悲品 华然邀 WeightedAvg qxnxx.snAunxB Examples: Towards (Strict) Taste for Variety [(Strictly) Convex Preferences] 17 Suppose that (where in the interior of the consumption set) Now consider where Is Is ,S[[MPP]SYYWIXLMWWPMHIXS TVIT JSVXIWXWERHUYM^^IW# as strongtasteforvariety AKAistnctgconuxpnetenenea.sn Goodgood Q Qiyesa.iay ehauayntty_ymhidg.uaNoQiNo Q_QyesA A 的 A Ba B is 13 13 (Strict) Taste for Variety; (Strictly) Convex Preferences 18 Convex Preferences have nothing to do with convex functions but do involve convex combinations Assume ) is differentiable Suppose that (where in the interior of the consumption set) Now consider where If Or equivalently for and all bundles in the consumption set then the consumer has Strictly Convex Preferences (aka Strong Taste for Variety) ;MXL KSSH KSSHWWXVMGXP]GSRZITVIJIVIRGIW implies that If Or equivalently for and all bundles in the consumption set then the consumer has Convex Preferences (aka Taste for Variety) ;MXL KSSH KSSHWGSRZITVIJIVIRGIWMQTPMIW that Onlyfolaigoodmnnnnnn Examples: (Strict) Taste for Variety [(Strictly) Convex Preferences] 19 Strictly Convex Preferences At Interior Bundles: Strictly Convex Preferences At Interior Bundles: Convex Preferences At Interior Bundles: Strictly Non-Convex Preferences At Interior Bundles: Strictly Convex Preferences At Interior Bundles: A A A A A B B B B B C C C C C Assume ) is differentiable Suppose that (where in the interior of the consumption set) Now consider where Ajaz Hussain, Economics, University of Toronto (STG) ‘SRWYQIV8LISV] Part 10 $&RQVXPHU V%XGJHW6HW Suppose all JRRGV LQWKHFRQVXPHU VFKRLFHVHWDUHsold at uniform prices Let GHQRWHWKHFRQVXPHU Vincome DOORFDWHGIRUSXUFKDVLQJJRRGV OXPS-VXP exogenous income) The set of affordable bundles EXGJHWVHW LV
The 2-good budget set consists of all bundles s.t: or 21 $&RQVXPHU V%XGJHW6HW 22 the set of affordable bundles in the choice set The equation of the budget line is: A B The 2-good budget set consists of all bundles s.t: The Slope of the budget line: What happens to the set of affordable choices if all pecuniary parameters by the same % amount Ajaz Hussain, Economics, University of Toronto (STG) ‘SRWYQIV8LISV] Part 11 2-Good Utility Maximization Problem (UMP) Assume 2-JRRG &KRLFH6HW $VVXPHFRQVXPHUSHUFHLYHVLQWHULRUEXQGOHVDV JRRG JRRGVLH interior bundles have ) Suppose all pecuniary parameters: Consumer chooses optimal bundle by solving UMP (Maximizing her utility subject to budget and other constraints) Typically: 24 2-Good UMP: Intuition 25 Infeasible bundle * Optimal choice Sub-optimal bundle Sub-optimal bundle An illustrative example 26 &OHDQ,QWHULRU%RXQGDU8036ROXWLRQV” 27 ECO204 2022-2023 UMP We will deal with KSSH KSSHutility functions in two categories: (MJJIVIRXMEFPI # Only those utility models with (strictly) convex preferences UYEWM-GSRGEZIJYRGXMSRW 2SR-(MJJIVIRXMEFPI # 0ISRXMIJ9XMPMX]1SHIP (Does it have (strictly) convex preferences ) Ajaz Hussain, Economics, University of Toronto (STG) ‘SRWYQIV8LISV] Part 12 2-Good UMP 29 914 -RTYXW Utility Model and its Parameters 914 3YXTYXW in terms of and Utility Parameters (Good 1 Demand Function) in terms of and Utility Parameters (Good 2 Demand Function) ;IGERTIVJSVQ GSQTEVEXMZI WXEXMGW*SVexample: (On your own) UMP Math: Watch 2020-2021 Videos and Read Consumer Theory Chapter 7KH *HQHUDO -Good UMP is a differentiable utility function with at interior bundles and / 30 7KH *HQHUDO -Good UMP / / / / 31 First, split this into 2 cases Next, split this into 2 cases FOCs: 7KH *HQHUDO -Good UMP 32 Case A Case B Case C Case D Suppose If so, then: Suppose If so, then: Suppose Suppose If so, then: If so, then: If so, then: Suppose If so, then: Suppose If so, then: If so, then: Suppose Suppose Suppose If so, then: Suppose If so, then: Suppose If so, then: Suppose If so, then: Suppose If so, then: Suppose If so, then: FOCs: *HQHUDO -Good UMP Cases: Intuition 33 8SWIIXLIMRXYMXMSRPIX WWYTTSWI A B C D Case A Consume Nothing / Case B Purchase good 1 only Case C Purchase good 2 only Case A Case B Case C Case D Suppose If so, then: Suppose If so, then: Suppose Suppose If so, then: If so, then: If so, then: Suppose If so, then: Suppose If so, then: If so, then: Suppose Suppose Case D Purchase both goods Violates constraint We will show that Indifference curve slope here is Budget line slope We will show that Indifference curve slope here is Budget line slope We will show that Indifference curve slope here is Budget line slope *HQHUDO -Good UMP Cases B, C and D 34 Case B Case C Case D If so, then: Suppose If so, then: Suppose If so, then: If so, then: Suppose If so, then: Suppose If so, then: Suppose Suppose Sub in If Case B is solution, then: To see when we need . Sub in Sub in Sub in If Case C is solution, then: To see when we need . Sub in Sub in Suppose neither Case B nor Case C arise; i.e. neither of the following expressions arise: If neither Case B nor Case C arise, the solution must be Case D: Optimal choice found by solving: and *HQHUDO -Good UMP Cases B, C, D: Summary 35 Case B (Only) Case C (Only) Case D (Only) If neither Case B nor C arise: Bundle D and found by solving: B C D Here: Indifference curve steeper than budget line Here: Indifference curve flatter than budget line Here: Indifference curve tangent to budget line Ajaz Hussain, Economics, University of Toronto (STG) ‘SRWYQIV8LISV] Part 13 *HQHUDO -Good UMP Cases B, C, D: Summary 37 Case B (Only) Case C (Only) Case D (Only) If neither Case B nor C arise: Bundle D and found by solving: B C D Here: Indifference curve steeper than budget line Here: Indifference curve flatter than budget line Here: Indifference curve tangent to budget line Quick Example: Cobb-Douglas UMP Recall: 38 Case B (Only) Case C (Only) Case D (Only) Since neither Cases B or C arise, the solution is Case D where For Bundle D: Solve Case B cannot be the solution Case C cannot be the solution and Quick Example: Linear UMP Recall: 39 Case B (Only) Case C (Only) Case D (Only) ‘EWI ( MW XLI WSPYXMSR [LIRIZIV Solve Case B is the solution whenever Case C is the solution whenever any bundle on See graphs on next slide Quick Example: Linear UMP 40 B C D Whenever Whenever Case B Case C Case D Whenever Whenever Whenever Whenever Whenever Whenever Here