More from Chapters 1-3 Marginal analysisToday: Four “mini-lectures”Size of governmentSlide 4(Table and figures)Summary: Size of governmentMarginal analysisSlide 8Example: Marginal utilityExample: Diminishing marginal utilityDiminishing marginal utilityThe rational spending ruleSlide 13Slide 14Slide 15MRS and utility maximizationMarginal cost, using calculusSummary: Marginal analysisEmpirical toolsCausationSlide 21Slide 22Randomized studySome pitfalls of randomized studiesSlide 25Observational studyConducting an observational studyRegression analysisInterpreting the parametersTypes of dataPitfalls of observational studiesData collected in non-experimental settingSpecification issuesQuasi-experimental studiesExample of quasi-experimental studyConducting a quasi-experimental studyDifference-in-difference methodInstrumental variables (IV) methodRegression-discontinuity methodPitfalls of quasi-experimental studiesSummary: Empirical toolsEdgeworth boxesSlide 43Pareto efficiencyPareto improvementContract curvePareto Efficiency in ConsumptionSummary: Edgeworth boxesWhat have we learned today?More from Chapters 1-3Marginal analysisToday: Government size; Marginal analysis; Empirical tools; Edgeworth boxesToday: Four “mini-lectures”Finish Chapter 1Introduction to government sizeMarginal analysisA review of what marginal meansChapter 2Causation versus correlationStatistical tools and studiesBegin Chapter 3Edgeworth boxesSize of governmentThe constitution gives the federal government the right to collect taxes, in order to fund projectsState and local governments can do a broad range of activities, subject to provisions in the Constitution10th Amendment: Limited power in the federal governmentLocal governments derive power to tax and spend from the statesSize of governmentHow to measure the size of governmentNumber of workersAnnual expendituresTypes of government expenditurePurchases of goods and servicesTransfers of incomeInterest payments (on national debt)Budget documentsUnified budget (itemizes government’s expenditures and revenues)Regulatory budget (includes costs due to regulations)(Table and figures)Table 1.1, p. 9Figure 1.1, p. 10Figures 1.2 and 1.3, p. 11Figures 1.4 and 1.5, p. 13Summary: Size of governmentGovernment spending in the US, as a percentage of GDP, has increased in the last 50 yearsOther industrialized countries spend more than the US (as a percentage of GDP)Composition of taxing and spending has changed in the last 50 yearsMarginal analysisQuick look at marginal analysisImportant in many tools we will use this quarterWe look at “typical” casesMarginal means “for one more unit” or “for a small change”Mathematically, marginal analysis uses derivativesMarginal analysisWe will look at four topics related to marginal analysisMarginal utility and diminishing marginal utilityThe rational spending ruleMarginal rate of substitution and utility maximizationMarginal cost, using calculusExample: Marginal utilityMarginal utility (MU) tells us how much additional utility gained when we consume one more unit of the goodFor this class, typically assume that marginal benefit of a good is always positiveExample: Diminishing marginal utilityBanana quantity (bananas)Total utility (utils) Marginal utility (utils/banana)0 0701 70502 120303 150104 16055 165Diminishing marginal utilityNotice that marginal utility is decreasing as the number of bananas increasesEconomists typically assume diminishing marginal utility, since this is consistent with actual behaviorThe rational spending ruleIf diminishing marginal utility is true, we can derive a rational spending ruleThe rational spending rule: The marginal utility of the last dollar spent for each good is equalGoods A and B: MUA / pA = MUB / pB Exceptions exist when goods are indivisible or when no money is spent on some goods (we will usually ignore this)The rational spending ruleWhy is the rational spending rule true with diminishing marginal utility?Suppose that the rational spending rule is not trueWe will show that utility can be increased when the rational spending rule does not hold trueThe rational spending ruleSuppose the MU per dollar spent was higher for good A than for good BI can spend one more dollar on good A and one less dollar on good BSince MU per dollar spent is higher for good A than for good B, total utility must increaseThus, with diminishing MU, any total purchases that are not consistent with the rational spending rule cannot maximize utilityThe rational spending ruleThe rational spending rule helps us derive an individual’s demand for a goodExample: ApplesSuppose the price of apples goes upWithout changing spending, this person’s MU per dollar spent for apples goes downTo re-optimize, the number of apples purchased must go downThus, as price goes up, quantity demanded decreasesMRS and utility maximizationUtility maximizationNecessary condition is that marginal rate of substitution of two goods is equal to the slope of the indifference curve (at the same point)At point E1, the necessary condition holdsUtility is maximized hereMarginal cost, using calculusSuppose that a firm has a cost function denoted by TC = x2 + 3x + 500, with x denoting quantity producedNote fixed costs are 500Marginal cost is the derivative of TC with respect to quantityMC = dTC / dx = 2x + 3Notice MC is increasing in x in this exampleSummary: Marginal analysisMarginal means “for one more unit” or “for a small change”We can use derivatives for smooth functionsMarginal analysis is important in many economic toolsUtilityRational spending ruleMRSCost functionsEmpirical toolsEconomic models are as good as their assumptionsEmpirical tests are needed to show consistency with good theoriesEmpirical tests can also show that real life is unlike the theoryCausationEconomists use mathematical and statistical tools to try to find the effect of causation between two eventsFor example, eating unsafe food leads you to get sickHow many days of work are lost by sickness due to unsafe food?The causation is not the other directionCausationSometimes, causation is unclearStock prices in the United States and temperature in AntarcticaNo clear causationNumber of police