Condensed Notes Part 1

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Department
Stern Economics
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ECON-UB 1
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All

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Kevin Jin 1 ECON-UB 1 Pre-Exam 1 Notes Basics • Positive analysis: statements that describe the relationship of cause and effect o Deal with explanation and prediction o E.g. these eggs costs $2 per dozen • Normative analysis: analysis examining questions of what ought to be o Often supplemented by value judgments o E.g. these eggs should only be $1.75 per dozen • Market: collection of buyers or sellers, through their actual or potential interaction, determine the prices of products • Price: signal to agents when making decisions o Market clearing price: price when quantity demanded equals quantity supplied o Nominal price: absolute or current dollar price of a good or service when it is sold  This is the price that a transaction went for o Real price: relative to an aggregate measure of prices or constant dollar price  This price must be calculated from nominal price  CPI: measures aggregate prices, i.e. a metric of inflation Real price= CP Ibase ye∗Nominal pric e  CPI current year current year • E.g. base year is today, price of current year is price we want to convert  Think of it as the nominal price of the base year, so that the ratio of the nominal price of the base year to the nominal price of the current year is equal to the ratio of the CPI of the base year to the CPI of the current year • Market mechanism: tendency in a free market for price to change until market clears o Surplus: excess supply  Market price is above equilibrium Kevin Jin 2 ECON-UB 1 Pre-Exam 1 Notes  Downward pressure on price until equilibrium is reached  Quantity demanded increases and quantity supplied decreases  Minimum wage is one way of government intervention that causes surplus, as well as taxes and subsidies o Shortage: excess demand  Market price is below equilibrium  Upward pressure on prices until equilibrium is reached  Quantity demanded decreases and quantity supplied increases  Rent controls is one way of government intervention that causes shortage, as well as taxes and subsidies o Relative size in direction of change and shape of supply and demand curves determine impact on equilibrium price and quantity • Types of good o Normal: ↑income↑demand, ↓income↓demand o Inferior: ↑income↓demand, ↓income↑demand o Luxury: ↑income↑↑demand Consumer theory • Demand graphs quantity vs. price but axes are transposed (price is on Y axis, quantity on X axis) o Negative slope, convex o Change in quantity demanded: movement along curve caused by a change in price  I.e. ΔP o Change in demand: shift of the curve caused by a change in something other than the price of a good  E.g. ΔI , change in tastes, cheaper substitutes, more expensive complements • Price elasticity of demand: The % change in demand induced by a 1% change in price Kevin Jin 3 ECON-UB 1 Pre-Exam 1 Notes dQ ∗P o Ed= dP Q o Measures sensitivity of quantity demanded with respect to a change in price o Slope of demand curve at a point  Relatively elastic: steep slope,1 • Decreasing the price increases revenue E <1  Relatively inelastic: flat slope, • Increasing the price increases revenue ∣ d=1  Unitary elastic:  Perfectly inelastic:d=0 • Constant demand no matter the price, e.g. “necessities” ∣ ∣=∞  Perfectly elastic:d • Demand goes to 0 when price is changed, e.g. price takers ∣ dk∀ P  Isoelastic: dQ k∗Q = • Demand curve is concave, not linear, becausdP P • Axioms of rational choice o Completeness: If A and B are any two situations, an individual can always specify exactly one of these possibilities: A is preferred, B is preferred, or indifferent  A ≽ B⊕B≽ A⊕ A B o Transitivity: If A is preferred to B and B is preferred to C, then A is preferred to C Kevin Jin 4 ECON-UB 1 Pre-Exam 1 Notes A ≽ B ∧B≽C ⇒ A≽C  o Continuity: If A is preferred to B, then situations suitably “close to” A must also be preferred to B  A≽ B ∧C≈ A⇒C ≽ B o Strict monotonicity: more is better o Strict convexity: averages are preferred to extremes x1+x 2 y1+y 2 x1+x2 y1+y 2  ( , )≽ ( 1 y 1 ( , )≽ ( 2 y2) 2 2 2 2 • Perfect substitutes – consumer does not prefer one good over the other o Slope of indifference curves is constant along entire curve, i.e. straight line o Indifference map consists of parallel straight lines whose slopes are the MRS • Perfect complements Slope of indifference curve is∞ at some points and 0 at others, meeting at a right angle at a Q=kP line • Bads are accounted for in preference analysis by redefining the commodity: o Air pollution  clean air o If both goods are goods, then slope is negative and graph is convex. Utility increases up and right o If a bad is on the y-axis and a good is on the x-axis of an indifference curve, then slope is positive and the graph is convex. Utility increases down and right o If bads are on both the x and y-axis, then the slope is negative and the graph is convex but the utility increases down and left o If a good that we’re entirely indifferent to is on y-axis, then the slope is infinity o If a good that we’re entirely indifferent to is on x-axis, then the slope is 0 • Utility functions Kevin Jin 5 ECON-UB 1 Pre-Exam 1 Notes o Utility rankings are ordinal but not proportional. Do not have any meaning of intensity but can be used to determine relative desirability x1 • Marginal utility: extra utility obtained from slightly more when other factors are held constant ∂U o MU = 1 ∂x 1 x ,…,x o Extra utility obtainable from more 1 n is ∂U=M U Δx 1…+M1 Δx n n ∂U= ∂U dx +…+ ∂U dx  ∂x 1 1 ∂xn n • Marginal rate of substitution (of good x1 for good x2 ): number of good x2 that consumer is willing to give up to obtain an additional unit of good , while maintaining same level of utility M U 1 −dx 2 o MRS 1 2 = ∣ M U 2 d x1 U=U x x  MRS is equal to ratio of marginal utility of1 to marginal utility of2 and is also equal to negative slope of indifference curve when utility is constant (which must be true of any indifference curve) • Cobb-Douglas utility function: each good has a weight, percentage of total utility α β o U ( 1x =2 x 1 2 α,β>0  and are constant • Perfect substitutes utility function:x(,1 =2)x +β1 2 M U 1 α o MRS 1 2 M U = β 2 Kevin Jin 6 ECON-UB 1 Pre-Exam 1 Notes U ( 1x =2)n α x{,β 1 2} • Perfect complements utility function: 0 α x1>βx 2 o MRS x12= { ∞ α x <1x 2 x x • Budget set: combination of good 1 and 2 such that the total price is less than the consumer’s income o (x1,x 2) ({x1:I≥2) p +x1p 1 2 2} x x o Budget line: maximizes quantity of 1 and 2 by utilizing all income I=P x1+1 x 2 2   Increase in income with constant price causes budget line to shift outward parallel to original line x x  If graphing the indifference curve with 2 on y-axis and 1 on x- axis: x • A decrease in the price of 1 will cause the slope of the budget line to decrease and pivot from a constant y-intercept (larger quantity of x 1 ) x2 • An increase in the price of will cause the slope of the budget line to decrease and pivot from a constant x-intercept (smaller x quantity of 2 ) dx 2 −p 1 • Slope of budget line, = , is the rate at which x1 and dx 1 p2 x 2 can be substituted without changing amount of money spent I=P x1+P1x 2 2 • Utility maximization: maximize utility subject to the budget constraint o Indifference curve is tangent to budget line Kevin Jin 7 ECON-UB 1 Pre-Exam 1 Notes o Therefore slope of indifference curve is equal to slope of budget line d x2 −p 1 −p 1 M U 1 p1 ∂U /∂x 1 p1  d x ∣ = p ⇔−MRS x12= p ⇔ M U = p ⇔ ∂U /∂x = p 1U=U 2 2 2 2 2 2 x x I p o “What amount of 1 and 2 maximizes utility with income? 1 and p2 are constant.”: ∂U x(,1 /∂2 1 p1  Solve for x 1 )2 or x2( 1 : rearrange = , the ∂U x(,1 /∂2 2 p2 utility maximization condition, where U ( 1 x2) is the utility function x (I) x (I) x x x x  Solve for 1 or 2 : substitute 1( 2 or 2( 1 into U x ,x I x ( 1 2) , the production function, and simplify to get ( )1 or −1 −1 I( 2 . x 1 =I ( 1 and x2I =I ( 2 o Marshallian demand: optimal value ¿ ¿ x 1x p1( 1 ,2I ,)x 2x p2( 1 , 2 )  E.g. α β • Maximizing Cobb-Douglas U x(,1 =2)x 1 2 : α−1 β ∂U /∂x 1 p1 α x1 x2 p1 o Solving systems of equations ∂U /∂x = p ⇔ α β−1= p , I=p 1 1p x2 2 2 2 β x1x 2 2 ¿ I ¿ I x 1α ,x 2β  ( p1 p2) • Substitution effect: change in item’s consumption associated with change in price of item, with utility constant o ↓price↑quantity Kevin Jin 8 ECON-UB 1 Pre-Exam 1 Notes • Income effect: change in item’s consumption associated with a change in purchasing power, with price constant o Purchasing power is either directly related to income inversely related to income depending on whether item is a normal or inferior good o Normal good: ↓income↑quantity o Inferior good: ↑income↑quantity  Never outweighs substitution effect • Budget line remains the same when income and all prices change by the same factor k∗I k∗p I p x 2 − 1x1⇔x =2 − 1 x1 o k∗p 2 k∗p 2 p 2 p2 • Income Consumption Curve o Applicable for a plot ofx1 (x axis) vs x2 (y axis) o Connects the utility maximizing market basket (i.e. tangent of budget line and indifference curve) for each income level (i.e. parallel budget lines) x1 o Positive slope means good is normal o Negative slope means good x1 is inferior x1 o Income consumption curve can bend on itself so that good can be normal and inferior depending on the point • Price Consumption Curve o Applicable for a plot ofx1 (x axis) vs x2 (y axis) o Connects the utility maximizing market basket (i.e. tangent of budget line and indifference curve) for each change in price ofx1 (i.e. pivoted budget line) • Engel Curve: relates quantity of product a consumer with a given income will buy o Applicable for a plot ofx1 (x axis) vs I (y axis) Kevin Jin 9 ECON-UB 1 Pre-Exam 1 Notes o Derived from income consumption curve in that income is from income level of budget line and quantity is from the quantity of the utility maximizing market basket o Positive slope means good x is normal o Negative slope means good x is inferior x 1 o Engel curve can bend on itself so that good can be normal and inferior depending on the point • Individual Demand Curve: relates quantity of product an individual consumer will buy at a given price o Applicable for a plot ofx1 (x axis) vs p1 (y axis) o Derived from price consumption curve in that price is from price level of budget line and quantity is from the quantity of the utility maximizing market basket o A decrease in price leads to a decrease in MRS (shallower slope) o Demand curve is average revenue curve for a firm o Demand curve for a competitive firm is horizontal because consumers won’t buy from firm if price is different than price of the rest of the market • Market Demand Curve: relates quantity that all consumers in a market buy to a good’s price o Applicable for a plot o
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