DEMAND FOURTH LECTURE February 14, 2012 William R. Eadington, Ph.D. Professor of Economics, College of Business Director, Institute for the Study of Gambling and Commercial Gaming University of Nevada, Reno www.unr.edu/gaming PROBLEM OF THE WEEK REQUEST: PLEASE SUBMIT HARD COPIES FOR HOMEWORKS FROM NOW ON. Suppose there has been a storm in Nebraska that has destroyed part of the corn crop in the field. The demand curve for corn has not changed. As a result, the market clearing prices and quantities before and after the storm are: Pb = 50, Qb = 2000; Pa = 100, Qa = 1500. (The subscripts a and b refer to “after the storm” and “before the storm”.) a. Assume a linear demand curve for corn, i.e. P = α + β Q. Calculate α, β with the provided information, and draw the demand curve with P on the y-axis and Q on the x-axis. Label the intercept and the slope on the graph. b. The supply curve for the period after the storm is P = (1/15) Q, and it is parallel to the supply curve before the storm. Is the supply curve before the storm above or below that after the storm? Calculate the slope and the intercept of the supply curve before the storm. Draw both supply curves on a new graph with P on the y-axis and Q on the x-axis. Add the demand curve (calculated in part a) to the graph. c. Suppose consumers care only about corn consumption and apple consumption (they live in a two-good world). How would the change in the price of corn affect the budget constraint of the typical consumer? Show graphically. How would the change in relative prices affect the typical consumer’s consumption of corn versus apples? Is this result consistent with your observation from the demand and supply framework (i.e. an increase in price of corn is associated with a decrease in the equilibrium quantity)? Explain. We see the dots, but nothing else. Can we derive the D, Sa and Sb curves? SPECIFIC KNOWLEDGE • Examples • idiosyncratic knowledge of particular circumstances (i.e. the kinds of food products purchased in a particular neighborhood, clothing tastes in an ethnic part of the city, etc.) • scientific knowledge (i.e. how a particular software system can be modified to bring about desired results, how to apply recent findings to a regimen for a disease) • assembled knowledge (i.e. the value of a team who have worked together for some time; accumulated knowledge from experience and mutual understandings) • Free markets make superior use of specific knowledge dispersed among many participants – It is not important for participants in the market to understand all the factors that drive markets through specific knowledge; they just respond to general knowledge available in the marketplace based on their own self interest – Prices and profits represent general (not specific) knowledge FREE MARKETS VERSUS CENTRAL PLANNING: THE ROLE OF KNOWLEDGE • Centralized decision-making versus decentralized, controlled by market prices and personal incentives – Challenge for the 2009 Stimulus Package in terms of efficiency => Where should the dollars have been spent? – Was that the point of the Stimulus Package? • General knowledge (i.e. prices) is freely transferable • Specific knowledge (i.e. scientific expertise, local understanding of a particular marketplace, understanding of local political issues and challenges or of industries) is expensive to transfer • Centrally planned economies fail because it is difficult to gather and use enough specific knowledge in the planning process EXTERNALITIES AND THE COASE THEOREM • Externalities occur when the actions of one party impose a benefit or cost on another party not involved in the exchange • Pollution, noise, graffiti, nice lawns & architecture • Foreclosed houses on the value of other houses in the neighborhood • If Externalities are present, markets may not be efficient (Too much or too little of the product is being produced) – tax or subsidize externalities to get closer to efficiency • Ronald Coase argued market exchange will be efficient if: – Property rights are well defined – Property rights can be traded – Transactions costs are sufficiently low • Example: Your neighbor at work smokes, and you object – Pass a law => could be inefficient (Why?) – Property rights? Course of action? Bribe or exemption purchase EXTERNALITIES AND PROPERTY RIGHTS • Consider the example of the train car with a smoker and non-smoker – Value of clean air: $100; value of smoking: $50 – Property rights vested in the smoker (1950) – Property rights vested in the nonsmoker (2012) • Consider the example of the bee keeper and the fruit tree grower – Definition of Property rights and passage of laws v. Entering into Mutually Advantageous Trade AN EXAMPLE OF THE COASE THEOREM (1) • Consider two business next door to one another: a doctor's office and a candy maker. The candy maker uses machinery which grinds up ingredients and which produce a low rumbling noise. The doctor needs to be able to hear quiet sounds like heartbeats and joint movements. The doctor desires to start treating patients in the room right next to the wall between his office and the candy maker, but the grinding noise makes it difficult for the doctor to carry on his business in that one room. • A lawsuit is filed, based on either: – Law #1: It is impermissible for noises to pass from one establishment to another. – Law #2: A business is allowed to do anything it wants on its own property as long as it doesn't endanger the health of anyone else. • What would be optimal for society? If the scarce resource goes to producing the more valuable (socially desired) output. • Conflicting parties should be allowed and encouraged to work out some mutually advantageous agreement. Assume this can be done at relatively low cost (TRANSACTIONS COSTS) AN EXAMPLE OF THE COASE THEOREM (2) • Suppose that value added of output produced by the candy maker in the disputed location is $20,000 per year and that the doctor would produce value added of $15,000. A judicial decision that would force the candy maker to shut down would clearly create an inefficient allocation of resources. • However, the cost to society of lost output is borne by the doctor in the form of the opportunity cost he faces by using that room. He might realize that it is worth any amount up to $20,000 to the candy maker for the right to run a grinding machine near that area. Thus, his using that room to treat patients would cost society $5,000. He could capture a portion of that through negotiation (a bribe to forego using the room in return for a payment of $15,000 to $20,000.) WHY DO FIRMS EXIST? THE ROLE OF TRANSACTION COSTS • Types of transaction costs • • • • search and information costs bargaining and decision costs policing and enforcement costs opportunity cost of inefficient resource allocation • Optimal economic organization minimizes transaction costs – You work on contract rather than renegotiating your salary each day or week FIRMS CAN REDUCE TRANSACTION COSTS • Advantages of firms over markets • fewer transactions • information specialization • reputational concerns DEMAND FUNCTION A mathematical representation of the relationship between the quantity demanded and all factors influencing demand: Q = f(X1, X2,… Xn) where Q is quantity demanded and the Xis are the factors influencing demand DEMAND FOR THEATER TICKETS Q = 117 - 6.6P + 1.66Ps - 3.3Pr + 0.00661I where P is Theater ticket price, Ps is price of symphony tickets, Pr is price of nearby restaurant meals, and I is average per capita income VARIABLE VALUES Suppose the variables have the following values: P = $30 Ps = $50 Pr = $40 I = $50,000 How many tickets will the Theater Company sell? THE DEMAND CURVE Substitute variable values (except for P) into the equation and simplify: P = 60 - 0.15Q This is the equation for the demand curve. Law of demand – as the price of a good rises, the quantity demanded falls GRAPHING THE DEMAND CURVE $ $ Ticket price (in dollars) Income = 51,000 61 60 60 Income = $50,000 D1 D D0 Q Q 400 Quantity of Theater tickets 406.0 Quantity of Theater tickets PRICE CHANGES AND TOTAL REVENUE • • • • Total revenue is P x Q For Theater Company, P=60-.15Q And TR = (60-.15Q)Q=60Q-.15Q2 Marginal revenue, MR, is TR/Q=60-.30Q • General rule for derivatives: If Y = a*Xb, then dY/dX = b*a*Xb-1 PRICE ELASTICITY OF DEMAND • Measures the responsiveness of quantity demanded to changes in price • Often referred to as elasticity of demand • “Inelastic demand” => buyers respond less than proportionately to changes in price • “Elastic demand” => buyers respond more than proportionately to changes in price • Helps firms determine the effect of price changes on total revenue DEMAND ELASTICITY • The price elasticity of demand is the ratio of the percentage change in output divided by the percentage change in price • It is computed as: %Q %P CALCULATING ELASTICITY ARC PRICE ELASTICITY • Using two data points to estimate elasticity • Information requirements: • Quantity demanded before and after the price change • Q1 • Q2 • Price before and after the price change • P1 • P2 CALCULATING ELASTICITY ARC PRICE ELASTICITY Note definition as a ratio of percentage changes, & causeeffect where price influences quantity demanded Q (Q1 Q2 ) Q (Q Q ) 2 2 1 P P ( P1 P2 ) ( P1 P2 ) 2 PRICE CHANGES AND TOTAL REVENUE • If demand is elastic (>1), price and total revenue move in opposite directions – If P↑ then TR↓ – If P↓ then TR↑ • If demand is inelastic (<1), price and total revenue move together – If P↑ then TR↑ – If P↓ then TR↓ RANGE OF PRICE ELASTICITIES $ $ Price (in dollars) Price (in dollars) D η=0 D η=∞ Q Quantity Perfectly Inelastic Q Quantity Perfectly Elastic DETERMINANTS OF PRICE ELASTICITY • Availability of substitutes – few substitutes for airplane trips, textbook for this class – many substitutes for out-of-home meals • Size of commodity in consumer budget – TV cable bill versus house payment or rent • Time period for consumer adjustment – Durable goods cannot be quickly and frequently replaced (i.e. SUVs, home heating systems) – over time, consumers will find alternative goods ELASTICITY AND TOTAL REVENUES DEMAND, TOTAL REVENUE, & MARGINAL REVENUE Ticket price (in dollars) $ 60 Elastic demand (n > 1) n=1 30 Inelastic demand (n < 1) Q Total revenue (in dollars) $ 6,000 200 Quantity of Theater tickets Q OTHER DEMAND INFLUENCES • Complements versus substitutes – Cross price elasticity of demand Q x Qx1 Qx 2 xy Py Py1 Py 2 or Ƞxy = dQx/dPy*Px/Qy CROSS PRICE ELASTICITY • For substitutes, ηXY > 0 • If the price of Pepsi rises, the demand for Coke rises • For complements, ηXY < 0 • If the price of peanut butter rises, the demand for jelly falls INCOME ELASTICITY • Income elasticity of demand Q x Qx1 Qx 2 I I I1 I 2 or ȠI = dQx/dI*I/Qx • Normal goods – demand rises as income increases (>0) • Inferior goods – demand falls as income increases (<0) • Luxury goods – demand rises more than proportionately as income increases (>1) NETWORK EFFECTS • Demand for a good increases as the number of users of the good increases – – – – – Telephone networks Mail: The internet versus the postal system Microsoft Outlook versus Netscape Beta-Max versus VHS High Definition DVD versus Blu-Ray • Without critical mass, a product will die – FAX machines PRODUCT ATTRIBUTES • What product attributes are important to consumers? – Price => affordability; comparability; value for money – product design => functionality, ergonomics – Packaging => attractiveness, shelf appeal – Promotion => perceptions, perhaps status; “bandwagon” or “snob” effects CROSS-PRICE ELASTICITY OF DEMAND EQX , PY %QX %PY d If EQX,PY > 0, then X and Y are substitutes. If EQX,PY < 0, then X and Y are complements. PREDICTING REVENUE CHANGES FROM TWO PRODUCTS Suppose that a firm sells two related goods. If the price of X changes, then total revenue will change by: R RX 1 EQX , PX RY EQY , PX %PX EXAMPLE: NORTHSTAR SELLS LIFT TICKETS AND RENTS SKI EQUIPMENT. IF LIFT TICKET PRICES ARE CUT BY 25%, AND THE ESTIMATED ELASTICITIES ARE -1.2 (OWN PRICE) AND -0.5 (CROSS PRICE), WHAT WILL HAPPEN TO TOTAL REVENUES? INCOME ELASTICITY EQX , M %QX %M d If EQX,M > 0, then X is a normal good. If EQX,M < 0, then X is a inferior good. If EQX,M > 1, then X is a luxury good. USES OF ELASTICITIES • Pricing strategies • Managing cash flows • Impact of changes in competitors’ prices • Impact of economic booms and recessions • Impact of advertising campaigns • Analyzing a combination of changes in the marketplace GAINS FROM TRADE • Consumer surplus - the difference between what consumers are willing to pay and what they actually pay – measured as the area below the demand curve and above the price • Producer surplus - the difference between the price received and willingness to produce – measured as the area above the supply curve and below the price CONSUMER AND PRODUCER SURPLUS P $20 Consumer surplus (Triangle A) Supply A Producer surplus (Triangle B) $10 B Incremental production Costs (Triangle C) C Demand 10 Q GOVERNMENT INTERVENTION • Consumer and producer surplus can be used to examine the effects of government intervention on gains from trade • Price caps limit the maximum price that can be charged • Price floors are a legally set minimum price at which goods can be traded GOVERNMENT PRICE CAP ON GASOLINE $/Gallon Supply Lost gains from trade A $4.00 B Excess demand (shortage) for gasoline $3.00 price cap $3.00 Demand QS QD Q MINIMUM WAGE LAWS Unemployment (excess supply of labor) Labor Supply Minimum Wage $7.25 A $6.00 Lost gains from trade B Labor Demand QS Q* QD Quantity of labor DECISION MAKING UNDER UNCERTAINTY • Since nothing is guaranteed, we make decisions based on the expected value of the outcome: E (V ) piVi • The amount of risk is measured by the standard deviation of the value of the outcomes: SDV pi (Vi V ) • People choose a balance between expected value (return) and risk RISK VERSUS RETURN THE TELEVISION GAME: DEAL OR NO DEAL • Rules of the game: 26 briefcases; dollar amounts from $1 to $1,000,000, all shown on a large Board • Choose one, then eliminate all the others • Offers are made along the way • Example: 3 briefcases remaining at $10, $10,000; and $1 million. Offer: $300,000. Deal or No Deal?