# Applying the Supply-and-Demand Model

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Applying the Supply-and-Demand Model
Chapter Three Applying the Supply-and-Demand Model

Topics To Be Covered How the shapes of demand and supply curves matter? Sensitivity of quantity demanded to price. Sensitivity of quantity supplied to price. Long run versus short run Effects of a sales tax. © 2009 Pearson Addison-Wesley. All rights reserved.

How shapes of demand and supply matter?
The shapes of the demand and supply curves determine by how much a shock affects the equilibrium price and quantity. Example: processed pork (same as Chapter 2) Supply depends on the price of pork and the price of hogs. © 2009 Pearson Addison-Wesley. All rights reserved.

Figure 3.1 How the Effect of a Supply Shock Depends on the Shape of the Demand Curve
(b) (c) D 2 D 1 e e 2 2 e 3.55 3.675 D 3 2 3.30 3.30 3.30 S 2 e e e S 2 1 1 S 2 1 S 1 S 1 S 1 176 215 220 176 220 176 205 220 Q , Million kg of pork per year Q , Million kg of pork per year Q , Million kg of pork per year © 2007 Pearson Addison-Wesley. All rights reserved.

Figure 3.1 How the Effect of a Supply Shock Depends on the Shape of the Demand Curve (cont’d)
When demand is very sensitive to price… a shift in the supply curve to S2… has no effect on the equilibrium price and a substantial effect on the quantity p, \$ per kg e2 3.30 D3 e1 S2 S1 176 205 220 Q, Million kg of pork per year © 2009 Pearson Addison-Wesley. All rights reserved.

Sensitivity of quantity demanded to price.
Elasticity – the percentage change in a variable in response to a given percentage change in another variable, all other factors held constant. © 2009 Pearson Addison-Wesley. All rights reserved.

Price elasticity of demand
(e) – the percentage change in the quantity demanded in response to a given percentage change in the price. Elastic demand E<-1 or |E| >1 Unit elastic demand E=-1 or |E| =1 Inelastic demand 0>E>-1 or 0<|E|<1 © 2009 Pearson Addison-Wesley. All rights reserved.

Price Elasticity and Total Revenue
Total revenue = price x quantity Elastic demand Price and total revenue inversely related Inelastic demand Price and total revenue are directly related Unit elastic demand No change in total revenue in response to a change in price © 2009 Pearson Addison-Wesley. All rights reserved.

Sensitivity of quantity demanded to price (cont).
Formally, where D indicates change. Example If a 1% increase in price results in a 3% decrease in quantity demanded, the elasticity of demand is e = -3%/1% = -3. © 2009 Pearson Addison-Wesley. All rights reserved.

Sensitivity of quantity demanded to price (cont).

Sensitivity of quantity demanded to price: Example.
The estimated linear demand function for pork is: Q = p where Q is the quantity of pork demanded in million kg per year and p is the price of pork in \$ per year. At the equilibrium point of p = \$3.30 and Q = 220 the elasticity of demand for pork is © 2009 Pearson Addison-Wesley. All rights reserved.

Elasticity: An Application and a practice problem
Varian (2002) found that the price elasticity of demand for internet use was -2.0 for those who used a 128 Kbps service -2.9 for those who used a 64 Kbps service. Practice problem: A 1% increase in the price per minute reduced the connection time by ________ for those with high speed access, and by _______ for those with slow phone line access. © 2009 Pearson Addison-Wesley. All rights reserved.

Elasticity Along a Demand Curve
The elasticity of demand varies along most demand curves. Along a downward-sloping linear demand curve the elasticity of demand is a more negative number the higher the price is. © 2009 Pearson Addison-Wesley. All rights reserved.

Figure 3.2 Elasticity Along the Pork Demand Curve
Q = p Perfectly elastic p Q a / b = 14.30 11.44 , \$ per kg e = -b = -20 x = -4 57.2 Elastic e < –1 p 11.44 e = –4 3.30 = -0.3 220 D a /(2 b ) = 7.15 Unitary: e = -1 Inelastic 0 > e > –1 3.30 e = –0.3 Perfectly inelastic a/5 = 57.2 a /2 = 143 220 a = 286 Q , Million kg of pork per year © 2009 Pearson Addison-Wesley. All rights reserved.

Elasticity Along The Demand Curve: Practice Problem
According to Agcaoli-Sombilla (1991), the elasticity of demand for rice is in Austria; -0.8 in Bangladesh, China, India, Indonesia, and Thailand; in Japan; in the EU and the US; and in Vietnam. In which countries is the demand for rice inelastic? In all the countries, since in all cases e > -1. In which country is the least elastic? In Vietnam, where e = -0.15 This is question #7 of the Questions at the end of the chapter. © 2009 Pearson Addison-Wesley. All rights reserved.

Figure 3.3 Vertical and Horizontal Demand Curves

Price Elasticity of Demand
The absolute percentage change in the quantity demanded is smaller than the absolute percentage change in price so that the price elasticity of demand is less than 1 and the good has inelastic demand. If the percentage change in the quantity demanded is infinitely large when the price barely changes, the price elasticity of demand is infinite and the good has perfectly elastic demand. © 2007 Pearson Addison-Wesley. All rights reserved.

Price Elasticity of Demand
If the absolute percentage change in the quantity demanded is greater than the absolute percentage change in price, the price elasticity of demand is greater than 1 and the good has elastic demand. © 2007 Pearson Addison-Wesley. All rights reserved.

Price Elasticity of Demand
The Factors That Influence the Elasticity of Demand The elasticity of demand for a good depends on: The closeness of substitutes The proportion of income spent on the good The definition of the market The time elapsed since a price change © 2007 Pearson Addison-Wesley. All rights reserved.

Constant elasticity demand function

Sensitivity of quantity demanded to income.
Formally, where Y stands for income. Example If a 1% increase in income results in a 3% decrease in quantity demanded, the income elasticity of demand is x = -3%/1% = -3. © 2009 Pearson Addison-Wesley. All rights reserved.

Sensitivity of quantity demanded to income: Example.
The estimated demand function for pork is: Q = 171 – 20p + 20pb + 3pc + 2Y where p is the price of pork (\$3.00), pb is the price of beef (\$4.00), pc is the price of chicken (\$3.33) and Y is the income (in thousands of dollars) (12.5). Question: what would be the income elasticity of demand for Pork if Q = 220 and Y = 12.5 Answer: Since = 2, then © 2009 Pearson Addison-Wesley. All rights reserved.

Calculating Elasticities
The estimated demand function for pork is: Q = 171 – 20p + 20pb + 3pc + 2Y where p is the price of pork (\$3.00), pb is the price of beef (\$4.00), pc is the price of chicken (\$3.33) and Y is the income (in thousands of dollars) (12.5). Then Q = 171 – 20(3.30) + 20(4) +3 (3.33) + 2 (12.5) Q= Q=20 © 2009 Pearson Addison-Wesley. All rights reserved.

Calculating Price Elasticity of Demand

Calculating Cross Price Elasticity

Sensitivity of quantity demanded to the price of a related good.
If the cross-price elasticity is positive, the goods are substitutes. Question: can you think of any examples of two goods that are substitutes? Roses and carnations. If the cross-price elasticity is negative, the goods are complements Question: can you think of any examples of two goods that are complements? Peanut butter and jelly © 2009 Pearson Addison-Wesley. All rights reserved.

Calculating Income Elasticity

Income Elasticity EY>0, normal good EY>1, normal and superior

Sensitivity of quantity supplied to price.
Formally, where Q indicates quantity supplied. Example If a 1% increase in price results in a 3% increase in quantity supplied, the elasticity of supplied is h = %/1% = 3. © 2009 Pearson Addison-Wesley. All rights reserved.

Sensitivity of quantity demanded to price: Example.
The estimated linear supply function for pork is: Q = p where Q is the quantity of pork supplied in million kg per year and p is the price of pork in \$ per year. At the equilibrium, where p = \$3.30 and Q = 220, the elasticity of supplied is: © 2009 Pearson Addison-Wesley. All rights reserved.

Sensitivity of quantity supplied to price (cont).

Figure 3.4 Elasticity Along the Pork Supply Curve

Demand Elasticities Over Time
Elasticities tend to be larger in the long-run. Can you think why? In the case of demand: Substitution and storage opportunities. In the case of supply: Converting fixed inputs into variable inputs. Answer As the page 57 of the textbook indicates, in the long-run people have more time to adapt to persistent price changes by substituting for other goods and by storing. © 2009 Pearson Addison-Wesley. All rights reserved.

Effects of a Sales Tax What effect does a sales tax have on equilibrium prices and quantity? Is it true, as many people claim, that taxes assessed on producers are passed along to consumers? Do the equilibrium price and quantity depend on whether the tax is assessed on consumers or on producers? © 2009 Pearson Addison-Wesley. All rights reserved.

Two Types of Sales Taxes
Ad valorem tax - for every dollar the consumer spends, the government keeps a fraction, α, which is the ad valorem tax rate. Unit tax - where a specified dollar amount, t, is collected per unit of output. © 2009 Pearson Addison-Wesley. All rights reserved.

Figure 3.5 Effect of a \$1.05 Specific Tax on the Pork Market Collected from Producers
A tax on producers shifts the supply curve downward by the amount of the tax (t = \$1.05)…. which causes the market price to increase… After the tax, buyers are worse off by \$0.70 (\$ \$3.30)… sellers are worse off by \$0.35 (\$ \$2.95) and the government collects \$216.3 in revenue. S2 , \$ per kg e2 t = \$1.05 p S1 p2 = 4.00 e1 p3 = 3.30 p2 – t = 2.95 T = \$216.3 million D 176 Q2 = 206 Q1 = 220 Q , Million kg of pork per year © 2009 Pearson Addison-Wesley. All rights reserved.

Solution to Excise Tax Problem Unit Tax on Producers

Figure 3.6 Effect of a \$1.05 Specific Tax on Pork Collected from Consumers
, \$ per kg but the new equilibrium is the same as when the tax is applied to suppliers p e2 Wedge, t = \$1.05 S p = 4.00 e2 p = 3.30 T = \$216.3 million p2 – t = 2.95 t = \$1.05 D1 The tax shifts the demand curve down by τ = \$1.05… D2 176 Q2 = 206 Q1 = 220 Q , Million kg of pork per year © 2009 Pearson Addison-Wesley. All rights reserved.

Solution to Excise Tax Problem Unit Tax on Consumers

How Specific Tax Effects Depend on Elasticities.
The government raises the tax from zero to t, so the change in the tax is Dt =t – 0 = t. The price buyers pay increases by: If e = -0.3 and h = 0.6, a change of a tax of Dt = \$1.05 causes the price buyers pay to rise by © 2009 Pearson Addison-Wesley. All rights reserved.

Solved Problem 3.2 If the supply curve is perfectly elastic and demand is linear and downward sloping, what is the effect of a \$1 specific tax collected from producers on equilibrium price and quantity, and what is the incidence on consumers? Why? © 2009 Pearson Addison-Wesley. All rights reserved.

Figure 3.7 Comparison of an Ad Valorem and a Specific Tax on Pork