ES_Eco200_UofT_Exam - Eco200 Equation Sheet Microeconomics the study of the allocation of scarce resources Positive analysis – statements that

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Unformatted text preview: Eco200 Equation Sheet Microeconomics - the study of the allocation of scarce resources. Positive analysis – statements that describe relationships of cause and effect. Normative analysis – analysis examining questions of what ought to be, i.e. when we ask questions such as: What is best? Shortage – a situation in which the quantity demanded exceeds the quantity supplied. A shortage puts upward pressure on price as consumers try to outbid one another for existing supplies and producers react by increasing price and expanding output.The price will eventually reach the equilibrium price. ---------------------------------------------------------------- -------------------------------------------------------------- Supply curve – (relates Qs and P) shows the quantity of a good that producers are willing to sell at a given price, holding constant any other factor that might affect the quantity supplied. The response of quantity supplied to changes in price can be represented by movements along the supply curve. any point is equal in magnitude to the slope of the indifference curve. Price elasticity of demand – denoting quantity by Q and price by P, E p = (% ∆Q) / (% ∆P) or E p = ∆Q / Q = P∆Q ∆P / P Q∆P Perfect substitutes – two goods for which the MRS of one for the other is a constant.The indifference curves for these goods will be negatively sloped straight lines. Clothing Other variables that affect supply are production costs, including wages, interest charges, and the costs of raw materials. The response of supply to changes in other supply-determining variables is shown graphically as a shift of the supply curve itself. Demand curve – (relates Qd and P) shows how much of a good consumers are willing to buy as the price per unit changes. The phrase change in quantity demanded refers to movements along the demand curve Other variables that affect demand are income, preferences, prices of other goods. The phrase change in demand refers to shifts in the demand curve. Food ( %∆Q means “percentage change in Q” and % ∆P means “percentage change in P”) Price elastic - When E > 1 , we say that p demand is price elastic. price inelastic - When E p < 1 , we say that Inferior good– (relates Qd and I) when an increase in income decreases demand x y Complements– (relates Qd and P ) when an increase in the price of y decreases demand of good x. x y Substitutes– (relates Qd and P ) when an increase in the price of y increases demand of good x. Market mechanism – the tendency in a free market for the price to change until the market clears – i.e. until the quantity supplied and the quantity demanded are equal. Surplus – a situation in which the quantity supplied exceeds the quantity demanded. To sell this surplus (or to prevent it from growing) producers will begin to lower prices.As the price falls, quantity demanded will increase and quantity supplied will decrease until the equilibrium price is reached. Clothing demand is price inelastic. Income elasticity of demand – the percentage change in quantity demanded, Q, resulting from a 1% increase in income, I. EI = ∆Q / Q I∆Q = Q∆I ∆I / I Food Cross-price elasticity of demand – percentage change in the quantity of one good resulting from a 1% increase in the price of another. E X ,Y = PY ∆Q X ∆Q X / Q X = ∆PY / PY Q X ∆PY ----------------------------------------------------Normal good– (relates Qd and I) when an increase in income increases demand Perfect complements – two goods for which the MRS is infinite. The indifference curves are shaped as right angles. Indifference curve – represents all combinations of market baskets that provide a person with the same level of satisfaction. Indifference map – graph containing a set of indifference curves showing the market baskets among which a consumer is indifferent. Utility function – a formula that assigns a level of utility to each market basket. For example, a utility function for food (F) and clothing (C) could be: u( F , C ) = F + 2 C . Budget line – all combinations of goods for which the total amount of money spent is equal to income. For example: PF F + PC C = I . The slope of the budget line is the negative of the ratio of the prices of the two goods. That is: ( − PF / PC ) with F on the horizontal axis, C on the vertical axis. Satisfaction in maximized when the marginal rate of substitution (of F for C) is equal to the ratio of prices (of F to C): MRS = PF / PC Marginal utility (MU) – the additional satisfaction obtained from consuming one additional unit of a good. Clothing U3 U2 U1 Food Marginal rate of substitution (MRS) – The MRS of good X for good Y is the amount of Y that a person is willing to give up to obtain one more unit of X. Measures the value that an individual places on 1 extra unit of a good in terms of another. The MRS of food F for clothing C is: MRS = − ∆C / ∆F . The MRS at Diminishing marginal utility: As more and more of a good is consumed, consuming additional amounts will yield smaller and smaller additions to utility. Equal marginal principle: Utility maximization is achieved when the consumer has equalized the marginal utility per dollar expenditure across all goods. For food F and clothing C: MU F = MU C . PF PC We’ve helped over 50,000 students get better grades since 1999! Need help for exams? Check out our classroom prep sessions - customized to your exact course - at Income and Substitution Effects A fall in the price of a good has two effects: Substitution effect - Consumers will tend to buy more of the good that has become cheaper and less of those goods that are now relatively more expensive. Income effect - Because one of the goods in now cheaper, consumers enjoy an increase in real purchasing power (They can buy the same amount of goods for less money and thus have money left over for additional purchases). The total effect of a change in price is given by: Total Effect = Substitution Effect + Income Effect Income and substitution effects: Normal goods Clothing (units per month) Average product – output per unit of a particular input. Total cost (TC) – total economic cost of production, TC = FC + VC. Increases with output. Marginal product – additional output produced when an input is increased by one unit. Average product of labour = output/labour input = Q/L Marginal cost (MC) – increase in cost due to the production of one extra unit of output. Marginal product of labour (MPL) = Change in output/change in labour input = ∆Q / ∆L AP = MP are equal when average product reaches its maximum. When MP > AP, average product is increasing. When MP < AP, the average product is decreasing. Law of diminishing marginal returns: As the use of an input increases, with other inputs fixed, the resulting additions to output will eventually decrease. A B SE I IE U2 U1 Food (units per month) Substitution effect – the change in consumption of a good associated with a change in relative price, with the level of utility held constant. Income effect – change in consumption of a good resulting from an change in purchasing power, with relative prices held constant. ---------------------------------------------------------------- -------------------------------------------------------------Marginal rate of technical substitution (MRTS) – amount by which the quantity of one input can be reduced when one extra unit of another input is used, so that output remains the same: MRTS = − ∆K / ∆L (for a fixed level of Q ) The slope of the isoquant is given by the MRTS with the negative sign removed. Marginal product of labour (MPL)– additional output per unit of additional labour. Marginal product of capital (MPK)– additional output per unit of additional capital. Production function – shows the highest output that a firm can produce for every specified combination of inputs.Describes what is technically feasible when the firm operates efficiently. If there are two inputs: labour L and capital K, then we can write the production function as: Q=F(K, L) . Increasing returns to scale – output more than doubles when inputs are doubled. Average total cost (ATC) – firm’s total cost divided by it’s level of output. ATC = TC / Q or ATC = AFC + AVC w Average fixed cost (AFC) – fixed cost divided by level of output: AFC = FC / Q Average variable cost (AVC) – variable cost divided by level of output: AVC = VC / Q Isocost line – shows all the possible combinations of labour and capital that can be purchased for a given total cost. The isocost line is given by: C = wL + rK . It has a slope of: ∆K / ∆L = − ( w / r ) -------------------------------------------------------------Cost Minimization: To produce Q1 at minimum cost, we select the combination of K and L such that the isocost curve is tangent to the isoquant Q1. Producing a Given Output at Minimum Cost Capital per year -------------------------------------------------------------- Isoquant – curve showing all possible combinations of inputs that yield the same output. MC = ∆VC / ∆Q = ∆TC / ∆Q Isoquant map – graph combining several isoquants, used to describe a production function. Short run – period of time in which one or more production factors cannot be changed. Fixed input – the production factor that cannot be varied (in the short run). Long run – the amount of time needed to make all inputs variable. ( MPL ) / ( MPK ) = − ( ∆K / ∆L ) = MRTS Returns to scale – rate at which output increases as inputs are increased proportionately. Constant returns to scale – output doubles when inputs are doubled. Decreasing returns to scale – output less than doubles when inputs are doubled. -------------------------------------------------------------Fixed cost (FC) – cost that does not vary with levels of output. Can be only be eliminated by going out of business. Variable cost (VC) – cost that varies as output varies. Increases with output. K1 A Q1 C1 L1 Labour per year When a firm minimizes the cost of producing a particular output: MRTS = MPL / MPK = w / r -------------------------------------------------------------------Game – any situation in which players (the participants) make strategic decisions that take into account each other’s actions and responses. Payoff – outcome of a game that generates rewards or benefits for the player. - For price-setting firms, the payoffs are profits. Strategy – rule or plan of action for playing a game. Optimal strategy – strategy that maximizes a player’s expected payoff. ---------------------------------------------------------------- Our Course Booklets - free at prep sessions - are the “Perfect Study Guides.” Need help for exams? Check out our classroom prep sessions - customized to your exact course - at Cooperative game – game in which players can negotiate binding contracts that allow them to plan joint strategies. Non-cooperative game – game in which negotiation and enforcement of binding contracts between players is not possible. Nash equilibrium is a set of strategies (or actions) such that each player is doing the best it can given the actions of its opponents (I’m doing the best I can given what you are doing. You’re doing the best you can given what I am doing) Pure strategy – strategy in which a player makes a specific choice or takes a specific action. Some games do not have any Nash equilibria in pure strategies. Mixed strategy – strategy in which a player makes a random choice among two or more possible actions, based on a set of chosen probabilities. All games have at least one Nash equilibrium in mixed strategies. people or two inputs between two production processes. Each axis describes the number of units of one of the goods. The length (height) of the horizontal (vertical) axis is the total number of the good available. Each point in the box describes the market basket of both consumers. Contract curve – shows all efficient allocations of goods between two consumers, or inputs between two production functions. Given by all the points of tangency between the indifference curves of the two consumers. First theorem of welfare economics: If everyone trades in the competitive marketplace, all mutually beneficial trades will be completed and the resulting equilibrium allocation of resources will be economically efficient. Utility possibilities frontier – shows the levels of satisfaction that each of two people achieve when they have traded to an efficient outcome on the contract curve. Moral hazard – occurs when an insured party whose actions are unobserved affects the probability or magnitude of a payment associated with an event. For example, if my home is fully insured against theft, I may be less diligent about locking doors when I leave, and I may choose not to install an alarm system. An agency relationship exists whenever there is an arrangement in which one person’s welfare depends on what another person does. The agent is the person who acts. The principal is the party whom the action affects. Principal-agent problem – problem arising when (agents) pursue their own goals, even when doing so results in lower profits for the principal. w -------------------------------------------------------------Externality – action by either a producer or consumer, which affects other producers or consumers, but is not accounted for in the market price. Can be negative: when the action of one party imposes costs on another party. Can be positive: when the action of one party imposes benefits on another party. ---------------------------------------------------------------Interest rate – the rate at which one can borrow or lend money. Bond – contract in which a borrower agrees to pay the bondholder (lender) a stream of money. Perpetuity – a bond paying out a fixed amount of money each year, forever. Net present value (NPV) criterion: Invest if the present value of the expected future cash flows from an investment is larger than the cost of the investment. Suppose a capital investment cost C and is expected to generate profits over the next 10 years of amounts π 1 , π 2 ,..., π 10 . We write the net present value as NPV = −C + π1 (1 + R) + π2 (1 + R) 2 +L+ π 10 (1 + R)10 where R is the discount rate. The firm should make the investment only if NPV > 0. ---------------------------------------------------------------Exchange economy – market in which two or more consumers (or countries) trade two goods among themselves. Efficient allocation of goods – an allocation such that no one can be made better off without making someone else worse off. Also called Pareto efficiency. Edgeworth box – diagram showing all possible allocations of either two goods between two Social welfare function – weight applied to each individual’s utility in determining what is socially desirable. The utilitarian social welfare function weights everyone’s utility equally and thus maximizes the total utility of all members of society. Second theorem of welfare economics: If individual preferences are convex, then every efficient allocation (every point on the contract curve) is a competitive equilibrium for some initial allocation of goods. Marginal external cost (MEC) – increase in cost imposed externally as one or more firms increase output by one unit. -------------------------------------------------------------- Marginal social benefit (MSB) – sum of the marginal private benefit and the marginal external benefit. MSB = MB + MEB Comparative Advantage – country 1 has a comparative advantage over country 2 in producing a good if the cost of producing that good, relative to the cost of producing other goods in 1, is lower than the cost of producing the good in 2, relative to the cost of producing other goods in 2. Absolute advantage – country 1 has an absolute advantage over country 2 in producing a good if the cost of producing the good in 1 is lower than the cost of producing it in 2. -------------------------------------------------------------Adverse selection – arises when products of different qualities are sold at a single price because buyers and sellers are not sufficiently informed to determine the true quality at the time of purchase. Too much of the low quality product and too little of the high quality product are sold. Marginal social cost (MSC) – sum of the marginal cost of production and the marginal external cost. MSC = MC + MEC Marginal external benefit (MEB) – increased benefit that accrues to parties as a firm increases output by one unit. -------------------------------------------------------------Public good – any good that is both nonexclusive and nonrival. Nonrival good – the marginal cost of its provision to an additional consumer is zero. For example, a highway during a period of low traffic volume. Because the highway already exits and there is no congestion, the additional cost of driving on it is zero. Non-exclusive goods – goods that people cannot be excluded from consuming. It is difficult or impossible to charge for their use. For example, national defense. Free-riders – consumer or producer who does not pay for a nonexclusive good in the expectation that others will. Our Course Booklets - free at prep sessions - are the “Perfect Study Guides.” ...
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This note was uploaded on 04/10/2010 for the course ECO ECO200 taught by Professor Carlosserrano during the Spring '10 term at University of Toronto- Toronto.

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