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Chapter 4 Subtleties of the Supply and Demand Model: Price Floors, Price Ceilings, and Elasticity

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Key Terms price controlprice control price ceilingprice ceiling price floorprice floor rent controlrent control minimum wageminimum wage price elasticity of demandprice elasticity of demand unit-free measureunit-free measure elastic demandelastic demand inelastic demandinelastic demand perfectly inelastic demandperfectly inelastic demand perfectly elastic demandperfectly elastic demand income elasticity ofincome elasticity of demanddemand cross-price elasticity ofcross-price elasticity of demanddemand price elasticity of supplyprice elasticity of supply perfectly elastic supplyperfectly elastic supply perfectly inelastic supplyperfectly inelastic supply

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Interference with Market Prices Price Control: a government control or regulation that sets or limits the price to be charged for a particular good. Two Broad Types of Price Controls: Price Floor Price Ceiling

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Price Ceilings and Floors Price Ceiling: a government price control that sets the maximum allowable price for a good or a service. Example: –Rent control: a government price control that sets a maximum allowable rent to a house or an apartment.

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Price Floor: a government price control that sets the minimum allowable price for a good or a service. Example: –Minimum wage: a wage per hour below which it is illegal to pay workers. Price Ceilings and Floors

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Side Effects of Price Ceilings If the government sets the price ceiling below the equilibrium price, a shortage will result. Ways We Deal with Persistent Shortages: Coupons Long lines Reduction in the quality of the good sold

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Figure 1: Effects of a Maximum-Price Law

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If the government sets the price floor above the equilibrium price, a surplus will result. Ways We Deal with Persistent Surpluses: Surpluses purchased by the government Surplus labor results in unemployment Side Effects of Price Floors

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Figure 2: Effects of a Minimum-Price Law (Top graph)

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Figure 2: Effects of a Minimum-Price Law (Bottom Graph)

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Elasticity of Demand Price Elasticity of Demand: the percentage change in the quantity demanded of a good divided by the percentage change in the price of that good.

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In Figure 3, the top graph shows a demand curve where an increase in the price from $20 to $22 results in a decrease in the quantity demanded from 60 million barrels to 48 million barrels. Figure 3: Elasticity of Demand

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Figure 3: Comparing Different Sizes of the Price Elasticity of Demand

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Percentage change in price Percentage change in Qty. demanded Elasticity of Demand

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The price elasticity of demand for the top graph in Figure 3 is: Note: A price elasticity of demand of 2 implies that a one percentage point increase in the price results in a two percentage point decrease in the quantity demanded. Price Elasticity of Demand Elasticity of Demand

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Size of the Elasticity: High versus Low We compare the demand curve found on the top graph with the demand curve found on the bottom graph on Figure 3. On the bottom graph, an increase in the price from $20 to $22 results in a decrease in the quantity demanded from 60 million barrels to 57 million barrels.

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Figure 3: Comparing Different Sizes of the Price Elasticity of Demand

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Size of the Elasticity: High versus Low Percentage change in Qty. demanded Percentage change in price

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Size of the Elasticity: High versus Low Price Elasticity of Demand The elasticity of demand for the top graph is: Note: A price elasticity of demand of 1/2 implies that a one percentage point increase in the price results in a one-half percentage point decrease in the quantity demanded.

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Note: The top graph in Figure 3 had a higher price elasticity of demand (elasticity = 2) than the price elasticity of demand for the bottom graph (elasticity = 1/2). Hence, the demand curve on the top graph is more sensitive to price changes than the demand curve on the bottom graph. Size of the Elasticity: High versus Low

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In the next slide, Figure 4 analyzes the effect of a decrease in the supply of oil on the equilibrium price of oil. The top graph features a demand curve with a higher elasticity (elasticity = 2) than the bottom graph (elasticity = ½). Impact of a Change in Supply on the Price of Oil

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Figure 4 : The Importance of the Size of the Price Elasticity of Demand

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Note: The same shift in the supply of oil to the left (decrease by 14 million barrels) results in a higher equilibrium price on the bottom graph, where the demand curve has a lower price elasticity (elasticity = ½) than in the top graph (elasticity = 2). Impact of a Change in Supply on the Price of Oil

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Figure 4A shows the daily crude oil prices in the world since January 2006. The large fluctuations of oil prices support the idea that demand for oil is inelastic. Impact of a Change in Supply on the Price of Oil

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Source: Department of Energy Figure 4A: World Oil and Gasoline Spot Prices (Daily), January 2006-August 2007

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Working with Demand Elasticities The general formula that we will use for demand elasticity (e d ) will be:

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Working with Demand Elasticities An attractive feature of the price elasticity of demand is that it is a unit-free measure; it allows the comparison of the price elasticity of different goods and different prices. Unit-Free Measure: a measure that does not depend on the unit of measurement.

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Working with Demand Elasticities Assume the price of rice rises by 10 cents, from 50 to 60 cents per pound, and the quantity demanded falls from 20 to 19 tons. This implies a decrease of 1 ton per 10 cent increase in the price, or: Elasticity of Demand:

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Working with Demand Elasticities Similarly, assume the price of steak rises by $1, from $5 to $6 per pound, and the quantity demanded falls from 20 tons to 19 tons. This implies a decrease of 1 ton per $1 increase in the price, or: Elasticity of Demand:

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slope Elasticity versus Slope One common mistake made when dealing with elasticity is to interchange the elasticity of the demand curve with its slope. These concepts are similar, but not the same. Elasticity of demand =

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Notes: The elasticity is a unit-free measure, while the slope is not. With a straight-line demand curve, the slope is constant, while the elasticity varies at different points in the line. Elasticity versus Slope

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The Midpoint Formula or

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Recall Figure 4. If we use the midpoint formula to calculate the elasticity on the top graph, the elasticity of demand is: The Midpoint Formula

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Talking About Elasticities Elastic Demand – demand where the elasticity is greater than one. Inelastic Demand – demand where the elasticity is less than one. Unit Elastic Demand – demand where the elasticity is exactly equal to one.

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Perfectly Inelastic Demand – demand (or part of the demand curve) where the price elasticity is zero, indicating no response to a change in price. A perfectly inelastic demand curve is a vertical line. Perfectly Elastic Demand – demand (or part of the demand curve) where the price elasticity is infinite, indicating an infinite response to a change in price. A perfectly elastic demand curve is a horizontal line. Talking About Elasticities

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Figure 6: Perfectly Elastic and Perfectly Inelastic Demand

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Revenue of a firm = (P X Q) = (price of a good) X (quantity of the good sold) Revenue and the Price Elasticity of Demand

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Example: If people purchase 60 million barrels of oil at $20, then the firms revenues equal: Revenue = 60 million X $20 = $1200 million = $1.2 billion Revenue and the Price Elasticity of Demand

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Figure 7 shows that if the price increases in an elastic demand curve, the firm revenues will decrease. If the price increases in an inelastic demand curve, the firm revenues will increase. Revenue and the Price Elasticity of Demand

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FIGURE 7: Effects of an Increase in the Price of Oil on Revenue

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If in the inelastic region of a straight-line demand curve, an increase (a decrease) in the price will result in an increase (a decrease) in revenues. If in the elastic region of a straight-line demand curve, an increase (a decrease) in the price will result in a decrease (an increase) in revenues. Revenue and the Price Elasticity of Demand

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Figure 8: Revenue and Elasticity of a Straight-Line Demand Curve

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What Determines the Size of the Price Elasticity of Demand? Determinants of the Price Elasticity of Demand: Degree of substitutability Big-ticket versus little-ticket items Temporary versus permanent price change Differences in preferences Long-run versus short-run elasticity

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Goods with a lot of substitutes have a high price elasticity of demand. Goods with few substitutes have a low price elasticity of demand. Degree of Substitutability

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Big-Ticket versus Little-Ticket Items If a good represents a large share fraction of peoples income, then the price elasticity will be high. If a good represents a small share fraction of peoples income, then the price elasticity will be low.

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Temporary versus Permanent Price Change If the price change is perceived to be temporary, then the price elasticity of demand will be high. If the price change is perceived to be permanent, then the price elasticity of demand will be low.

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Differences in Preferences Some goods have varying price elasticity of demand across different consumer groups. Examples: 1)New smokers have a higher price elasticity of demand for cigarettes than established (addicted?) smokers. 2)Retired persons have a lower price elasticity of demand for motor homes than persons in the 18-26 age group.

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Long Run vs. Short Run The length of time elapsed since a price change affects the price elasticity of demand. Example: If the price of gasoline rises, the price elasticity of demand for gasoline may be lower for SUV owners in the short run (just immediately after the price change) than in the long run (when they can buy a different car).

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Income Elasticity of Demand Income Elasticity of Demand Income Elasticity of Demand: the percentage change in the quantity demanded of a good divided by the percentage change in income.

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If the income elasticity of demand is positive (i.e., you buy more as income increases), then the good is a normal good. If the income elasticity of demand is negative (i.e., you buy less as income increases), then the good is an inferior good. Note: With income elasticity of demand, it is incorrect to take the absolute value of the computed elasticity. Income Elasticity of Demand

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Cross-Price Elasticity of Demand Cross Price Elasticity of Demand: the percentage change in the quantity demanded of a good divided by the percentage change in the price of a related good (a substitute or a complement).

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Cross-Price Elasticity of Demand If the cross-price elasticity of demand is positive (i.e., you buy more as price of the other good increases), then the two related goods are substitutes. If the cross-price elasticity of demand is negative (i.e., you buy less as price of the other good increases), then the two related goods are complements.

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Price Elasticity of Supply Elasticity of Supply Elasticity of Supply: the percentage change in the quantity supplied of a good divided by the percentage change in the price of a same good.

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Elasticity of Supply The general formula that we will use for price elasticity of supply (e s ) will be:

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Elastic versus Inelastic Supply Elastic Supply: supply where the price elasticity is greater than one. Inelastic Supply: supply where the price elasticity is less than one. Unit Elastic Supply: supply where the price elasticity is exactly equal to one.

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Perfectly Elastic versus Perfectly Inelastic Supply Perfectly Elastic Supply: supply where the price elasticity is infinite, indicating an infinite response to a change in price. A perfectly elastic supply curve is a horizontal line.

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Perfectly Inelastic Supply: supply where the price elasticity is zero, indicating no response to a change in price. A perfectly inelastic supply curve is a vertical line. Examples: The Mona Lisa Super Bowl Tickets Perfectly Elastic versus Perfectly Inelastic Supply

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Figure 9: Perfectly Elastic and Perfectly Inelastic Supply

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Figure 10: Comparing Different Sizes of the Price Elasticities of Supply

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Elastic vs. Inelastic Supply In the next slide, Figure 11 shows that the same shift in the demand for oil to the left results in a lower equilibrium price in the bottom graph, where the supply curve has a lower price elasticity than in the top graph, which has a higher price elasticity.

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Figure 11: Importance of Knowing the Size of the Price Elasticity of Supply

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Key Terms price controlprice control price ceilingprice ceiling price floorprice floor rent controlrent control minimum wageminimum wage price elasticity of demandprice elasticity of demand unit-free measureunit-free measure elastic demandelastic demand inelastic demandinelastic demand perfectly inelastic demandperfectly inelastic demand perfectly elastic demandperfectly elastic demand income elasticity ofincome elasticity of demanddemand cross-price elasticity ofcross-price elasticity of demanddemand price elasticity of supplyprice elasticity of supply perfectly elastic supplyperfectly elastic supply perfectly inelastic supplyperfectly inelastic supply

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