Microeconomics (PGP-I) Session 1 to Session 5 Joysankar Bhattacharya Session One : Overview 1.Defining Microeconomics 2. Analytical tools of Microeconomics • Constrained Optimization • Equilibrium Analysis • Comparative Statics 3. The Types of Microeconomic Analysis 2 Microeconomics Defined Microeconomics studies the economic behavior of individual decision makers, such as a consumer, a worker, a firm or a manager. How individual economic decision-makers allocate scarce resources among alternate uses. This study involves both the behavior of these economic agents on their own and the way their behavior interacts to form larger units, such as markets. 3 Microeconomic Modeling Choice vs. Alternatives Models are like maps – using visual methods, they simplify the process and facilitate understanding of complex concepts. Microeconomic models need to: Resemble Reality Be Understandable Be an Appropriate Scale 4 Exogenous & Endogenous Variables Defined: Variables that have values taken as given in the analysis are exogenous variables. Variables whose values are determined as a result of the model’s workings are endogenous variables. “How would a manager hire the maximum possible workers on a budget of $100?” vs. “How would a manager minimize the cost of hiring three workers?” OR “How much food and clothing should the consumer purchase in order to maximize satisfaction on a budget of Rs. 2000 ?” vs. “What is the minimum level of expenditure that the consumer must receive in order to reach a subsistence level of satisfaction?” 5 The Objective Function Defined: The Objective Function specifies what the agent cares about. • Does manager care more about raising profits or increasing “power”? 6 The Constraints Defined: Constraints are whatever limit is placed on the resources available to the agent. Time Budget Other Resources Technical Capabilities The Marketplace Rules, Regulations, and Laws 7 The Constraint Optimization Behavior can be modeled as optimizing the objective function, subject to various constraints. • Consumers Maximize Utility Subject to the Budget Constraint • Producers Maximize Profits Subject to 1. Consumer Demand 2. Input Costs 8 The Constraint Optimization Behavior can be modeled as optimizing the objective function, subject to various constraints. Manager’s Investment Choice • Facilities ( F ): Facilities workers cost $30 • R&D ( R ): R&D workers cost $100 • Max N (F,R) • Subject to: expenditure < $250 • Where: N is the number of workers 9 The Constraint Optimization Consumer purchases Food (F), Clothing(C), Income (I) Price of food (Pf), Price of clothing (Pc) 𝐹𝐶 Utility from purchases: U = 2 Max U(F,C) subject to: Pf F + Pc C < I (F,C) 10 Fundamental Questions Societies must answer these questions that relate to microeconomics: 1. What goods and services will be produced and in what quantities 2. Who will produce the goods and services and how 3. Who will receive these goods and services and how will they get them 11 Equilibrium Defined: Equilibrium is defined as the point where demand just equals supply in this market (i.e., the point where the demand and supply curves cross). Equilibrium analysis is an analysis of a system in a state that will continue indefinitely as long as the exogenous factors remain unchanged. 12 Equilibrium Example – Sale of Coffee Beans 13 Equilibrium Example – Sale of Coffee Beans • Demand (P,I) 14 Equilibrium Example – Sale of Coffee Beans P* • Demand (P,I) Q* 17 Comparative Statics Analysis Defined: A Comparative Statics Analysis compares the equilibrium state of a system before a change in the exogenous variables to the equilibrium state after the change. 18 Comparative Statics Analysis 19 Marginal Impact Defined: The Marginal Impact of a change in the exogenous variable is the incremental impact of the last unit of the exogenous variable on the endogenous variable. 20 Microeconomic Analysis Positive Analysis (the way things are): • Is an analysis that attempts to explain how an economic system works Normative Analysis (the way things should be): • Is an analysis of what should be done 21 Microeconomic Analysis Some Examples • If USA lifts the prohibition on imports of Cuban cigars, the price of cigars will fall. • To provide revenues for public schools, taxes on alcohol and tobacco should be raised instead of increasing income taxes. • If telephone companies are allowed to offer cable TV service, the price of both types of service will fall. • Government subsidies to farmers are too high and should be phased out over the next decade. • If the tax on cigarettes is increased by 50 cents per pack, the equilibrium price of cigarettes will rise by 30 cents per pack. 22 Session Two: Overview 1. Consumer Preferences and the Concept of Utility 3. The Utility Function • Marginal Utility and Diminishing Marginal Utility 4. Indifference Curves 5. The Marginal Rate of Substitution 6. The Budget Constraint 7. Consumer Choice 23 Objective • Our aim is to understand the consumer decisionmaking process that generates demand functions for goods and services • It is important to know how changes in various prices, changes in income distribution, and changes in the ‘attribute mix’ of a product will affect demand Rationality assumption • Every consumer has well-defined preferences over goods and services, and given his/her constraints (prices and incomes), (s)he chooses a commodity bundle that maximizes his/her well-being Consumer Preferences Consumer Preferences tell us how the consumer would rank (that is, compare the desirability of) any two combinations or allotments of goods, assuming these allotments were available to the consumer. These allotments of goods are referred to as baskets or bundles. These baskets are assumed to be available for consumption at a particular time, place and under particular physical circumstances. 26 Consumer Preferences Preferences are complete if the consumer can rank any two baskets of goods (A preferred to B; B preferred to A; or indifferent between A and B) Preferences are transitive if a consumer who prefers basket A to basket B, and basket B to basket C also prefers basket A to basket C A B; B C = > A C 27 Consumer Preferences Preferences are monotonic if a basket with more of at least one good and no less of any good is preferred to the original basket. 28 Types of Ranking Students take an exam. After the exam, the students are ranked according to their performance. An ordinal ranking lists the students in order of their performance (i.e., A did best, B did second best, C did third best, and so on). A cardinal ranking gives the mark of the exam, based on an absolute marking standard (i.e., A got 80, B got 75, C got 74 and so on). 29 The Utility Function The three assumptions about preferences allow us to represent preferences with a utility function. Utility function – a function that measures the (maximum) level of satisfaction a consumer receives from any basket of goods and services. – assigns a number to each basket so that more preferred baskets get a higher number than less preferred baskets. 30 The Utility Function • An ordinal concept: the precise magnitude of the number that the function assigns has no significance. • Utility not comparable across individuals. • Any transformation of a utility function that preserves the original ranking of bundles is an equally good representation of preferences. e.g. U = y vs. U = y + 2 represent the same preferences. 31 Marginal Utility Marginal Utility of a good Y • additional utility that the consumer gets from consuming a little more of Y • i.e. the rate at which total utility changes as the level of consumption of good Y rises • MUy = 𝜕𝑈 𝜕𝑌 • slope of the utility function with respect to Y 32 Diminishing Marginal Utility The principle of diminishing marginal utility states that the marginal utility falls as the consumer consumes more of a good. 33 Diminishing Marginal Utility 34 Marginal Utility The marginal utility of a good, X, is the additional utility that the consumer gets from consuming a little more of X when the consumption of all the other goods in the consumer’s basket remain constant. • U(X, Y) : Utility Function • 𝜕𝑈 𝜕𝑋 (Y held constant) = MUX • 𝜕𝑈 𝜕𝑌 (X held constant) = MUY 35 Marginal Utility Example of U(B) and MUB U(B) = 10B – B2 MUB = 10 – 2B B 1 2 4 6 8 10 B2 1 4 16 36 64 100 U(B) MUB 9 8 16 6 24 2 24 -2 16 -6 0 -10 36 Marginal Utility U(B) = 10B – B2 MUB = 10 – 2B 37 Marginal Utility Example of U(B) and MUB • The point at which he should stop consuming hotdogs is the point at which MUB = 0 • This gives B = 5. • That is the point where Total Utility is flat. • Beyond B=5, the utility is diminishing. 38 Indifference Curves An Indifference Curve or Indifference Set: is the set of all baskets for which the consumer is indifferent - shows all combinations of consumption along which an individual is indifferent An Indifference Map : Illustrates a set of indifference curves for a consumer 39 Indifference Curves 1)Indifference curves have negative slope (Monotonicity) 2)Indifference curves do not cross (Transitivity) 3)Each basket lies (Completeness) on only one indifference curve 40 Indifference Curves 41 Indifference Curves Suppose that B preferred to A. But … by definition of IC, B indifferent to C A indifferent to C => B indifferent to C by transitivity. And thus a contradiction !! 42 Indifference Curves U = xy2 . for U 144 x 8 4 3 1 y 4.24 6 6.93 12 xy2 143.8 144 144.07 144 43 Indifference Curves Example: Utility and the single indifference curve. Indifference Curve for U = xy2 14 12 10 8 y 6 U = 144 4 2 0 0 1 2 3 4 5 6 7 8 9 X 44 Marginal Rate of Substitution The marginal rate of substitution: is the maximum rate at which the consumer would be willing to substitute a little more of good X for a little less of good Y; It is the increase in good X that the consumer would require in exchange for a small decrease in good Y in order to leave the consumer just indifferent between consuming the old basket or the new basket; It is the rate of exchange between goods X and Y that does not affect the consumer’s utility; It is the negative of the slope of the indifference curve: MRSx,y = − 𝒅𝒀 𝒅𝑿 (for a constant level of preference) 45 Marginal Rate of Substitution 46 Convex Indifference Curves Quantity of Pepsi 14 MRS=6 A 8 1 4 3 B MRS=1 Indifference curve 1 0 2 3 6 7 Quantity of Pizza At point A, the consumer has little pizza and much Pepsi, so he requires a lot of extra Pepsi to induce him to give up one of the pizzas: The marginal rate of substitution is 6 cans of Pepsi per pizza. At point B, the consumer has much pizza and little Pepsi, so he requires only a little extra Pepsi to induce him to give up one of the pizzas: The marginal rate of substitution is 1 can of Pepsi per pizza. 47 Marginal Rate of Substitution MUx(dX) + MUy(dY) = 0 …along an IC Mux MUy = − 𝑑𝑌 𝑑𝑋 = MRSx,y Positive marginal utility implies the indifference curve has a negative slope (implies monotonicity) Diminishing marginal rate of substitution implies the indifference curves are convex to the origin (implies averages preferred to extremes) 48 Marginal Rate of Substitution Implications of this substitution: • Indifference curves are negatively-sloped, bowed out from the origin, preference direction is up and right • Indifference curves do not intersect the axes 49 Indifference Curves Averages preferred to extremes => indifference curves are bowed toward the origin (convex to the origin). 50 Indifference Curves y Example: Graphing Indifference Curves Preference direction IC2 IC1 x 51 Key Definitions Budget Set: • The set of baskets that are affordable Budget Constraint: • The set of baskets that the consumer may purchase given the limits of the available income. Budget Line: • The set of baskets that one can purchase when spending all available income. PxX + PyY = I Y = I/Py – (Px/Py)X 52 The Budget Constraint Assume only two goods available: X and Y • Price of X: Px ; Price of Y: Py • Income: I Total expenditure on basket (X,Y): PxX + PyY The Basket is Affordable if total expenditure does not exceed total Income: PXX + PYY ≤ I 53 A Budget Constraint Example Y I/PY Budget line = BL1 • -PX/PY •C • I/P X X 54 A Budget Constraint Example Y Shift of a budget line If income rises, the budget line shifts parallel to the right (shifts out) If income falls, the budget line shifts parallel to the left (shifts in) BL2 BL1 X 55 A Budget Constraint Example Y Rotation of a budget line If the price of Y rises, the budget line gets flatter and the vertical intercept shifts in (BL2 ) BL1 If the price of Y falls, the budget line gets steeper and the vertical intercept shifts out (BL1 ) BL2 X 56 Consumer Choice Assume: Only non-negative quantities "Rational” choice: The consumer chooses the basket that maximizes his satisfaction given the constraint that his budget imposes. Consumer’s Problem: Max U(X,Y) Subject to: PxX + PyY < I 57 Interior Consumer Optimum (an optimum at which the consumer purchases both commodities (X > 0 , Y > 0) Y B Preference Direction • • Optimal Choice (interior solution) IC C 0 • BL X 58 Interior Optimum Interior Optimum: The optimal consumption basket is at a point where the indifference curve is just tangent to the budget line. Tangency Equal Slope MUx Px MRSx,y = = MUy Py “The rate at which the consumer would be willing to exchange X for Y is the same as the rate at which they are exchanged in the marketplace.” 59 Equal Slope Condition MUx MUy = Px Py “At the optimal basket, each good gives equal bang for the buck” Now, we have two equations to solve for two unknowns (quantities of X and Y in the optimal basket): 1. MUx MUy = Px Py 2. PxX + PyY = I 60 •Consumer’s optimal basket. •Thus, we can tell – for a given income and prices of other goods – how much a consumer will demand of X for a given price of X. •We can find different amounts of X demanded by changing the price of X(PX) and determining how much of X the consumer will demand – prices of other goods and income are held constant. 61 Price Consumption Curves Y (units) The price consumption curve for good x can be written as the quantity consumed of good x for any price of x. PY = 4 I = 40 10 Price Consumption Curve • • • PX = 1 PX = 2 PX = 4 0 XA=2 XB=10 XC=16 20 X (units) 62 Price Consumption Curves The Price Consumption Curve of Good X: Is the set of optimal baskets for every possible price of good x, holding all other prices and income constant. 63 Individual Demand Curve PX Individual Demand Curve For X PX = 4 • PX = 2 PX = 1 XA • XB • XC U increasing X 64 Change in Income & Demand The income consumption curve of good X is the set of optimal baskets for every possible level of income. 65 Income Consumption Curve 66 Engel Curves The income consumption curve for good X also can be written as the quantity consumed of good X for any income level. This is the individual’s Engel Curve for good X. When the income consumption curve is positively sloped, the slope of the Engel Curve is also positive. 67 Engel Curves I Engel Curve “X is a normal good” 92 68 40 0 10 18 24 X 68 Definitions of Goods • If the income consumption curve shows that the consumer purchases more of good X as her income rises, good X is a normal good. • Equivalently, if the slope of the Engel curve is positive, the good is a normal good. • If the income consumption curve shows that the consumer purchases less of good X as her income rises, good X is an inferior good. • Equivalently, if the slope of the Engel curve is negative, the good is an inferior good. 69 Impact of Change in the Price of a Good •If price of a good falls – consumer substitutes into the other good to achieve the same level of utility •When price falls – purchasing power increases the consumer can buy the same amount and still have money left 70 Impact of Change in the Price of a Good Pizza-Pepsi Story • Reduction in price of Pepsi • Now that the price of Pepsi has fallen, I get more Pepsi for every Pizza that I give up. Because Pizza is now relatively more expensive, I should buy less Pizza and more Pepsi (Substitution Effect, change in consumption on the same IC with a different MRS ) • Now that Pepsi is cheaper, my income has greater purchasing power. I am, in effect, richer than I was. Because I am richer, I can buy both more Pizza and more Pepsi (Income Effect, change in consumption that results from the movement to a higher IC) 71 Impact of Change in the Price of a Good • Substitution Effect: Change in relative price affects the amount of good that is bought as consumer tries to achieve the same level of utility • Income Effect: Consumer’s purchasing power changes and affects the consumer in a way similar to effect of a change in income 72 The Substitution Effect • As the price of X falls, all else constant, good X becomes cheaper relative to good Y •This change in relative prices alone causes the consumer to adjust his/ her consumption basket. • This effect is called the substitution effect. • The substitution effect always is negative(in direction). 73 Impact of Change in the Price of a Good Definition: As the price of X falls, all else constant, purchasing power rises. As the price of X rises, all else constant, purchasing power falls. This is called the income effect of a change in price. The income effect may be positive (normal good) or negative (inferior good). 74 Y Clothing The Substitution and Income Effects • Initial Basket • Final Basket • Decomposition Basket BLd A C B U2 U1 BL1 XA XB XC BL2 X Food The Substitution and Income Effects 76 The Substitution and Income Effects 77 Giffen Goods – Income and Substitution Effects 78 Giffen Goods If a good is so inferior that the net effect of a price decrease of good X, all else constant, is a decrease in consumption of good X, good X is a Giffen good. For Giffen goods, demand does not slope down. When might an income effect be large enough to offset the substitution effect? The good would have to represent a very large proportion of the budget. A Giffen good has to be an inferior one, but the converse is not necessarily true. 79 Individual Demand Curve The consumer is maximizing utility at every point along the demand curve As the price of X falls, it causes the consumer to move down and to the right along the demand curve as utility increases in that direction. The demand curve is also the “willingness to pay” curve – and willingness to pay for an additional unit of X falls as more X is consumed. 80 The Market Demand Function Defined: The Market Demand Function tells us that the quantity of a good all consumers in the market are willing to buy is a function of various factors. 81 Market Demand as the Sum of Individual Demands Catherine’s demand + Price of Ice-Cream Cones $3.00 Nicholas’s demand $3.00 $3.00 DNicholas 2.50 2.50 2.00 2.00 2.00 1.50 1.50 1.50 1.00 1.00 1.00 0.50 0.50 0.50 0 1 2 3 4 5 6 7 8 9 10 11 12 Quantity of Ice-Cream Cones 0 Market demand Price of Ice-Cream Cones Price of Ice-Cream Cones DCatherine = 1 2 3 4 5 6 7 2.50 0 DMarket 2 4 6 8 10 12 14 16 18 Quantity of Ice-Cream Cones Quantity of Ice-Cream Cones 82 The Market Demand Curve Defined: The Market Demand Curve plots the aggregate quantity of a good that consumers are willing to buy at different prices, holding constant other demand drivers such as prices of other goods, consumer income, quality. 83 The Law of Demand Defined: The Law of Demand states that the quantity of a good demanded decreases when the price of this good increases. 84 Demand Curve Rule Defined: A move along the demand curve for a good can only be triggered by a change in the price of that good. Any change in another factor that affects the consumers’ willingness to pay for the good results in a shift in the demand curve for the good. 85 Shifts of the Demand Curve The Demand Curve shifts when factors other than own price change If the change increases the willingness of consumers to acquire the good, the demand curve shifts right If the change decreases the willingness of consumers to acquire the good, the demand curve shifts left 86 The Demand for Cars We always graph P on vertical axis and Q on horizontal axis, but we write demand as Q as a function of P… If P is written as function of Q, it is called the inverse demand. Markets defined by commodity, geography, time. 87 Market Supply Tells us that the quantity of a good supplied by all producers in the market depends on various factors Plots the aggregate quantity of a good that producers are willing to sell at different prices. 88 Market Supply as the Sum of Individual Supplies Ben’s supply Price of Ice-Cream Cones Jerry’s supply = + Price of Ice-Cream Cones Market supply Price of Ice-Cream Cones SBen $3.00 $3.00 2.50 2.50 2.50 2.00 2.00 2.00 1.50 1.50 1.50 1.00 1.00 1.00 0.50 0.50 0.50 SJerry 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Quantity of Ice-Cream Cones Quantity of Ice-Cream Cones $3.00 SMarket 0 2 4 6 8 1012141618 Quantity of Ice-Cream Cones 89 The Law of Supply Defined: The Law of Supply states that the quantity of a good offered increases when the price of this good increases. 90 Supply Curve Rule Defined: A move along the supply curve for a good can only be triggered by a change in the price of that good. Any change in another factor that affects the producers’ willingness to offer for the good results in a shift in the supply curve for the good. 91 The Law of Supply The Supply Curve shifts when factors other than own price change If the change increases the willingness of producers to offer the good at the same price, the supply curve shifts right If the change decreases the willingness of producers to offer the good at the same price, the supply curve shifts left 92 Market Equilibrium • Market Equilibrium • is a price such that, at this price, the quantities demanded and supplied are the same. • is a point at which there is no tendency for the market price to change as long as exogenous variables remain unchanged. Demand and supply curves intersect at equilibrium 93 Example: Market Equilibrium for Cranberries Qd = 500 – 4p Qs = -100 + 2p p = price of cranberries (dollars per barrel) Q = demand or supply in millions of barrels per year The equilibrium price of cranberries is calculated by equating demand to supply: Qd = Qs … or… 500 – 4p = -100 + 2p …solving p* = $100 Plug equilibrium price into either demand or supply to get equilibrium quantity: Q* = 500 – 4(100) = 100 units 94 Market Equilibrium for Cranberries Q* = 100 95 Excess Demand/Supply Excess Demand: A situation in which the quantity demanded at a given price exceeds the quantity supplied. Excess Supply: A situation in which the quantity supplied at a given price exceeds the quantity demanded. If there is no excess supply or excess demand, there is no pressure for prices to change and thus there is equilibrium. When a change in an exogenous variable causes the demand curve or the supply curve to shift, the equilibrium shifts as well. 96 Excess Demand/Supply Excess supply when price is $5 Price (dollars per bushel) S 5.00 E 4.00 3.00 Excess demand when price is $3 8 9 D 11 13 14 Quantity (billions of bushels per year) 97 Shifts in Demand, Supply Unchanged Demand Increases: P Q 98 Shifts in Supply, Demand Unchanged Supply Decreases: PQ 99 Three Steps Decide whether the event shifts the supply curve, the demand curve, or, in some cases, both curves. Decide whether the curve shifts to the right or to the left. Use the supply-and-demand diagram • Compare the initial and the new equilibrium. • Effects on equilibrium price and quantity. 100 Consumer Surplus • The individual’s demand curve can be seen as the individual’s willingness to pay curve. • On the other hand, the individual must only actually pay the market price for (all) the units consumed. • Consumer Surplus is the difference between what the consumer is willing to pay and what the consumer actually pays. 101 Consumer Surplus Definition: The net economic benefit to the consumer due to a purchase (i.e. the willingness to pay of the consumer net of the actual expenditure on the good) is called consumer surplus. The area under an ordinary demand curve and above the market price provides a measure of consumer surplus 102 Demand Curve • The demand curve measures how many people would want to by the commodity at any particular price • The demand curve slopes down; as the price of the commodity decreases more people will be willing to buy. • If there are many people and their reservation prices differ only slightly from person to person, the demand curve would slope smoothly downward How the Price Affects Consumer Surplus (a) Consumer Surplus at Price P1 Price Price P1 (b) Consumer Surplus at Price P2 A A Consumer surplus Initial consumer surplus C P1 Additional consumer surplus to initial consumers C Consumer surplus to new consumers B B F P2 0 Q1 Quantity E D Demand 0 Q1 Demand Q2 Quantity Initial price P1, Quantity Q1, Consumer surplus is the area ABC. New lower price P2, Quantity Q2, Consumer surplus rises and becomes ADF. Increase : 1) from initial buyers BDEC and 2)from new buyers CEF 104 Consumer Surplus Consumer Surplus and Demand Consumer Surplus Generalized For the market as a whole, consumer surplus is measured by the area under the demand curve and above the line representing the purchase price of the good. Here, the consumer surplus is given by the yellow-shaded triangle and is equal to 1/2 × ($20 − $14) × 6500 = $19,500. Applying Consumer Surplus When added over many individuals, it measures the aggregate benefit that consumers obtain from buying goods in a market. Consumer Surplus G = .5(10-3)(28) = 98 H+I= 28 +2 = 30 CS2 = .5(10-2)(32) = 128 106 Network Externalities • If one consumer's demand for a good changes with the number of other consumers who buy the good, there are network externalities. Network Externalities • Bandwagon effect: A positive network externality that refers to the increase in each consumer’s demand for a good as more consumers buy the good. • Snob effect: A negative network externality that refers to the decrease in each consumer’s demand as more consumers buy the good. Bandwagon effect D60 PX Bandwagon Effect: • (increased quantity D30 20 10 demanded when more consumers purchase) • A • B Pure Price Effect • C Market Demand Bandwagon Effect 60 Snob Effect PX Snob Effect: Market Demand • (decreased quantity demanded when more consumers purchase) • A 900 • • C B D1000 D1300 Snob Effect Pure Price Effect X (units) Price Elasticity Elasticity - Measure of the responsiveness of quantity demanded or quantity supplied - To a change in one of its determinants Price elasticity of demand How much the quantity demanded of a good responds to a change in the price of that good 111 Price Elasticity Price elasticity of demand Percentage change in quantity demanded divided by the percentage change in price Elastic demand Quantity demanded responds substantially to changes in price Inelastic demand Quantity demanded responds only slightly to changes in price 112 Price Elasticity Defined: The Price Elasticity of Demand is the percentage change in quantity demanded brought about by a one-percent change in the price of the good. p Q/Q Q Q,P= ( ) = ( )( ) p Q p/p 113 Price Elasticity • Slope is the ratio of absolute changes in quantity and price. (= Q/P). • Elasticity is the ratio of relative (or percentage) changes in quantity and price. 114 Price Elasticity • When a one percent change in price leads to a greater than one-percent change in quantity demanded, the demand curve is elastic. • When a one-percent change in price leads to a less than one-percent change in quantity demanded, the demand curve is inelastic. • When a one-percent change in price leads to an exactly onepercent change in quantity demanded, the demand curve is unit elastic. 115 Elasticity – Linear Demand Curve Qd = a – bP Where: • a and b are positive constants • P is price • b is the slope • a/b is the choke price(price at which quantity demanded falls to zero) Re-writing, we have: P = a/b – (1/b)Q Elasticity is: εQ,P = ( ΔQ P P )( ) = − b( ) ΔP Q Q Elasticity falls from 0 to - along the linear demand curve, but slope is constant. Example: Calculate elasticity when P = 30 and Qd = 400 – 10P Answer: εQ,P = -3 “elastic” 116 Elasticity – Linear Demand Curve P a/b Q,P = - Elastic region a/2b • Q,P = -1 Inelastic region Q,P = 0 0 a/2 a Q 117 Price Elasticity Value of ε 0 Demand Curve Classification Meaning Perfectly Inelastic Quantity Demanded is Demand completely insensitive to Price Between 0 and -1 Inelastic Demand -1 Unitary Elastic Demand % change in Quantity Demanded is equal to % change in Price Elastic Demand Quantity Demanded is relatively sensitive to Price Relatively Flatter Perfectly Elastic Demand Any increase(decrease) in Price results in Quantity Demanded decreasing (increasing)to zero(infinity) Horizontal Between -1 and - - Quantity Demanded is relatively insensitive to Price Vertical Relatively Steeper Mid-Point of Linear Demand 118 Price Elasticity and Total Revenue • Total Revenue (TR) = P × Q P Q • Demand is elastic • Fall in Q > Rise in P TR falls • Demand is inelastic • Fall in Q < Rise in P TR rises 119 Paradox of Public Policy • New hybrid of wheat – increase production per acre 20% Supply curve shifts to the right Higher quantity; lower price Demand – inelastic Total revenue falls Paradox of public policy Induce farmers not to plant crops 120