Topic 3 - Slope and Elasticity PDF

Topic 3. Slope and Elasticity Bibliografía:  [BM] Appendices A.3.- A.5. [M] Cap. 5 Humberto Llavador Rosemarie Nagel WE WILL LOOK FOR THE ANSWERS TO THESE QUESTIONS: What is elasticity? What kinds of issues can...

Topic 3. Slope and Elasticity Bibliografía:  [BM] Appendices A.3.- A.5. [M] Cap. 5 Humberto Llavador Rosemarie Nagel WE WILL LOOK FOR THE ANSWERS TO THESE QUESTIONS: What is elasticity? What kinds of issues can elasticity help us understand? What is the price elasticity of demand and supply? How is it related to the demand/supply curve? How is it related to revenue & expenditure? What are the income and cross-price elasticities of demand? 2  Importance of topic Important to understand how much of the burden of the taxes is shared by the consumers and how much by producers Importance for the size of dead weight loss BUT also change of quantity, change of price, Change of revenue, EXAMPLE FISHERMEN! 3  A SCENARIO… You design websites for local businesses. You charge 200€ per website, and currently sell 12 websites per month. Your costs are rising (including the opportunity cost of your time), so you consider raising the price to 250€. The law of demand says that you won’t sell as many websites if you raise your price. How many fewer websites? How much will your revenue fall, or might it increase? 4  ELASTICITY Basic idea: Elasticity measures how much one variable responds to changes in another variable. – One type of elasticity measures how much demand for your websites will fall if you raise your price. Definition: Elasticity is a numerical measure of the responsiveness of Qd or Qs to one of its determinants, where Qd and Qs are short form for quantity demanded and quantity supplied. 5  INTRODUCTION We will study two core concepts in economics: – Slope – Elasticity Supply / demand curves: show the relationship between the quantity supplied / demanded and price. In general, if the price rises: – the quantity demanded falls (slope (-)) – the quantity supplied rises (slope (+)) But … by how much does it fall / rise? => difference before and after price change! 6  SLOPE: DEFINITION Slope: – The sensitivity of demand (or supply) to price changes depends on the slope of the demand curve. – The change in quantity demanded when price increases by one unit. In general: – Supply curve: positive slope: when the price increases by one unit the quantity supplied increases. – Demand curve: negative slope: when the price increases by one unit the quantity demanded decreases. – The more horizontal the curve  the greater the change in quantity – The more vertical the curve  the lesser the change in quantity 7  SLOPE Shallow slope  highly sensitive Steeper slope Little sensitive 8  CALCULATION OF THE SLOPE ∆P – With differences: slope = ∆Q dP – With derivatives: slope = dQ 9  EXAMPLES Horizontal (flat) Demand Vertical (steep) Demand 10  EXAMPLES Demand 1: P = 200 − 3Q Demand 2: P = 140 − (1 / 2)Q dP d ( 200 − 3Q ) Demand 1 Slope = = = −3 dQ dQ dP d (140 − (1 / 2)Q ) Demand 2 Slope = = = −0.5 dQ dQ 11  SLOPE The problem is that the slope of the demand curve depends on the units in which we measure price and quantity. – For example, if initially the price of the vertical axis is measured in cents and now we measure it in euros, the resulting demand curve will be only a hundredth of the slope than before. Economists usually measure the sensitivity of one variable to another by estimating the percentage change the first variable would experience if the amount of the second variable increased by 1 percent. 12  EXAMPLE Demand for apples (kilo), price (cents): P = 200 − Q – Slope: -1 Demand for apples (kilo), price (euros): Q P = 2− – Slope: -0.01 100 13  ELASTICITY: DEFINITION The price-elasticity of demand is the percentage change in quantity caused by a change in the price of 1 percent (as we move along the demand curve). The price-elasticity of supply is the percentage change in quantity caused by a change in the price of 1 percent (as we move along the supply curve). 14  WHAT DETERMINES PRICE ELASTICITY? To learn the determinants of price elasticity, we look at a series of examples. Each compares two common goods. In each example: – Suppose the prices of both goods rise by 20%. – The good for which Qd falls the most (in percent) has the highest price elasticity of demand. Which good is it? Why? – What lesson does the example teach us about the determinants of the price elasticity of demand? 15 EXAMPLE 1: BREAKFAST CEREAL VS. SUNSCREEN The prices of both of these goods rise by 20%. For which good does Qd drop the most? Why? – Breakfast cereal has close substitutes (e.g., pancakes, waffles, leftover pizza), so buyers can easily switch if the price rises. – Sunscreen has no close substitutes, so consumers would probably not buy much less if its price rises. Lesson: Price elasticity is higher when close substitutes are available. 16 EXAMPLE 2: “BLUE JEANS” VS. “CLOTHING” The prices of both goods rise by 20%. For which good does Qd drop the most? Why? – For a narrowly defined good such as blue jeans, there are many substitutes (khakis, shorts, Speedos). – There are fewer substitutes available for broadly defined goods. (There aren’t too many substitutes for clothing, other than living in a nudist colony.) Lesson: Price elasticity is higher for narrowly defined goods than broadly defined ones. 17 EXAMPLE 3: INSULIN VS. CARIBBEAN CRUISES The prices of both of these goods rise by 20%. For which good does Qd drop the most? Why? – To millions of diabetics, insulin is a necessity. A rise in its price would cause little or no decrease in demand. – A cruise is a luxury. If the price rises, some people will forego it. Lesson: Price elasticity is higher for luxuries than for necessities. 18 EXAMPLE 4: GASOLINE IN THE SHORT RUN VS. GASOLINE IN THE LONG RUN The price of gasoline rises 20%. Does Qd drop more in the short run or the long run? Why? – There’s not much people can do in the short run, other than ride the bus or carpool. – In the long run, people can buy smaller cars or live closer to where they work. Lesson: Price elasticity is higher in the long run than the short run. 19  THE DETERMINANTS OF PRICE ELASTICITY: A SUMMARY The price elasticity of demand depends on: – the extent to which close substitutes are available – whether the good is a necessity or a luxury – how broadly or narrowly the good is defined – the time horizon – elasticity is higher in the long run than the short run 20  ELASTICITY: DEFINITION Price elasticity Percentage change in Q = of a curve Percentage change in P 21  COMPUTING THE ELASTICITY We need: Two points in a curve: – Initial price and quantity: P y Q – New price and quantity: P’ y Q’ Step 1: Compute percent changes – Percent change in price: Q '− Q ∆Q – Percent change in quantity: 100 × Q = 100 × Q Step 2: Compute the price elasticity: ∆𝑄 ∆𝑄 100 𝑄 𝑃 ∆𝑄 𝑃 𝑑𝑄 Elasticidad = 𝑄 ∆𝑃 = ∆𝑃 = → 100 𝑃 𝑄 ∆𝑃 𝑄 𝑑𝑃 𝑃 22  CALCULATION OF ELASTICITY – With differences: – With derivatives: Slope 23  RELATIONSHIP BETWEEN THE SLOPE AND ELASTICITY The more horizontal the curve  the greater the change in quantity The more vertical the curve  the lesser the change in quantity With linear demand or supply curves, the slope is constant throughout, but the elasticity changes depending on the point in the curve where you are located. Why? 24  EXAMPLES: Demand: P = 50 − 0,25Q (1) Slope? Answer: (2) Price-elasticity when P = 40? => Calculate first corresponding Q! Now P=10 => Q= 40*4=160 Answer: E=10/160*1/-0.25=-1/4 25  PROPERTIES OF THE PRICE ELASTICITY If |ED| > 1, we say that demand is elastic – When price rises, the quantity demanded falls more than proportionally – Elastic Demand: − ∞ < ED < -1 If |ED| < 1, we say that demand is inelastic – When price rise, the quantity demanded falls less than proportionally. – Inelastic Demand: -1 < ED < 0 If ED = -∞, demand is Perfectly Elastic If ED = 0, demand is Perfectly Inelastic The terms apply similarly to the supply curve – Elastic Supply: 1 < EO < + ∞ – Inelastic Supply: 0 < EO < 1 26  EXAMPLES: Example: P = 50 - 1 / 4 Q (demand curve), the elasticity at P = 40 and Q = 40 is: P dQ = 40  − 1  = −4 Q dP 40  1 / 4  This demand is elastic. Example: Q = 15 (supply curve), the elasticity at any price and quantity is: Q dP = 0 P dQ This supply is perfectly inelastic. 27 DEMAND: NEGATIVE PRICE-ELASTICITY EXTREME CASES P ED → −∞ perfectly elastic Q P ED = 0 perfectly inelastic Q 28  SUPPLY: POSITIVE PRICE-ELASTICITY EXTREME CASES P EO → +∞ perfectly elastic Q P EO = 0 perfectly inelastic Q 29  ELASTICITY AND TOTAL REVENUE Was it good for the fishermen to have lots more fish? Total revenue = Price × Quantity (so without reducing the costs!) – If the fishermen increase their catch, the quantity increases and the price decreases. – What then will happen with total revenue (P*Q) when there is a change in price and quantity? Well, when the price decreases more than the quantity increases, does P*Q increase or the opposite? The answer lies in the elasticity of the demand!!! 30  Elasticity and total revenue Demand elastic: Demand inelastic ↓ price ⇒ ↑ revenue ↓ price ⇒ ↓ revenue 31  INTUITION If demand is elastic with respect to price (–∞ < Ed < – 1), then if P drops, Q increases more than proportionately and therefore total revenue increases. If demand is inelastic with respect to price (–1 < Ed < 0), then if P falls, Q increases less than proportionally, and hence total revenue decreases. 32  ELASTICITY AND REVENUES Proposition: With a negative sloping demand curve, as we move along the demand curve: a) price and total revenue vary in the same direction if demand is inelastic with regard to price. b) the price and total revenue vary in the opposite direction if demand is elastic with regard to price. 33  EXAMPLE: SNOW AND ORANGES When we go from A to B, what happens to total revenues (P×Q)? We loss area D We win area C Revenues RISE 34 APPLICATION: DOES DRUG INTERDICTION INCREASE OR DECREASE DRUG-RELATED CRIME? One side effect of illegal drug use is crime: Users often turn to crime to finance their habit. We examine two policies designed to reduce illegal drug use and see what effects they have on drug-related crime. For simplicity, we assume the total dollar value of drug-related crime equals total expenditure on drugs. Demand for illegal drugs is inelastic, due to addiction issues. 35  POLICY 1: INTERDICTION Interdiction new value of drug- reduces Price of related crime the supply Drugs S2 D1 of drugs. S1 Since demand P2 for drugs is inelastic, initial value P1 P rises propor- of drug- tionally more related than Q falls. crime Result: an increase in Q2 Q1 Quantity total spending on drugs, of Drugs and in drug-related crime 36  POLICY 2: EDUCATION new value of drug- Education Price of related crime reduces the Drugs demand for D2 D1 drugs. S P and Q fall. P1 initial value Result: of drug- A decrease in P2 related total spending crime on drugs, and in drug-related Q2 Q1 Quantity crime. of Drugs 37  OTHER ELASTICITIES Income elasticity of demand: measures the response of Qd to a change in consumer income Income elasticity Percent change in Qd = of demand Percent change in income  Recall: An increase in income causes an increase in demand for a normal good.  Hence, for normal goods, income elasticity > 0.  For inferior goods, income elasticity < 0. 38  OTHER ELASTICITIES Cross-price elasticity of demand: measures the response of demand for one good to changes in the price of another good Cross-price elast. % change in Qd for good 1 = of demand % change in price of good 2  For substitutes, cross-price elasticity > 0 (e.g., an increase in price of beef causes an increase in demand for chicken)  For complements, cross-price elasticity < 0 (e.g., an increase in price of computers causes decrease in demand for software) 39  SUMMARY Elasticity and demand calculate the sensitivity of the quantity supplied / demanded to a change in the price. – Slope: slope of the curve. – Elasticity: measures the percentage change in the amount caused by a change in the price of 1 per cent. Relationship between the slope and elasticity. Elasticity and total revenue: – Inelastic: price and total revenue vary in the same direction – Elastic: the price and total revenue vary in the opposite direction 40 ELASTICITY OF A LINEAR DEMAND CURVE P The slope of a linear demand curve is constant, Elastic but its elasticity ED