ECON210现代观点

决策理论导论在任何决策问题中，都有两件根本不同的事情要做考虑：什么是可行的，什么是可取的。我们首先讨论第一个要素。我们会的1.看一些简单的例子，然后2.使我们的框架专门用于建立一个有竞争力的市场。可行集示例你有8个小时在微观经济学
期末考试你可以花每睡一小时或学习可行集示例你的微观经济学和宏观经济学

1 Intermediate Microeconomics

ECON210 Budgets Aleksandra Balyanova1 Introduction to decision theoryIn any decision making problem, there are two fundamentally different things to takeinto account: what is feasible, and what is desirable.We begin by addressing the first element. We will1. see some simple examples, then2. specialise our framework to the setting of a competitive market.2/20Examples of feasible setsYou have 8 hoursbefore yourmicroeconomicsfinal examYou can spendeach hour sleepingor studying3/20Examples of feasible setsYourmicroeconomicsandmacroeconomicsfinal exams areboth tomorrow andyou have0 hoursleft to study Each hour spentstudying for theMicro exam adds10 marks to yourgrade, each hourspent studying forthe Macro examadds 5 marks toyour grade4/20Budget constraint in market settingIn a market setting with L goods (commodities), a consumption bundle is anL-dimensional vectorx = (x1, x2, . . . , xL)wherex` ≥
0 represents the quantity of commodity ` in the consumption vector x;
0 represents the market price of good `; andp = (p1, . . . , pL) represents the vector of prices.The consumption space X is the collection of all available bundles.If goods are perfectly divisible, the consumption space is X = RL+Even in a market setting, consumption choices are restricted by various considerations,but we focus on budgetary restrictions.5/20Budget constraint in market settingA consumer (Anne) is endowed with (disposable) income m > 0.If Anne can afford to buy x at prices p, it must be thatp1x1 + . . . + pLxL ≤ mGiven prices p (p1, . . . , pL) and income m > 0, the collection of all affordable bundlesforms Anne’s budget set:B(p,m) ={x ∈ X : p1x1 + . . . + pLxL ≤ m}.The bundles that are exactly affordable belong to the budget line: the outer boundaryof the budget set. If L = 2, the budget line is a line segment.6/20Two goods caseWe will focus on the two-goods case for the remainder of our analysis of the consumerproblem. Why?A two-good world allows us to capture a fundamental trade-off: whenever youbuy some of one good, you give up the possibility of buying some of another7/20Two goods caseIn the two-good case we have X = R2+, x = (x1, x2) and p =(p1, p2).Thus, 2 x1.The slope of the budget line captures the opportunity cost in terms of good 1 unit.9/20Comparative statics: income A change in income,keeping relative prices fixed,does not change the slopeof the budget lineThe budget line movesparallel to the originalbudget linehigher income linemoves out lower income linemoves in10/20Comparative statics: incomeAn ad valorem sales tax at arate t increases the pricefrom p1 to (1+ t)p1. A uniform sales tax isapplied uniformly to allgoods. Old budget line:p1x2 = m. Relative prices don’tchange.11/20Comparative statics: pricesIncreasing the price of onegood with respect to otherspivots the budget lineinward.In the picture, the price ofgood 1 = (1+ t) p′112/20The numeraire For any k afford We can choose k to normalise one good’s price to equal (the numeraire)13/20Bulk discountsSometimes vendors offer bulk discounts, e.g. “buy two for less than twice the price ofone”14/20Bulk discountsBulk discounts can also take the form of receiving “money off” your total if you spendmoreIn both of these cases, the bulk discount creates a discontinuity in the price ratio.15/20Bulk discounts: a simple example You have m = 100 that youcan spend on books or othergoods The price of other goods is1, while chocolates cost $2each if you buy 20 andSAVE $20!!”.16/20Multiple constraints Choices in the real world areconstrained by more thanbudgetary restrictions.Time constraints.Technological andphysical constraints(e.g., indivisiblegoods).Regulations and lawprovisions. In general ---i.e., not just incompetitive market settings--- a choice bundle isfeasible (or affordable) onlyif it meetseveryconstraintimposed by theenvironment.17/20Budget sets: You spend money on books and other goodsYour initial income is m = 100, and pg = pb = 1. Your budget set is therefore B= {(xb , xg ) : xb + xg ≤ 100}.You are given a gift card for $40 to spend at your local bookstore.Graphically depict your budget in the following two scenarios:1. A secondary market is available to exchange your gift card for actual dollars at a1:rate2. No secondary market is available18/20Budget sets: exercise 1The case with no secondary
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