Study Guide for MT1
Study Guide for MT1 FIN 501
Popular in Financial Economics
Popular in Finance
This 3 page Study Guide was uploaded by D S on Tuesday October 20, 2015. The Study Guide belongs to FIN 501 at University of Illinois at Urbana-Champaign taught by Tatyana Deryugina in Summer 2015. Since its upload, it has received 91 views. For similar materials see Financial Economics in Finance at University of Illinois at Urbana-Champaign.
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Date Created: 10/20/15
Formulas Utility Maximization Problem UMP maxmyum ystpma pyy 3 mac y 2 0 Consumer decision theory Utility Maximization w Budget Constraint Utility Maximization Problem UMP maxmyum ystpma pyy 3 mac y 2 0 Optimal point is point of tangency between the budget line and an indifference curve How to Solve UMP algebraically wo LaGrangian slope of budget line pmac pyy mz Z slope of indifference curve 8U1y 3Uwy 8 y The reason for the slope to be equal is that if Usepm lt Uypy then the consumer should spend more on x and less on y since x provides more utility per dollar Practice Problems on this 211 217 Readings 219 From utility maximization to demand curves Demand Function functions of budget constraint and prices Change in wealth m will shift the demand curve up and right or down and left Income and substitution effects De nitions Substitution effect effect of the change 11 relative prices of the goods Way to measure demands response to changes consumer remains on the same indifference curve but faces the new prices Income or wealth effect effect of the change in the size of the consumer s budget set choice when a the consumer faces the new prices on the new postprice change indifference curve and b the consumer faces the new prices on the old preprice change indifference curve Reason people care about them 0 while theoretical concepts lawmakers like to compensate people for price increases 0 people strictly better off if you give people just enough to afford original bundle Readings 35 36 Elasticities 390139 Impact api Elasticity unit free measure of the impact of a change 3 z In some factor 1 Income Elasticity of demand for x 83 m 8pma 0 Normal 77 gt 0 Inferior 77 lt 0 0 Luxury 77 gt 1 Necessity 77 lt 1 2 Own Price Elasticity of demand for x 3 0 89 pw 8pw a 0 generally neg DIVERSIFICATION 0 Elastic demand gt 1 o Inelastic demand lt 1 0 Unit Elastic demand e 1 o Giffen Good 5 gt 05 o Perfectly Elastic at line a 2 oo o Perfectly Inelastic Vertical line a 0 4 Cross price Elasticity of demand for x with respect to y 390 py pr a o o Substitutes 7790103 gt 0 o Complements 7790103j lt 1 0 these are technically gross since complements include income effects 0 make sure understand graphs on 233 o if y is a substitute for x and py increases x shifts out o if y is a complement for x and py increases then demand shifts in LeChatelier Effect people adjust more in the long run than the short run Practice Questions 232 Normal versus inferior goods Normal Good A normal good is a good with an income elasticity greater than 0 That means that an increase in m increases the quantity demanded of a good Video Slides 73 Inferior Good An inferior good is a good with an income elasticity smaller than 0 That means that an increase in m decreases the quantity demanded Status Good Veble Video Slides 74 Practice Problems PS14 38 Readings 39 310 316 Firm behavior The production function returns to scale FK L K capital L labor Purpose tells how many units of output are produced from K capital and L labor 0 greater inputs produce more output 0 isoquants move up and right output increases Marginal Product amount by which output increases M PK 2 WMPL frequent assumption declining marginal product as you produce more marginal 2 2 benefit decreases a gEK a 3 lt Ola gfL a Fag lt 0 Marginal Rate of Technical Substitution MRTS substitutability between inputs IE small changes its the slope of the isoquant MRTS Z IE 113 1 Compute slope of diff Q1 FK L gt dQl g gdK g de How to compute 8F 2 Set to 0 35 gL 44113 MRTS 8K Return to Scale captures how efficiently production can be scaled up Constant Return to Scale a 7 1 FaK aL aFK L Increasing Return to Scale a 7 1 FaK aL 7 aFKL Decreasing Return to Scale a 7 1 FaK aL 7 aFK L Can have different RTS at different output levels IRS for low Q not great use of capital DRS for high Q overtaxing capital CRS is used as a benchmark since IRS too small rm industry and DRS some factor blocking replication Practice Problem 333 334 isoquant curve connection combinations of K and L that produce the same output Q Technological Progress ceteris paribus assumption in production is that the technology remains xed FKL will change with new technology can isoquants that represent two different technologies cross Yes no constraints For the same technology they cannot cross bc one has to be strictly greater Practice Problem PS22 Pro t maximization cost function gives the cost of the least expensive method of producing a particular level of output price taking assumption is necessary for a perfectly competitive market to work well Practice Problem 14 Cost minimization cost of LK w L v K C minLKwL vatFK L 2 Q rms want to minimize cost cost function vK wL C Cost Function Cwv Q wLwv Q vKwv Q How to Solve 1 FK L Q MPL w 2 MRTS slope of the isocost IMPK v Again you want the point of tangency between the isocost curve and production FLK isoquant MLPL gt MLPK need to reduce cost by using more capital and les labor MLPL 2 PK 2 Marginal Cost cost of producing a little more output isocost curves lines with slow 2 1 1 Practice Problems 43 Fixed versus variable costs Fixed Costs mostly unavoidable month month leases on of ces cost of janitor Variable Costs always avoidable Unavoidable Fixed costs should not affect decision making since already a sunk cost Readings 413 Average versus marginal costs Average costs only tell whether a rm is making money or not Marginal Cost s tell whether you make more money by changing the output Long run versus short run Long term all costs are avoidable Short Run some xed costs are avoidable and others are not If you have avoidable xed xed costs shut down can be an attractive option From pro t maximization to supply curves rms need to think about things on the margin Should I produce another unit 1 marginal bene ts sell it at p 2 marginal costmarginal cost at current Q MCQ 3 produce another unit if p L mCQ If rms produce a positive quantity it produces Q where p 2 MC if multiple Q s where P MCQ need to check to see if its positive Practice Problem 417 Supply Elasticities rms responsiveness to chanes in price 5 changeianupplied BS P 5 17 changeinP BS 625 0 positive quantity supplied rises with price 0 high values small changes have large Q changes gt Elastic 0 low values small changes min Q changes gt Inelastic 0 Perfect Elastic Supply horizontal constant MC CRS 0 Perfect InElastic Supply vertical supply xed Determinants of Supply Elasticity 0 Technology 0 Timing 0 Input Supplies 0 Number of rms and ease of entry and exit Accounting pro t versus economic pro t Economists think about the opportunity cost in what you had to give up to take the job Opportunity Cost is the value of the asset in its best alternative Labor wage or pay per hour in the next best alternative Capital Costs accountant use a deprecation rule base on historical cost Economists use rental rate which includes the normal return Notes that s how we ve been looking at problems with MRS how many apples to get an orange MRTS how much capital if reduced spending on labor Markets bring two sides together Assumptions of the competitive model 0 Homogeneous private product 0 Firms and consumers take prices as given 0 Firms maximize pro t consumers maximize utility 0 Perfect information 0 NO transaction costs Gains from trade and arbitrage Arbitrage with Price Discrimination 1st They ae playing their full willingness to pay so yes low value people are incentivized to sell to high value people 2nd people self selected and thus the chose exactly where they wanted to be yes if the low fee manages to sell to the high fee if the school doesn t stop them Perfect Competition Price taking assumption implies that individuals do not think their actions will affect prices and also that they don t think others actions will affect prices Goods are homogeneous entry exit is easy and rms are price takers Equilibrium of supply and demand equilibrium is a pair QP st at P SP DP Q at this price the markets are clean since consumer are willing to buy all that producers are willing to sell Short run versus long run If the supply of a particular security is xed in the short run vertical line th only the price will change but the quantity will remain xed In the short run the number of rms is xed Firms may earn a pro t which is the MC ACQ This is temporary In the long run rms may adapt its technology and inputs to t market conditions They will produce output level for which price is equal to their long run MC Also rms can enter or exit p i min AC rms make negative pro t and thus rms will exit p L min AC rms make positive pro t and thus rms will enter go until p min AC when rms make zero pro t note if all rms are identical they earn zero pro t in the LR competitive equilibrium if rms have lower costs than other then they will earn positive pro ts zero pro t applies to the marginal rm entries continues until the marginal rm is just indifferent between entering and not Practice Problem 510 Consumer and producer surplus Consumer Surplus extra bene t that consumers receive by being able to make market transactions at the prevailing price How to calculate basic case area under the demand curve left of Q less the total payment the consumers make to producers Producer Surplus excess of revenue over variable economic cost of producing Q units and selling them at P Its the area above the supply curve and does not include xed costs so a positive PS but negative pro t Total value created by all market participants is PS CS Deadweight loss reduction in overall ef cient Perfect Price Discrimination ef cient with no dead weight loss CS 2 0 Q unites are still exchanged Price Controls causes deadweight loss Qm Q so this distortion in qty leads to DWL x it no price ceiling but producers pay consumer a cost Minimum Wage same sort of issue there will be a reduced qty and there will be deadweight loss if demand is perfectly inelastic there will be no reduction in employment Tax incidence Ef cient market has price consumers pay 2 price producers receive not true when there are taxes t acts like a per unit increase in costs there is dead weight loss with taxation since the quantity is distorted but this DWL is revenue for the government Why it doesn t matter who gets tax The same amount of revenue is collected even if the consumer has to mail in checks It s more convenient to tax producers though Tax vs Subsidies subsidy acts like a reverse tax it increases supply because the essential cost f supplying the goods has declined 1 st and 2 nd Theorems of Welfare Economics 1st Theorem of Welfare Economics any competitive equilibrium leads to a Pareto ef cient allocation of resources Pareto Optimal no other allocation that can make one participant better off without making another participant worse off 2nd Theorem of Welfare Economics that any ef cient allocation can be sustainable by a competitive equilibrium General versus partial equilibrium Intertemporal Choice and Risk Intertemporal involving different points in time focus on the general pattern of consumption income savings over time less concerned with trade offs among goods within periods Saving and borrowing Investments Min price we care about is the interest rate which relates to general price level today and tomorrow UC0C391 lifetime utility 2 Period Time 1 Period 0 current Period 1 future period p0 1p1 m if r increases then p1 decreases Intertemporal UMP max uC390 C1 st Co S m if you hav Co today and you save m Co and invest that money into r C1 m Co1 7 optimal point is the tangency between the indifference curves for UC390 Cl and the budget line aUaoo 01 BU801 1rm Co 17 Know the substitution and income effects and total effect from an increase or decrease in r MRS 2 price ratio since consumption is a normal good this consumer will spend all money Budget Line 2 p000 p1 C1 m Practice Problem 1111 Choices over time discounting Timing of Income whether the consumer is impatient Fisher s Separation Theorem If the consumer can borrow and save at the same interest rate then consumer maximizes utility by choosing the income stream with the highest present value regardless of his utility function Discounting 6 captures people impatience bc people would prefer to consumer today instead of tomorrow Investment Fisher s Theorem rate of saving and borrowing are different May force someone to take a job instead of going back to school Thus improving capital markets could lead to Pareto improvement Capital markets prevent people from investing NPanest gt NPVdont Choices under uncertainty Expected Value 2521mm underline expected utility that denotes a person s utility function for money as uw 25173de Risk Averse always prefer the certain outcome as opposed to an uncertain lottery with the same expected value Risk Neutral indifferent between a certain outcome and any lottery with the same expected value A risk neutral decision maker tries to maximize expected value Risk Loving take the risky situation prefers an uncertain lottery to getting the lottery s expected fo sure Risk characteristics and types of curve risk averse strictly concave uw CE i EV risk neutral linear uw CE 2 EV risk loving convex uw CE L EV Note that the concavity can change across different regions in that it s not one or another Certainty Equivalent amount of money that individual is indifferent between the lottery and the money underlineRisk Premium 2 EV CE what individual would pay to have EV instead of lottery EUL uCE u EV RP Absolute Risk Aversion TAw ulw Relative Risk Aversion u w TRw w 26111 Readings 915 Practice Problems 918 Portfolio final wealth in state s wazlmzsai expected payoff from the portfolio a1a2 an 221p3Uwazlmisaz st a1 a2 a3 1 always optimal to put money in the risk free asset Practice problem 936 Externalities and Public Goods Public Good goods that are non excludable and non rival can t stop people from using it and multiple people can enjoy it at once military radio knowledge Public Good exhibit positive externalities since under provided Free riding people who didn t pay for public good can still enjoy it Common Good goods that are non excludable and rival non toll roads sh in international waters public land common good exhibit negative externalities since over consumed Reading 644 PS34 Imperfect Information Moral hazard and adverse selection Used these terms in discussion of insurance with what you re supposed to ask 1 Expected Loss 25 chance of losing 20K so 20K 4 5K 2 Pay a premium of 105 Compare utility ith insurane 3 Max amount to play for full plugging pmaac to EU 4 Why diversify risk through risk pooling and risk spreading LLN 5 Will market exist WTP high enough to cover costs Practice Problem V19 adverse selection those who buy insurance are those who are more likely to need it sick people have greater demand moral hazard when people are insured they take risky actions they otherwise wouldn t take building homes where there are hurricanes Other forms of competition High Barrier Low Barrier High Div Monopoly Mono competition Low div CournotOligopoly Perfect Monopoly Monopolistic Competition situations where there are many firms and low barriers to entry but products are somewhat differentiated so each firm has some market power by recipe location no strategic effects Optimal price sets MR 2 MC an if P L AC in the short run firms earn a positive profit positive profit is really a rent to have rights to the valuable technology assets Oligopoly there are significant barriers to entry and thus small number of firms can have identical or differentiated firms in the case of identical firms Bertrand firms choose what price to charge note this reduces down to the competitive outcome so everything at the same price where P 2 MC Cournot Cournot Sample Problem PS51 156 Reaction Function players reaction function gives its optimal strategy choice as a function of the other player s strategy choice Nash Equilibrium Cournot Game is where the firms reaction functions intersect Stackelberg Cournot game where players are moving sequentially Player 1 is called first mover advantage Practice Problem 1531 Price Discrimination charging different prices to different consumer 0 First charging each consumer his willingness to pay 0 Second offering menu of option and have consumers self select 0 Third charging diff prices to diff type of consumers based on an observable characteristic First Degree Perfect monopolist can observe each individuals willingness to pay for the product Impact profit is equal to max total surplus Feasible No require way too much information like FAFSA Depending on how well sellers gauge buyer s could be better or worse Practice Problem 819 Second Degree rm knows diff consumers but cannot identify them illegal to identify thus have consumers self select quantity price or quality price bundles Third Degree different prices to different groups of consumers based on an observable characteristic How to solve 1 Pro t P1 q1q1 p2q2q2 Cql q2 2 TO max take the partial derivative of q1 an qg 3 Set MR1 and MR2 2 MC the MR are the same else sell more one group 4 If price discrimination is allowed then you solve for the different price 5 If price discrimination not allowed then add quantities and solve for price since it s the same for both Practice Problem V177 Game Theory too for analyzing strategic problems Strategy study of situations in which the participants benefits depend on others actions start needing to think about how players decisions affect your own Practice Problem 132 Two Tiered Offer Practice Problem 139 Nash Equilibrium each party s strategy is a best response to what his rial is doing stable strategy Maxmin play when there is little guidance which eq Reading 137 Decision Tree Corporate Raider corporate Raider is deciding whether to attempt a hostile takeover of a Target company Sequential Move Games Practice Problem Simultaneous move games Penalty Shot Players shooter and goal keeper Actions kick left or right OR defend left or right Payoffs entries in the grid represent utilities just the expected value Nash Equilibrium randomizing strategies Practice Problem GS1 Prisoner s Dilemma Dominant strategy is to both defect as well s Nash Equilibrium Coast THeorem there are clear property rights and enforcement of contracts then negotiation leads to efficient outcomes like CC Ways to Solve it creating laws and enforcing penalties Chicken no dominant or dominated strategies if rival choose R best to choose R if rival chooses L best choose L stable Nash is RR and LL
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