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Study Guide for Prelim 1

by: Eunice

Study Guide for Prelim 1 PAM 2000

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Compiled notes from lecture and discussion
Intermediate Microeconomics
McDermott, E
Study Guide
Micreconomics, PAM
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This 17 page Study Guide was uploaded by Eunice on Thursday March 10, 2016. The Study Guide belongs to PAM 2000 at Cornell University taught by McDermott, E in Fall 2015. Since its upload, it has received 54 views. For similar materials see Intermediate Microeconomics in Political Science at Cornell University.


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Date Created: 03/10/16
PAM 2000 McDermott Spring 2016 Prelim 1 Study Guide Compiled Class and Discussion Notes  Define economics: study of how people allocate scarce resources o “father” of economics: Adam Smith  General equilibrium effects: price changes in other markets that would need to be explicitly included within a model  Preferences o Differentiates social sciences from physical sciences o Utility o Depending on the number of dimension  4 apples > 3 oranges  2 apples 3 oranges > 2 oranges 3 apples?  Given max input/resources/time/income M, two choices X and Y, prices thereof (pxand p )yand quantities thereof (q axd q ) y o Function: M = p x xp q y y o X-intercept: M/p x o Y-intercept: M/py o Slope = -p xp y o If given a function where the maximum quantity of one choice is not possible, the function becomes a step function, not linear  in reality can’t have 11.66 beers or 3.18 wines, keep it as a fraction or decimal though  Opportunity cost of choosing an option: VALUE OF the next best alternative  Economic v. accounting profits o Accounting profit = revenue – cost o Economic profit = revenue – opportunity cost o Example  A firm can:  Invest $1M in a factory  $100,000 profit from leasing factory out for 1yr  Sell factory for $950,000 after 1yr  Opportunity cost: invest money at 6% per year  Accounting profit?  $100k +$950k – $1000k = $50k  Economic profit?  Opportunity cost: $60,000  Budget constraints o Two-input budget constraint (see notes from previous lecture and discussion)  M = p x xp q y y  M ≥ p qx+x q iy yhe function of all affordable/possible bundles (the line and the area underneath would be shaded in) o Known as the budget set  M = p qx+x q iy yhe function of the budget boundary/constraint o Known as the boundary of the budget set  Changing the function  The slope is determined by the prices  When the income changes, the slope remains the same; the function shifts up or down  A point on the graph of a BC is a combination of options (called a bundle) o Points inside the linear function (between the axes and the line of the function) are bundles that can be afforded o Points on the line are bundles that can be afforded and that uses the entire budget or income (the line is the boundary) (this maximizes utility) o Points outside (above the linear function) are bundles that cannot be afforded o Assumptions on consumer preferences (two things)  Consumers prefer more to less  Consumers select bundles that are on the boundary of the BC  Tastes are stable, consistence, unchanged  Consumption bundles are not chosen at random  Lecture 4: review notes with the referenced slides for the graphs o Assumptions on consumer preferences  People prefer more to less  Assures people select a bundle that is on the boundary of the BC  Marginal utilities will be non-negative (usually positive)  Tastes are stable (consistent, unchanging)  People won’t be random about their desired consumptions o Taxes (BC)  Tax is same on all goods = reduction in income  Some public goods may become available  excise taxes (percentage taxes): Symbol tau: τ  Sales tax o Assuming BC: M= p b+p b w  Taxed BC: M=p (1b τ)b+p (1+ w)w  Or: w= M/(p w1+ τ)) – (p (b+ τ))/(p (w+ τ)) = M/(p (1+ τ)) - p b/p w b w  BC with single tax o Tax on only one of the two products o M=p (b+ τ)b+p w w o w= M/p –w(p (b+ τ))/p w o choices will be distorted away from option b (Law of Demand)  tax T symbol for fixed per unit tax  M = (p bT)b + p w w  If all goods cost the same amount, T is identical to τ  If prices are different, a single per unit tax is heavier on the less expensive good o T=$1 per unit is smaller on a $20,000 car than on a $3 sandwich  T is more distortionary than excise taxes o Regressive tax: tax the lower incomes more than higher incomes  As opposed to progressive tax (the US federal income tax): higher incomes get higher tax rates  calculate per unit tax as a percentage tax for each good (excise tax equivalent) o τ = T /p x x x o τy= T yp y o M = p x1+τ )x +p (1yτ )yy o conversion from per unit tax to excise tax only works for a given price  distortions and types of tax proposals  flat tax: everyone pays the same marginal tax rate (same percentage) regardless of income o pros: easy to pay, reduces incentive to hide income, simple taxation would require fewer resources (private accountants, IRS)  proposal may be paired with a large transfer to the poorest, reduces incentive to hide income or not work o cons: regressive  consumption tax o state and local level exists already o proposal: replace income taxes with increased consumption tax nationally o can’t hide income: people are still consumers  somewhat progressive: wealthier people consume more (although a smaller portion of their income)  distortions o tax code distorts away from optimal choices (BC) o lab taxed at a different rate than capital = sub- optimal/less productive capital-labor ratio (inefficient allocation)  similar to: time, effort, resources put in to reducing tax burdens in the complex tax system (if system was simpler, this wouldn’t be possible so time, effort, resources would be saved)  quantity discounts: o differentiation: six pack is different from a single beer (different customer target and price sensitivity) o quantity discounts may encourage firms to merge o graphically:  the plateau occurs because at the 6 unit, th the per price unit drops so at the 6 unit, you are able to purchase more than 6 units with your original budget constraint in mind  because you have more money to spend  example, $1 beer: at 6 units, you would have paid 6$ but the discount changes the price to $.90 o you now have $.th more to spend at the 6 unit  units within the horizontal line are technically free  tax above a threshold o threshold above which consumers are allowed to purchase tax free o graphically  the bend point/kink is the threshold  the kink would not exist for someone who’s budget is below the price of the quantity at the kink  quotas o example: insurance  one of the goods is insurance o graphically  consumer must purchase above the horizontal line even if the optimal bundle is on the black line (budget constraint) and below the red dashed line [unconstrained point]  consumer would select the bundle at the intersection of the two lines [constrained point]  gifts (non-transferable) o similar to quota: consumer is obliged to consume(/waste) a good (not purchase) o graphically  the jump shows the gifted 1 unit of one good which cannot be transferred/traded/sold for the other good  coordinate of kink: (1, M/p y  intercept of x: 1 + M/p x  subsidies/discounts behave likes taxes but are negative (because they lower the price) o example on a problem with a discount (two possible calculation methods)and a problem with a gift  Weak Axiom of Revealed Preference (WARP): if A is revealed to be preferred to B, then B won’t be revealed to be preferred to A o given that A and B are both available in the initial and new BC o if A is more expensive and yet it’s still preferred, then the consumer’s preference is obvious separate to affordability since he has rejected the cheaper bundle o only assumption: more of both is always preferred  monotonicity  utility theory: the attempt to quantify happiness o utility: numerical measure of happiness (utility is always ordinal)  ordinal numbers: options are ranked in order of preference  cardinal numbers: a degree of utility is assigned to a bundle (impossible) o assumptions made  people maximize utility (firms will maximize profit)  more goods means higher utility  preferences are stable, consistent, unchanging  preferences are complete  given A and B, consumer will either o strictly prefer A over B o strictly prefer B over A o be indifferent between A and B  Preferences are transitive  if A is preferred over B, and B over C, then A must be preferred over C  indifference is also transitive o utility with 1 good  diminishing marginal utility  U(x)=x^(1/2)  represents consumer preferences o marginal utility  change in utility for a change in quantity consumed  MU=∆U/∆Q  derivative or slope  steepness means higher marginal utility o utility with 2 goods  3D graph  height of graph (z component) is the utility  if you graph all the bundles of one utility (take a slice and drop the line down to the x-y plane) it would be the indifference curve (IC)  a level set of the 3D utility graph o BC and IC  BC slope = -p xp y  the MU of x and y individually = partial derivative  MU x∆U /∆x o ∆U xMU *x∆x)  MU =∆U /∆y y y o ∆U yMU *(yy)  ∆U=MU (∆xx+MU (∆y) y o set ∆U=0 because on an IC, the utility is the same everywhere so the change=0 o then  ∆y/∆x = -MU /Mx y  slope of the IC: the trade off a consumer faces between goods X and Y in terms of utility  slope of BC = -p xp y -MU /MUx= y slope of IC o px/py=MU /xU =MyS o ratio of marginal benefits = ratio of marginal costs o MRS (marginal rate of substitution)  rate at which a consumer is ready to give up one good in exchange for another good while maintaining the same level of utility  MRS=MU /MUx y  useful because where the BC is tangent to an IC is the optimal bundle o constrained optimization  consumer wants to maximize U under a BC o Max x,yU(x,y) o s.t. (subject to) M=p x+p y y  tangency o consumers will maximize utility = choose a bundle om the “highest” indifference curve possible o the optimal curve will be where the IC and BC are tangent  where the slope of the BC (-p /px) y slope of the IC (MRS = -MU xMU )y  MRS is calculated by taking the partial derivative of the utility function in respect to x and then y (professor will give us the MU values)  the ratio of marginal benefits is equal to the ratio of marginal costs at the optimal bundle o NOTE: just having the same slope does not mean that that the BC and IC are tangent. the point at which the slopes are the same must also be a point that satisfies the function of the BC.** o the algebra  cobb-douglas utility function  u(x,y) = x y 1-a  ensures that fractions of earnings go to each good, regardless of income/prices  a + (1-a) = 1 (usually the case)  typically 2/3 goes to capital and 1/3 goes to labor in the case that the cobb-douglas function is applied as a production function  cobb-douglas IC  always smooth and will never touch the axes o u(x,y) = x y 1-a o is x or y is zero then u = 0 o this assumes that the consumer will always want some of both o interior solution  the optimal bundle lies in the interior of the first quadrant  (often at the point of tangency between BC and IC) o exceptions being: Leontief and kinked BCs o Corner Solution (complement of Interior Solution)  consumer is constrained from having a negative quantity of x or y (consumer wants to be on the outside of the quadrant)  the optimal bundle is on one of the axes (the IC touches the BC at the corner of the BC)  in order to calculate, plug in x=M/p axd y=0, y=M/p and xy0 to find the optimal bundle  Linear Preferences o perfect substitute o u(x,y) = Ax + By  MU =xA  MU =yB o the BC is linear (as always between two choices) and the IC are also all linear o in order to know precisely how many of good x or y will be bought, you need to know the entire BC  if you just want to know which good will be preferred over the other, then you just need to know the slope of BC  this would be the same as knowing whether MU /MU > x y p xpy o if the two are equal, the IC is the same as the BC  MU /x x MU /p y y o this rearrangement makes it clear that in this scenario, good x is much more preferred o so then quantity of x wanted is MU /px xmit  and y = 0 o to calculate slope of IC = - MU /xU y  Leontief o perfect complements (extreme) o consumer wants a certain ratio  consumer wants more of BOTH; more of one won’t change their preference o graphs look like right angles  at the kink/angle, the consumer gets his/her preferred ratio and there’s no waste of one good  the equation that runs through all of them is Ax=By (optimality condition 1)  with this equation and the equation of BC (optimality condition 2), you can determine the optimal point  Cobb-Douglas o standard, no kinks, BC is tangent o without calculus, the IC must be given o IC will never touch x or y axis o tangency gives one optimality condition  MU /xU = y /p x y  other optimality condition: BC  optimality conditions o 1 : BC: consumer will spend all their money nd o 2 :  Cobb-Douglas: MU /MU x p /y x y  don’t need explicitly the prices, you can find the optimal bundle in terms of p axd p y  Leontief: given min[Ax,By], Ax=By  Linear: MU /xU > yr < or = p /p x y  don’t need M  demand curves o necessary information for determining price o is the sum of individual demands and tells how much a good will be demanded at a given price o Ordinary demand: uncompensated or Marshallian  for Cobb-Douglas (C-D)  by using the utility function, find the demand function o x* = M/(cp ) x  c being some constant  need to know M  x is on the x axis, p xs on the y axis  for Leontief  by using the utility function, find the demand function o x* = M/(cp +x ) y  need to know specific M and p y  x is on the x axis, p xs on the y axis  for Linear  demand is unusual  three types of solutions o MU /MU > p /p x y x y  only good x wanted o MU xMU <yp /p x y  only good y wanted o MU xMU =yp /p x y  all bundles on the BC are equally satisfying  when looking at the demand for good x, given M and p , y the situation is: o the vertical bit: MU /Mx < p yp x y  while the is p xigher than (MU /MUx)* p yhe y consumer will only purchase good y o the horizontal bit: MU /MU x p /y x y  the is pxequal to (MU /Mx )* y andythus they will purchase any quantity between 0 and M/p xthe max of good x they can afford) o the curved bit: MU /MU x p /y x y  p xas fallen below (MU /MUx)* pyso nyw the consumer will purchase only good x  the function of this bit: x = M/p x  asymptotic o compensated or Hicksian demand: measures changes in consumer welfare and other things  when there is a price change, changes are observed in demand by ordinary demand  this doesn’t show how much of these changes are due to different trade-off (different relative prices) and how much are due to the feeling of losing wealth during purchase  determine how much worse off a consumer is by compensating them to find out the cost of getting the consumer back to his original utility  requires models  done with surveys  Income and Substitution Effects o Substitution effect: change in consumption due to the relative change in the price only  as price of one good increases, the relative price of both goods change  consumer may substitute away from the more expensive good  towards the less expensive good o income effect: change in consumption due to the decrease in perceived income only o income and total(=income + substitution) effects results in 4 categories of goods  income effect  normal good: consumption increases as income increases  inferior good: consumption decreases when income increases  total effect (just substitution effect is uninteresting: consumer always substitutes away from the more expensive good)  Giffen good: consumption increases as price increases  ordinary good: consumption decreases as price increases  observing effects o compensate the consumer  allow consumption at the same utility level as before but with a new price ratio  price change pivots the budget constraint (changing the slope)  to compensate, find the point of tangency between the original/initial IC and a line of the same slope (the same price ratio) as the new BC  the shift/difference between the new BC and the theoretically shifted (to be tangent to the IC) one = compensation variable  what will observed  substitution effect: decrease in demand for x relative to the price increase, utility constant o assumes Py is constant and Px increases  income effect: change in demand for x due to decrease in purchasing power (Px increased) o using the new price ratio, comparing income required to buy the un-/compensated bundles o compensation variable: the amount of income that you have to compensate the consumer so that he or she is as happy as before (the shifting of the BC out to be tangent to the original IC)  compensated demand o Cobb-Douglas  consumer can substitute towards less expensive good with no utility change  as price increases the compensated consumer can afford more than an uncompensated one but the two have different amounts demanded  think of perfect complements o you can be at the same IC again thanks to compensation but without the exact same bundle (of left and right shoes for ex), you won’t be satisfied o compensated vs. ordinary demand  A and B are ordinary  C is at a point of compensated demand o with Leontief, the utility doesn’t change as Px changes  thus the compensation behaves/influences demand differently  the demand function is a vertical line at a specific quantity of good x  consumer surplus  price change x the quantity the consumer will buy (slide 14, lecture 10) o with Linear  the consumer’s utility as satisfied by compensation so the graph drops straight down to the x axis since more units of x would not increase utility  unlike ordinary demand where buying more units would increase utility (at a decreasing rate) o relevance  Leontief preferences and Social Security and COLA  cost of living adjustments o the ss admin uses the CPI-W (consumer price index for urban wage earners and clerical workers) o implicitly assumes consumers have Leontief preference  Leontief always yields a fixed optimal ratio of goods  change in income or prices does not affect this. o effects on various preferences  C-D: better off: the consumer can use substitution effect so the compensation is excess utility  Leontief: if the preferences are precisely the assumed bundle then the consumer is equally well off (no substitution effect)  if the bundle doesn’t match the preferences, then worse off  linear: better off (more than C-D): substitution effect  elasticities o the impact of a price increase (depending on how substitutable other goods are for the good at hand) o cross-price elasticities gives us a measure of how substitutable goods are o price elasticity of Demand  ε = %∆Q/%∆P = ((Q -Q 2/Q1)/(1P -P2)/1 ) 1  extremely important for monopolists  price elasticity of demand will usually change as we move along the demand curve (even if it’s linear) o elastic: |ε| > 1 o inelastic: |ε| < 1  ε is closer to zero o unit elastic: if ε is -1 (|ε|=1)  assume ε is negative (not Giffen) o assuming the law of Demand holds  First Law of Demand: as price increases, demand decreases (vice versa)  not Giffen o income elasticity:  if income increases and consequently influences demand o complement vs. substitute  complement: price goes up on a complement, the other’s demand goes down  substitute: price goes up on a substitute, the other’s demand goes up  Armendariz preferences o Giffen goods o price of a good and its quantity demanded are positively correlated  finding optimalities on kinked budget constraints o there will be tangency at each BC  use the two optimality conditions to solve o check the kinks to see if they’re optimal  firms o determine optimal level of production  marginal cost: additional cost of producing one additional unit of a good (also the derivative of total cost)  MC = ∆TC/∆Q = ∆VC/∆Q = w∆L/∆Q = w/(∆Q/∆L) = w/MPL  Q: quantity  VC: variable cost  TC: total cost (fixed + variable)  L: labor  MPL: marginal product of labor o if diminishing, costs are increasing  fixed cost (usually capital) vs. variable cost (VC) o VC: costs that change with the production of every additional unit (usually labor, exception being cases like union contracts) o MC curve cross AC curve at its minimum o profit maximization  profit = total revenue – total cost  discussion of firms as price takers (they don’t decide the price)  profit (π)  π = P(Q) – C(Q) o price: P o cost: C o quantity: Q  π = TR – TC = P(Q) – F – VC o =Q(p-((TC)/Q)) o F: fixed costs  price = AVC, firm is breaking even o >, profit o <, loss  decisions o output decision: firm produces, what output level (Q) maximizes its profits/minimizes losses o shutdown decision: is it more profitable to produce or shut down  π < 0 when P < AVC + AFC  if p<AVC, shut down  p=AVC, π = F  p = ATC, π = 0 o SR  if firm is making a loss and price < AVC  if AVC < F and π is positive  then continue production in the short run so fixed costs can be paid off even if not with an optimal level of production  marginal revenue (MR) is price for profit taking firms (derivative of total revenue)  to determine whether increasing production is profitable, see if MR > MC o profit is maximized where MC = MR  P>MC, next unit is profitable, increase production  P=MC, keep production constant  P<MC, production not optimal, reduce o producer surplus  perfect competition o short run v. long run  long run: entry/exit decision  no fixed costs  P>ATC, positive profits so firms enter  P<ATC, positive profits so firms exit  in LR equilibrium, P=ATC, profits=0  assuming there are no barriers to entry  long run: firms don’t lose money because if they did they will have exited  shutdown decision in the short run  based on fixed cost  revenue < VC, shutdown o π < 0 when P < AVC + AFC o if p<AVC, shut down o p=AVC, π = F o p = ATC, π = 0  if firm is making a loss and price < AVC o if AVC < F and π is positive o then continue production in the short run so fixed costs can be paid off even if not with an optimal level of production  output decision: firm produces, what output level (Q) maximizes its profits/minimizes losses o supply  first law of supply: as price increases, quantity supplied increases, ceteris paribus  same as the MC curve above the ATC curve  elasticity  market supply function (aggregate supply function) o total quantity of good that’ll be suppled at each price o sum of all individual firm supply functions  price elasticity of supply o amount producers will change the quantity suppled in response to a change in price o ε=%∆Q /%sP  positive value  if o ε= infinite, perfectly elastic  infinity> ε>1 : elastic supply o ε=0, perfectly inelastic  1> ε>0 : inelastic supply  second law of supply: the more time that producers have to react to a price change, the more elastically it’ll be supplied  monopoly o governments creates monopoly  patents o monopolies occur if a firm is more efficient or is superior in technology/production  the firm controls an essential facility: a scarce resource rivals need o natural monopoly  the firm can produce the total output of the market at a lower cost than other firms  governments allow monopolies to public utilities o barriers to entry  often it’s the government  patent: an exclusive right granted to the inventor to sell a new product, process, substance, design for a fixed period of time o profit maximization  no close substitutes in the market for a monopoly  monopoly is the price maker  MR=MC still applies  MR curve has twice the slope of monopoly demand curve o deadweight loss: the total surplus that isn’t captured due to an efficient equilibrium not being reached  efficient market: (perfectly competitive) allocation of goods will make it so that the marginal benefit of society is the same as marginal cost  returns to input o increasing: you get more the more you put in  monopolies are like this o decreasing: you get less back each time you put in more


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