Exam 1 Study Guide
Exam 1 Study Guide ECON 3010
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This 7 page Study Guide was uploaded by Emily-Kathryn Hoey on Monday February 22, 2016. The Study Guide belongs to ECON 3010 at Tulane University taught by Benjamin Sperisen in Spring 2016. Since its upload, it has received 67 views. For similar materials see Intermediate Microeconomics in Economcs at Tulane University.
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The content was detailed, clear, and very well organized. Will definitely be coming back to Emily-Kathryn for help in class!
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Date Created: 02/22/16
Exam 1 Review Summary February 22, 2016 • Introduction (Chapter 1) – What is a production possibility frontier (PPF)? Shows all the different combinations of goods a rational individual can produce with fixed resources- as you produce more and more of the alternate good, the opportunity costs increase (diminishing returns & outward curve) ∗ What is opportunity cost? Cost of a unit of good measured in terms of the other goods that must be forgone to obtain it ∗ Given a PPF, how would you calculate opportunity cost? ∗ Opportunity cost of X is change in Y inter terms of Y – What is perfect competition? What is a demand curve? What is a supply curve? Perfect competition: many buyers/sellers, homogenous products, same information, no market power- price takers Demand Curve: graph of demand schedule demand is a function/schedule stating the maximum quantity a consumer is willing & able to purchase at a specific price P, all else equal (ceteris paribus) Supply Curve: graph of supply schedule supply a function or schedule showing the max quantity of a good or service producers are willing to sell at specific price P, ceteris paribus – What is the difference between demand (supply) and quantity demanded(quantity supplied)? Demand vs Quantity Demanded: a change in price causes changes in quantity demand which are movements along the demand curve, changes in demand are population, income change (normal goods- I inc. D inc., inferior goods I inc. D dec.), changes in price of related goods (compliments P* inc., D’ dec., substitutes P* inc., D’ inc.), changes in taste and expectations and cause shifts of the demand curve Supply vs Quantity Supplied: changes in price cause changes in quantity supply which are movements along the supply curve, changes in supply are changes in expectations, prices of resources & related goods, technology, change in # of firms which shift the supply curve – What are the laws of demand and supply? Law of Demand: the higher the price, the lower the quantity demanded Law of Supply: the higher the price, the higher the quantity supplied – Given demand and supply curves, can you find the equilibrium price and quantity? P* where Qd=Qs Graph: – If a price floor/ceiling is imposed, can you find the surplus/shortage that is caused? Price ceiling can cause a shortage Price floor can cause a surplus Graph: 1 • Utility and Choice (Chapter 2) – What is a budget constraint? Straight line representing all combinations of goods that a consumer can obtain at current prices and a fixed income: I=(P )xX) + (P )(y) ∗ How do budget constraints change when income goes up/down? What about when a price of a good goesup/down? When Income goes up/down: upparallel shift right / downparallel shift left When Price of a good goes up/down: uprotates inward around other good / downrotates outward around other good Graph: – Wetake consumer preferences as given, but make three key assumptions about them. What assumptionsarethey? 1) completeness: for every 2 possible bundles, one is preferred over the other or the consumer is indifferent; prevents comparisons of apples to oranges 2) transitivity: if B2 is preferred to B1, and B3 is preferred to B2, then B3 is preferred to B1 3) more is better: suppose X2> X1 & Y2>Y1, then (X2,Y2) is preferred to (X1,Y1) – What is a utility function? How do we use it to represent preferences? Utility function: scores bundles according to how preferred they are – What is an indifference curve? What properties do indifference curves satisfy? Indifference curve: connects bundles between which a consumer is indifferent/has the same utility 1) Downward sloping: because more is better 2) Do not cross: bundles on the same indifference curves have the same utility; bundles on different indifference curves have different utilities 3) Convex to the origin: because of diminishing MRS – What is marginal rate of substitution (MRS)? How can it be stated in terms of marginal utility? MRS: the number of units of Y that must be forgone given an extra unit of X to keep the consumer indifferent MRS= | ΔY/ ΔX| In terms of MU: ΔU(ΔX, ΔY)= MU (X) X MU (Y) Ywhen U=0) ΔY/ ΔX = MU / MU = MRS Y X ∗ How does it relate to indifference curves? MRS is the absolute value of the slope of indifference curves ∗ Generally we have preferences that satisfy“diminishing MRS.” What is the intuition behind this property? Diminishing MRS: MRS decreases as you move from left to right, as one good becomes more scares the consumer needs to be allotted more of the other good to remain indifferent The increasing reluctance to trade one good away reflects the notion that the consumption of any one good can be pushed too far. The conclusion of a diminishing MRS is based on the idea that people prefer balanced consumption bundles to unbalanced ones. The assumption of a diminishing MRS (or convex indifference curves) reflects the notion that people prefer variety in their consumption choices. – Recall the“extreme”indifference curves we discussed. What are they? 2 1) Perfect Substitutes: linear because MRS & MU is constant 2) Perfect Compliments: right angles because MU is zero beyond a point 3) Useless Goods: if Y is useless vertical if X is useless horizontal ∗ Can you give real world examples for which people might havesuch preferences? 1) Gallons of Mobil & Shell 2) Right & Left Shoes 3) Smoke Grinder ∗ Can you give examples of utility functions with such indifference curves? 1) Perfect Substitutes: U(A,G)= 4A+3G put all of income towards good A since higher utility than good G 2) Perfect Compliments: treat both goods as one good and solve for one good in terms of the other using the MRS, so you only have one variable in your budget constraint 3) Useless Goods: U=X if Y is useless; U=Y if X is useless – Fora given consumer with some utility function (and MRS), income, and prices, how do they decidewhichbundletopurchase? The consumer’s goal is to maximize utility given a budget contraint ∗ Can you calculate that bundle? The optimal bundle is where the indifference curve is tangent to the budget constraint, i.e., equal slopes MRS (slope of indifference curve) = P /x (ylope of budget constraint) = MUx/MU =Y/y ∗ Can you depict that bundle graphically with a budget constraint and indifferencecurves? Graph: ∗ If the consumer has “extreme” preferences, you might need a different technique — do you know why? For each “extreme” case, how will you solve it? 1) Useless Good Y: only consume X, where Y=0 X=I/P x 2) Perfect Substitutes: if MRS>Px/Py (IC are steeper than Budget) only consume X if MRS<Px/PY (IC are shallower than Budget) only consume Y 3) Perfect Compliments: Optimal bundle is at a right angle of some IC because people will only consume in pairs – What is a composite good? Composite good: combining expenditures on several different goods whose relative prices doe not change into a single good for convenience analysis We can treat a bunch of goods (Y1, Y2, …, Yn) as one composite good Y to focus on changes with respect to ALL other good X • Demand (Chapter 3) – Given consumer with some utility function (and MRS), income, and prices, do you know how to 3 findtheirdemandcurve? Given U(X,Y), Price of one good, Income, use MRS= P /P soxve yor Y substitute Y in terms of X into I=(P x(X) + (P )(y) solve for X demand of X as a function of Px Example: – Can you compute their demand as their income changes, i.e. give their income consumption curve? Income consumption curve: is the response of demand to income Graph: ∗ What is the difference between a normal and inferior good? Normal good: demand of good increases with income (ICC slopes up with respect to that direction) Inferior good: demand of good decreaseds with income (ICC slopes downward in that direction) – When the price of apples decreases, you feel (a) richer/happier and (b) like apples are relatively cheap to everything else. These effects are called the “income effect” and “substitution effect,” which sum to the “total effect.” ∗ Can you show graphically how to separate theseeffects? Graph: ∗ From the graph, can you tell how to actually (numerically) calculate these two effects? Can you do this in an example? Example: ∗ Is it possible that a good is “so inferior” that when its price increases, the income effect dominates the substitution effect? What is it called? What does its demand curve look like? Giffen good: a good that is so inferior that the income effect dominates substitution effect, a price increases causes more quantity demanded The demand curve is upward sloping- violating Law of Demand 4 – Do you know how to get market demand if you know the individual demand curves of consumers in the market? To construct market demand X(Px), add individual demand curves – Do you know what (own-)price elasticity of demand is? Income elasticity of demand? Cross-price elasticity of demand? How to calculate them? -∞ -1 0 1 ∞ Price elasticity of demand: a measure of change in quantity demanded in response to a change in the good’s own price (generally negative) Calculation: (ΔQ/Q) /(ΔP/P) Midpoint Formula: [(ΔQ)/(0.5*(Q+Q’))] / [(ΔP)/(0.5*(P+P’))] Income elasticity of demand: normal elasticity >0 inferior elasticity <0 Calculation: (ΔQ/Q) /(ΔI/I) Cross-price elasticity of demand: generally expect goods to be more elastic when there are many close substitutes (P’ is the price of a different good) Calculation: (ΔQ/Q) /(ΔP’/P’) • Uncertainty (Chapter 4) – What is expected utility? Given a utility function, incomes and probabilities of different states, can you calculate it? Expected Utility: Eu = (Prob 1(u(C 1)+ (Prob 2(u(C 2)+…+ (Prob )(n(C ))n Expected Income: EC = (Prob )(1 )+1(Prob )(2 )+2+ (Prob )(C n n *For Risk Adverse: Eu(C1,C2)= u(EC) expected utility of gamble/risk < utility of receiving average consumption for certain – How does a utility function for a risk averse person look? Can you give an example? How does this relate to diminishing marginal utility of consumption? 5 It is concave down because it has diminishing marginal returns Eu(C1,C2)< u(EC) Example: ∗ How about a risk neutral person? Risk loving? Risk neutral: doesn’t care about risk, only cares about expected income. Graph is linear, no diminishing marginal utility Eu(C1,C2)= u(EC) Risk loving: prefers risk. Graph is convex up, enjoys every additional increase in utility Eu(C1,C2) > u(EC) – Canyougrapha gambleasa consumption bundle, whereconsumptionineachstateisinterpreted as a “good?” Graph: ∗ If a gamble gives a certain income in all states, where must it lie on such a graph? It must lie on the certainty line where you get the same income in both states – Why can insurance and diversification make risk averse people better off? Can it do the same for risk neutral or risk loving people? (s – What is an actuarially fair insurancepolicy/gamble? Actuarially fair insurance: insurance for which the premium is equal to the expected value of the loss Fair gamble: game with an expected value of zero 6 • Production (Chapter 6) – What is a production function? Production Function: a relationship between inputs and outputs q= f(K,L) Cobb-Douglas Production Function: q= (K )(L ) where α+β=1 – What is an isoquant? (indifference curve) – Production isoquants: curves that show all combinations of inputs that produce a certain level of outputs – What is total product (TP), average product (AP), marginal product (MP)? Total Product (TP): total output Average Product (AP): total output per unit of variable input AP LTP/L Slope of a line from the origin to the corresponding point on the TP graph for some input L output= TP The intersection of the MP Lnd AP cuLves occurs at the maximum height of the AP L Marginal Product (MP): (slope of TP) change in output from one additional unit of input MP =LTP/ΔL – What is the rate of technical substitution (RTS) (MRS)? RTS: the rate at which one input can be substituted for another without a loss of output RTS=ΔK/ΔL= MP /MP L k – What are constant/increasing/decreasing returns to scale? Given a production function, do you know how to check which of these three is thecase? Constant returns to scale: if doubling all of the inputs doubles exactly the outputs Ex: Increasing returns to scale: if doubling all of the inputs more than double the outputs Ex: Decreasing returns to scale: if doubling all of the inputs less than double the outputs Ex: Cobb-Douglas Production function: α+β=1 CRS α+β>1 IRS α+β<1 DRS 7
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