Nonlinear Budget ConstraintsA. Introduction1. So far, we have considered a very simple description ofthe budget constrainta. wages are constant as hours increaseb. non-labor income is fixed and does not depend onother characteristics such as income2. In this section, we are going to consider more realisticbudget constraints that account for taxes, governmentsubsidies, work costs and the like3. A common feature of these modifications is that they leadto non-linear budget constraints, which in turn lead toestimation issuesB. Examples of non-linear budget constraints1. Fixed money costs of worka. consider several possible expenses associated withwork such as child care, union dues, uniformsb. sometimes these expenses do not vary with thenumber of hours worked (i.e., are lump-sum expenses)c. effect on budget constraint1) let the (initial) budget constraint without fixedcosts of work be Y = WH + N2) with fixed costs, the (new) budget constraint isY = N if the person does not workY = WH + N – F if the person works3) the resultingbudgetconstraint hasa notch at theno work pointd. effect on laborsupply1) comparebehavior forpeople whodo and do notface fixed costs of work2) for peoplewho workmany hours(like person Aon right), theimposition offixed costs issimilar to adrop in non-labor income;it will causethese peopleto work more3) for people who work few hours (like person Babove), it may be optimal to stop working4) imposition of a fixed cost increases the reservationwage and results in a discontinuous labor supplyfunction2. Effect of taxes on labor supplya. effect of a flat proportional tax on earnings1) consider an individual with a pre-tax budget-constraint Y = WH + N2) assume that the government imposes a flatproportional tax of t on earnings; the after-taxbudget constraint isY = WH + N – tWH= (1–t)WH + N3) graphically,proportionaltax decreasesthe effectivewage from Wto (1–t )W4) equivalent toa wagedecrease5) will causesubstitution(–) and income (+) effects; net effect on laborsupply will be ambiguous6) is this a realistic description of the tax system?S describes social security & some state systemsS poor description of federal systemb. progressive income tax1) the federal income tax is mostly progressive2) progressive means that the marginal tax rateincreases with income (what would regressivemean?)3) in 2007, the marginal tax rates for a singletaxpayer are:S 10% for adjusted incomes below $7,825S 15% on the next increment up to $31,850S 25% on the next increment up to $77,100S 28% on the next increment up to $160,850S 33% on the next increment up to $349,700S 35% on adjusted incomes thereafter4) tax rates only apply to “adjusted income” (incomeless deductions, exemptions)5) initial tax rate is 0 up to adjustment amount6) the effect of a progressive tax on the budgetconstraint is shown belowS first segment corresponds to income belowadjusted amountS next segment corresponds to first taxablebracket (10% marginal tax rate)S final segment corresponds to second taxablebracket (15% marginal tax rate)7) general concave shapec. 2001 Tax Relief Act1) cuts tax rates over next several years2) for instance, introduced the 10% bracket into the15% bracket3) 28% bracket from 2000 has been reduced to 25%4) highest tax bracket has been reduced from 40% to35%5) graphically, budget constraint has swivelled out6) what are the effects on labor supply?d. other features of the federal income tax system1) these rates aren’t the only feature of the federalsystem; there are other exclusions, credits, etc.2) retirement related features: exclusion of pensioncontributions from income; deferment of earningson pension savings; exclusion of some individualretirement savings and Social Security benefits3) poverty related: Earned Income Tax Credit4) health related: exclusion of employer contributionsfor insurance and medical care; exclusion ofMedicare benefits; deductibility of large medicalexpenses5) employment related: dependent care tax credit;exclusion of employer-provided child care;targeted jobs tax credits; exclusion of certainemployee benefits6) housing related: mortgage interest deduction7) these features make the actual tax system muchmore complicated to modele. state and local taxes add to the complexity3. Means-tested transfersa. consider a transfer program (program that transfersmoney from the government to people) that1) provides a guaranteed benefit G for people withoutincome, and2) reduces the benefit by a rate BRR for each dollar ofincome they receive3) total benefits would beB = Max(G – BRR×Y, 0)b. graphically,1) assume pre-transfer budget constraint is Y = WH(i.e., no non-labor income); also, ignore other taxes2) people with no income receive G3) earnings are effectively taxed at a rate BRR untilbenefits are exhaustedc. big work disincentived. what effect would an increase in the benefit reductionrate to 100% have on labor supply and programparticipation?1970 1975 1980 1985 1990 1995 2000RecipiencyBenefitsAFDC Benefits & Recipiency1) people whodon’t work orwork littleinitially (likea and b) willnot work2) people wereparticipatingbut working(like c) nearthe cut-offwill work more3) people who were not participating (like d) will notbe affectede. AFDC and TANF1) AFDC – Aid to Families with Dependent Children;old welfare program2) TANF – Temporary Assistance for NeedyFamilies; program after 1996 reforms3) trends inprogramsS real value ofbenefitspeaked in the1970s;benefitssteadilyerodedthereafter (when Food Stamps and Medicaidare added, benefits still fall through the 1980sand 90s)S recipiency rose sharply during the late 1960sand early 1970s then declinedS recipiency also rose sharply during the late1980s and early 1990s but has fallendramatically since; recipiency is now lowerthan in 1970Differences between AFDC and TANFAFDC TANFFederal funding Unlimited matching Fixed grantState funding Matching required Maintenance of effortrequirementEligibility Single parent familieswith children; twoparent families withunemployed parentSet by stateIncome limits Set by state Set by stateBenefit levels Set by state Set by stateEntitlement States required to assistall families eligibleunder income standardsNo entitlementWork requirement Participation in JOBSprogramBy 2002, half of state’scaseload must be inspecified work activitiesExemptions from work requirementParents with childrenunder 3 (or 1 at state’sdiscretion)None, though states mayexempt single parentswith children under