To do today: S & D in algebra and introduction to elasticities

Transcription

1 To do today: S & D in algebra and introduction to elasticities The math of S and D (linear curves) What is elasticity? Concept and calculation Determinants of elasticity 2011 Pearson Education

2 Market Equilibrium: Why it is stable Price Adjustments If P > P*, a surplus forces the price down. If P < P*, a shortage forces the price up. At P*, price doesn t change until some event changes either demand or supply Pearson Education

3 Market Equilibrium: StabilityMarket 2011 Pearson Education

4 The mathematics of S & D D: P = a - bq D S: P = c + dq S Market equilibrium: (* means =ium level) P* = a - bq* P* = c + dq* 2011 Pearson Education

5 Solving for Q* P* = a - bq* P* = c + dq* Therefore a - bq* = c + dq* Solving for Q*: 2011 Pearson Education

6 Solving for P* Can use either demand or supply equation Using demand: P* = a bq* P* = a b[(a-c)/(b+d)] P* = P* = 2011 Pearson Education

7 Key concept: Responsiveness to price change Key point is how responsive demanders and suppliers are to price change If responsive, change quantity demanded or supplied a lot if p changes D or S curve will be relatively shallow 2011 Pearson Education

8 Example: Shift the S Curve When shift the S curve, slide along the given D curve to the new equilibrium New equilibrium always on the given D curve So, slope of the given D curve affects the new equilibrium p and q 2011 Pearson Education

9 Equilibrium on a graph a Graph Check intuition: Shallow D slide more out than down Price S 1 E 1 E 2 S 2 D 1 Quantity 2011 Pearson Education

10 Equilibrium on a Graph Check intuition: Shallow D slide more out than down Price Quantity 2011 Pearson Education

11 Equilibrium on a Graph Check intuition: Steeper D, more price change, less quantity change Price S 1 E 1 S 2 E 2 D 1 Quantity 2011 Pearson Education

12 Equilibrium on a Graph Check intuition: Steeper D, more price change, less quantity change Price Quantity 2011 Pearson Education

13 Price elasticity for broad consumption groups, 2005 Country Food, Beverages & tobacco Clothing & footwear Housing Medical & health Recreation Education Congo, Dem. Rep a a Pakistan Switzerland United Kingdom United States Source: US Department of Agriculture

14 Elasticity Defined Price elasticity of demand is a measure of the responsiveness of quantity demanded to changes in price. Compare the percentage change in the quantity demanded with the percentage change in price.

15 Price Elasticity of Demand A Units-Free Measure Elasticity is a ratio of percentages, so a change the units of measurement of price or quantity leaves the elasticity value the same. Minus Sign and Elasticity The formula yields a negative value, because price and quantity move in opposite directions. But it is the magnitude, or absolute value, that reveals how responsive the quantity change has been to a price change.

16 The Price Elasticity of Demand: A Price Rise Suppose Starbucks raises the price of a latte from $3 to $5 a cup. What is the percentage change in price? Percent change in price = New price Initial price Initial Price x 100 Percent change in price = x 100 = percent

17 Price Elasticity of Demand: A Price Cut Suppose Starbucks cuts the price of a latte from $5 to $3 a cup. What is the percentage change in price? Percent change in price = New price Initial price Initial Price x 100 Percent change in price = x 100 = percent

18 A Measure Independent of Direction of Change Same price change, $2, over the same interval, $3 to $5, is a different percentage change depending on whether the price rises or falls. Need a measure of percentage change that does not depend on the direction of the price change. Use the average of the initial price and the new price to measure the percentage change.

19 The Midpoint Method How to do it: Divide the change in the price by the average price and then multiply by 100. The average price is at the midpoint between the initial price and the new price. Percent change in price = New price Initial price (New Price + Initial Price) 2 x 100

20 Midpoint Price Elasticity of Demand: Price change from 5 to 3 or 3 to 5 Percent change in price = ( ) 2 x 100 Percent change in price = percent. The percentage change in price calculated by the midpoint method is the same for a price rise and a price fall.

21 Percentage Change in Quantity Demanded If Starbucks raises the price of a latte, the quantity of latte demanded decreases. Percent change in quantity = New quantity Initial quantity (New quantity + Initial quantity) 2 x 100 Percent change in quantity = 5 15 (5 + 15) 2 x 100 = 100 Percent

22 Use Absolute Values Price and quantity always change in directions. To compare the percentage change in the price and the percentage change in the quantity, use the absolute values. Elasticity in this case: % change in quantity/% change in price = 100/50 = 2 This is elastic demand.

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24 Elastic and Inelastic Demand Five cases of elasticity Elastic: % change in the quantity demanded > % change in price. Unit elastic: % change in the quantity demanded = % change in price.

25 The Next Cases of Price Elasticity of Demand Inelastic: % change in the quantity demanded < % change in price. Perfectly elastic: quantity demanded changes by a very large (infinitely large) % in response to an almost zero % change in price. Perfectly inelastic: quantity demanded remains constant as the price changes.

26 Graphing a Perfectly Elastic Demand Curve

27 Graphing an Elastic Demand Curve 1. When the price of a Sony PlayStation rises by 10%, 2. The quantity demanded decreases by 20%. 3. Demand for Sony Playstations is elastic.

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30 THE PRICE ELASTICITY OF DEMAND Figure shows an inelastic demand. 1. When the price of gum rises by 20%, 2. The quantity demanded decreases by %. 3. The demand for gum is inelastic.

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32 Perfectly Inelastic Demand 1. When the price rises, 2. The quantity demanded does not decrease. 3. Demand is perfectly inelastic.

33 Graphing Perfectly Inelastic Demand 1. When the price rises, 2. The quantity demanded does not decrease. 3. Demand is perfectly inelastic.

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35 What Determines Elasticity? Influences on the price elasticity of demand fall into two categories: Availability of substitutes Proportion of income spent Availability of Substitutes The demand for a good is elastic if a substitute for it is easy to find. The demand for a good is inelastic if a substitute for it is hard to find.

36 When are Substitutes Available? Luxury Versus Necessity A necessity has poor substitutes, so the demand for a necessity is inelastic. Food is a necessity. A luxury has many substitutes, so the demand for a luxury is elastic. Exotic vacations are luxuries. Narrowness of Definition The demand for a narrowly defined good is elastic. The demand for a broadly defined good is inelastic. Not many substitutes for food but many for bread and even more for sourdough bread.

37 What Determines Elasticity? Time Elapsed Since Price Changed The longer the time elapsed since the price change, the more elastic is the demand for the good. Proportion of Income Spent A price rise, like a decrease in income, means that people cannot afford to buy the same quantities. The greater the proportion of income spent on a good, the more elastic is the demand for the good.

38 The Computed Elasticity and its Type Price elasticity of demand = Percentage change in quantity demanded Percentage change in the price If > 1, demand is elastic. If = 1, demand is unit elastic. If < 1, demand is inelastic.