CHAPTERS FOUR AND FIVE: DEMAND (OR KNOWING YOUR CUSTOMER) Demand Function – The relation between demand and factors influencing its level. Quantity of product X demanded = Qx = f(Price of X, Prices of Related Goods, Consumer Income, Advertising Expenditure, etc.) THE MARKET DEMAND FUNCTION, CONT. The model: Qx = a0 + a1Px + a2Pz + a3Y + a4POP + a5i + a6AD + e The terms a0 , a1 , etc. are the parameters of the model. This is what we need to estimate. Estimation of the model: Q = 100 + -.002Px + .001Pz + .00008Y + .22POP + -800i + .002A Interpretation of the model: If the average price increases by $1, the demand for the product falls by .002 units THE DEMAND CURVE Demand Curve – The relation between price and the quantity demanded, holding all else constant. General Form: P = a – bQ Why is this the general form? Moving from the Demand Function to the Demand Curve. CONNECTING THE CURVE TO THE FUNCTION Changes in quantity demanded – movement along a given demand curve reflecting a change in price and quantity. Shift in demand – Switch from one demand curve to another following a change in a non-price determinant of demand IF AN INDEPENDENT VARIABLE CHANGES, OTHER THAN PRICE OF THE GOOD, YOU MUST DRAW A NEW DEMAND CURVE!!! Demand Analysis and Estimation: Discussion Outline • • • • • Demand Sensitivity Analysis: Elasticity Price Elasticity of Demand Cross Price Elasticity of Demand Income Elasticity of Demand Additional Demand Elasticity Concepts Demand Sensitivity Analysis: Elasticity • Elasticity – The percentage change in a dependent variable resulting from a 1% change in an independent variable. • Elasticity = % change in Y / % change in X • ELASTICITY IS A RATIO!!! Percentage Change Elasticity = Percentage Change in Quantity (Sales) / Percentage Change in (X) Percentage change = (X2-X1)/X1 Price Elasticity of Demand Price Elasticity of Demand (Own-Price): ◦ Measure of the magnitude by which consumers alter the quantity of some product they purchase in response to a change in the price of that product. ◦ Responsiveness of the quantity demanded to changes in the price of the product, holding constant the values of all other variables in the demand function. Estimating from the Demand Function. Estimating from the Demand Curve. The Point Formula ((Q2-Q1)/Q1) / ((P2-P1)/P1) Problems: 1. Order of events dictate outcomes 2. Does not impose ceteris paribus. The Arc Formula ((Q2-Q1)/(Avg.Q) / ((P2-P1)/(Avg.P) Problem: 1. Does not impose ceteris paribus The Slope Formula Elasticity = %ΔQ / %ΔP = ((Q2-Q1)/Q1) / ((P2-P1)/P1) ◦ Note: Q2-Q1 = ΔQ and P2-P1 = ΔP ◦ Therefore: Elasticity = ΔQ /Q / ΔP/P ◦ Note: If you divide by a fraction you multiply by the reciprocal. ◦ Therefore: Elasticity = ΔQ /Q * P/ΔP or Elasticity = ΔQ / ΔP * P/Q Where do we get ΔQ / ΔP? This is the inverse slope of the demand curve, which we can estimate empirically (via basic econometrics), and therefore we can impose ceteris paribus. Interpretation of Price Elasticity % change in Q > % change in P ◦ (elastic or responsive) Ep > 1 % change in Q < % change in P ◦ (inelastic or unresponsive) Ep < 1 % change in Q = % change in P ◦ (unitary elastic) Ep = 1 Own Price Elasticity and the Demand Curve Own-price elasticity = %ΔQ / %ΔP How does elasticity vary along a linear demand curve? The upper half of a linear demand curve is elastic. The lower half of a linear demand curve is inelastic. BE ABLE TO EXPLAIN WHY!!! ◦ The search for substitutes as price increases ◦ Big number, small number explanation ◦ Calculating elasticity at the midpoint. Price Elasticity Along a Demand Curve $10 9 8 7 6 5 4 3 2 1 0 Ed = Elasticity declines along demand curve as we move toward the quantity axis Ed > 1 Ed = 1 Ed < 1 Ed = 0 1 2 3 4 5 6 7 8 9 10 Quantity Elasticity and Total Revenue Connecting Elasticity to Total Revenue If % change in Q > % change in P decreasing the price will increase TR and marginal revenue must be positive. If % change in Q < % change in P increasing the price will increase TR and marginal revenue must be negative. BE ABLE TO ILLUSTRATE THE RELATIONSHIP Marginal Revenue Marginal Revenue - amount of revenue from the last unit sold. ◦ the rate of change in total revenue ◦ the slope of the total revenue curve. If demand is downward sloping, then price will exceed marginal revenue. In other words, the amount of revenue generated by an additional sale will be less than the price the firm charges. Why? To increase quantity the firm will need to lower the price, not just for the last unit sold, but also for every unit the firm wishes to sell. Profit and Elasticity Profit = Total Revenue - Total Cost If demand is inelastic (i.e. % change in Q < % change in P) an increase in price will increase TR. Because Q falls (law of demand), so too will Total Cost Why? Total Cost (which we will discuss later) is an increasing function of output. The more you produce, the higher your total cost. Consequently, if demand is inelastic, a firm can raise its price and increase its profits. Summarizing Demand The Law of Demand - Quantity demanded rises as price falls, ceteris paribus. Quantity demanded falls as price rises, ceteris paribus ◦ The Law of Demand is based upon Gossen’s First and Second Laws. ◦ The Law of Demand gives us the Demand Curve ◦ Via own-price elasticity, we move from the demand curve to total revenue. Total Revenue = Price * Quantity ◦ Without own-price elasticity we do not know how changes in price and quantity will impact total revenue. ◦ The variation in total revenue gives us the concept of marginal revenue. Optimal Pricing Policy MR = P [1 + 1/EP] Be able to show why this relationship exists. To maximize profits: MR = MC MC = P [1+1/EP] P = MC / [1 + 1/EP] Lerner Index Lerner Index (Measure of Inequality) L = (p - MC)/p Lerner Index is bound between (0,1) Closer to 1 the more pricing power the firm has. NOTE: Mark-up power reflects monopoly power. The Lerner Index Own Price Elasticity is Always Negative. MR = P[1 – 1/EP] and therefore MC = P[1 – 1/EP] or MC = P - P/EPor P – MC = P/ EP or [P-MC]/P = 1/EP PUNCHLINE: If elasticity increases, markup will decline. If the product becomes less elastic, mark-up will increase. Determinants of Price Elasticity The extent the good is considered a necessity. Proportion of income spent on the product Time Availability of substitutes HINT: The fourth determinant encompasses the first three. PUNCHLINE: The key to establishing market power is the elimination of substitutes in the minds of consumers. WHAT IMPACT DOES ADVERTISING HAVE ON ELATICITY? • Substitutes – products for which a price increase for one leads to an increase in demand for the other. • NOTE: Two goods are substitutes only if the consumer behavior indicates this relationship. • Complements – products for which a price increase for one leads to a decrease in demand for the other. Cross Price Elasticity of Demand Substitutes vs. Complements • Responsiveness of demand for one product to changes in the price of another. • Calculating from the Demand Function • Note: We already know if two goods are substitutes or complements from the demand function. We do not know the magnitude of the relationship without calculating elasticity. Cross- Price Elasticity • Normal Goods – products for which demand is positively related to income. • Inferior Goods – products for which demand is negatively related to income. • Note: What is normal or inferior can vary across time and geographic distance. Income Elasticity Normal vs. Inferior Goods • Responsiveness of demand to changes in income. • Calculating from the Demand Function • Note: We already know if two goods are normal or inferior from the demand function. We do not know the magnitude of the relationship without calculating elasticity. Income Elasticity • Counter-cyclical goods – inferior goods • During recessions demand will increase. • During expansion demand will decrease. • Non-cyclical normal goods – income elasticity is less than 1. • Cyclical normal goods – superior goods – luxury goods – income elasticity is greater than 1. Income Elasticity and the Business Cycle • Advertising Elasticity • Interest Rate Elasticity • Weather Elasticity • Any factor that can be included in a demand function can be analyzed in terms of elasticity. Additional Demand Elasticity Concepts Product Tobacco products Electicity (household) Health Services Nodurable toys Movies/motion pictures Beer Wine University tuition Price elasticity Short Run Long Run 0.46 1.89 0.13 1.89 0.20 0.92 0.30 1.02 0.87 3.67 0.56 1.39 0.68 0.84 0.52 — Income elasticity Product Short Run Long Run Motion pictures 0.81 3.41 Foreign travel 0.24 3.09 Tobacco products 0.21 0.86 Furniture 2.60 0.53 Jewelry and watches 1.00 1.64 Hard liquor — 2.50 Private university tuition — 1.10 Commodities Beef in response to price change in pork Beef in response to price change in chicken U.S. automobiles in response to price changes in European and Asian automobiles European automobiles in response to price changes in U.S. and Asian automobiles Beer in response to changes in wine Hard liquor in response to price changes in beer Cross-Price Elasticity 0.11 0.02 0.28 0.61 0.23 - 0.11 Linear Functional Form Y = β0 + β1 X1 + β2 X2 + ε Slope = β1 Impact of X1 on Y is independent of the quantity of X2. Elasticity = β1 * [X1/ Y] Double-Log Functional Form What if you wished to estimate the following model? Y = β0 X1 β1 X2β2 To make this linear in the parameters InY = β0 + β1 InX1 + β2 InX2 + ε Slope = β1 = ΔlnY / ΔlnX1 = [ΔY / Y] / [ΔX1 / X1] What is this? The elasticity, which is constant across the sample. What is the slope in a double log functional form? Slope = β1 * (Y/X) = [ΔY / Y] / [ΔX1 / X1] * (Y/X) = ΔY / ΔX Impact of X1 on Y depends upon the quantity of X2 In other words, the slope of X1 varies across the sample. Why would this be a realistic property?