# Price, Income and Cross Elasticity

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Price, Income and Cross Elasticity

Elasticity – the concept
The responsiveness of one variable to changes in another When price rises, what happens to demand? Demand falls BUT! How much does demand fall?

Elasticity – the concept
If price rises by 10% - what happens to demand? We know demand will fall By more than 10%? By less than 10%? Elasticity measures the extent to which demand will change

Elasticity 4 basic types used: Price elasticity of demand
Price elasticity of supply Income elasticity of demand Cross elasticity

Elasticity Price Elasticity of Demand
The responsiveness of demand to changes in price Where % change in demand is greater than % change in price – elastic Where % change in demand is less than % change in price - inelastic

Elasticity The Formula: % Change in Quantity Demanded
___________________________ Ped = % Change in Price If answer is between 0 and -1: the relationship is inelastic If the answer is between -1 and infinity: the relationship is elastic Note: PED has – sign in front of it; because as price rises demand falls and vice-versa (inverse relationship between price and demand)

Elasticity Price (£) Quantity Demanded
The demand curve can be a range of shapes each of which is associated with a different relationship between price and the quantity demanded. Quantity Demanded

Elasticity Total Revenue Price £5 D 100 Quantity Demanded (000s)
Total revenue is price x quantity sold. In this example, TR = £5 x 100,000 = £500,000. This value is represented by the grey shaded rectangle. The importance of elasticity is the information it provides on the effect on total revenue of changes in price. £5 Total Revenue D 100 Quantity Demanded (000s)

Elasticity D Total Revenue Price £5 £3 100 140
If the firm decides to decrease price to (say) £3, the degree of price elasticity of the demand curve would determine the extent of the increase in demand and the change therefore in total revenue. £5 £3 Total Revenue D 100 140 Quantity Demanded (000s)

Elasticity % Δ Price = -50% % Δ Quantity Demanded = +20%
Producer decides to lower price to attract sales 10 % Δ Price = -50% % Δ Quantity Demanded = +20% Ped = -0.4 (Inelastic) Total Revenue would fall 5 Not a good move! D 5 6 Quantity Demanded

Elasticity Producer decides to reduce price to increase sales
% Δ in Price = - 30% % Δ in Demand = + 300% Ped = - 10 (Elastic) Total Revenue rises 10 Good Move! 7 D 5 20 Quantity Demanded

Elasticity If demand is price elastic:
Increasing price would reduce TR (%Δ Qd > % Δ P) Reducing price would increase TR (%Δ Qd > % Δ P) If demand is price inelastic: Increasing price would increase TR (%Δ Qd < % Δ P) Reducing price would reduce TR (%Δ Qd < % Δ P)

Elasticity Income Elasticity of Demand:
The responsiveness of demand to changes in incomes Normal Good – demand rises as income rises and vice versa Inferior Good – demand falls as income rises and vice versa

Elasticity A positive sign denotes a normal good
Income Elasticity of Demand: A positive sign denotes a normal good A negative sign denotes an inferior good

Elasticity For example:
Yed = - 0.6: Good is an inferior good but inelastic – a rise in income of 3% would lead to demand falling by 1.8% Yed = + 0.4: Good is a normal good but inelastic – a rise in incomes of 3% would lead to demand rising by 1.2% Yed = + 1.6: Good is a normal good and elastic – a rise in incomes of 3% would lead to demand rising by 4.8% Yed = - 2.1: Good is an inferior good and elastic – a rise in incomes of 3% would lead to a fall in demand of 6.3% This slide has a ten second gap in between each example to allow the teacher to explain how the figures have been calculated. This gap can be increased or reduced as appropriate using the custom animation tool.

Elasticity Cross Elasticity:
The responsiveness of demand of one good to changes in the price of a related good – either a substitute or a complement % Δ Qd of good t __________________ Xed = % Δ Price of good y

Elasticity Goods which are complements: Goods which are substitutes:
Cross Elasticity will have negative sign (inverse relationship between the two) Goods which are substitutes: Cross Elasticity will have a positive sign (positive relationship between the two)

Elasticity Price Elasticity of Supply:
The responsiveness of supply to changes in price If Pes is inelastic - it will be difficult for suppliers to react swiftly to changes in price If Pes is elastic – supply can react quickly to changes in price % Δ Quantity Supplied ____________________ Pes = % Δ Price

Determinants of Elasticity
Time period – the longer the time under consideration the more elastic a good is likely to be Number and closeness of substitutes – the greater the number of substitutes, the more elastic The proportion of income taken up by the product – the smaller the proportion the more inelastic Luxury or Necessity - for example, addictive drugs

Importance of Elasticity
Relationship between changes in price and total revenue Importance in determining what goods to tax (tax revenue) Importance in analysing time lags in production Influences the behaviour of a firm This slide also has an automatic response with ten second gaps in between each point. At this stage we have tried to keep things as simple as possible but to introduce issues that will be dealt with later in the course.

Elasticity of Demand And Supply
The focus of this lecture is the elasticity. Students will learn about the price elasticity of demand, price elasticity of supply, cross elasticity and income elasticity. OBJECTIVES 1. Understand the definition of elasticity. 2. Be able to compute  the elasticity coefficients. 3. Analyze the elasticity characteristics. 4. Illustrate the determinants of the elasticity. 5. Explain the total revenue test and understand the relationship between total revenue and price elasticity of demand. TOPICS Please read all the following topics. PRICE ELASTICITY OF DEMAND DETERMINANTS OF Ed TOTAL REVENUE TEST PRICE ELASTICITY OF SUPPLY CROSS ELASTICITY OF DEMAND INCOME ELASTICITY OF DEMAND

Price Elasticity of Demand
Definition: Law of demand tells us that consumers will respond to a price drop by buying more, but it does not tell us how much more. The degree of sensitivity of consumers to a change in price is measured by the concept of price elasticity of demand. Price elasticity formula: Ed = percentage change in Qd / percentage change in Price. If the percentage change is not given in a problem, it can be computed using the following formula: Ed = Q2-Q1) /P2-P1)X (P1 + P2)/(Q1+Q2) Because of the inverse relationship between Qd and Price, the Ed coefficient will always be a negative number. But, we focus on the magnitude of the change by neglecting the minus sign and use absolute value Examples: 1.  If the price of Product A  increased by 10%,  the quantity demanded decreased by 20%. Then the coefficient for  price elasticity of the demand of Product A is: Ed = percentage change in Qd / percentage change in Price = (20%) / (10%) = 2 2. If the quantity demanded of Product B has decreased from 1000 units to 900 units as price increased from \$2 to \$4 per unit, the coefficient for Ed is: Ed = (Q2-Q1) /P2-P1)X (P1 + P2)/(Q1+Q2)= Take the absolute value of , Ed = 0.16

Characteristics: Ed approaches infinity, demand is perfectly elastic. Consumers are very sensitive to price change. Ed > 1, demand is elastic. Consumers are relatively responsive to price changes. Ed = 1, demand is unit elastic. Consumers’ response and price change are in same proportion. Ed < 1, demand is inelastic. Consumers are relatively unresponsive to price changes. Ed approaches 0, demand is perfectly inelastic. Consumers are very insensitive to price change. Ed is usually greater in the higher price range than in lower price range. Demand is more elastic in upper left portion of the demand curve than in the lower right portion of the curve. However, it is impossible to judge elasticity of a demand curve by its flatness or steepness. Along a linear demand curve, its elasticity changes. This relationship is demonstrated in the following example:

An Example DEMAND FUNCTION FOR PRODUCT X: P = 2.5-0.01Q
P = PRICE; Q = QUANTITY, TR = TOTAL REVENUE Ed = PRICE ELASTICITY OF DEMAND           A     B      C       D       E        F        G        H         I        J Q:       0    50   100    150   200    250    300   350   400   450 P:       4.5   4     3.5     3       2.5       2       1.5      1      0.5      0 Ed:      17    5     2.6   1.57       1     0.64   0.38    0.2    0.06 ELASTICITY OF DEMAND; FROM A TO E Ed >1 FROM E TO F Ed =1 FROM F TO J Ed <1

Determinants of Price Elasticity of Demand
Various factors influence the price elasticity of demand. Here are some of them: 1. # of Substitutes: If a product can be easily substituted, its demand is elastic, like Gap's jeans. If a product cannot be substituted easily, its demand is inelastic, like gasoline. 2. Luxury Vs Necessity: Necessity's demand is usually inelastic because there are usually very few substitutes for necessities. Luxury product, such as leisure sail boats, are not needed in a daily bases. There are usually many substitutes for these products. So their demand is more elastic. 3. Price/Income Ratio: The larger the percentage of income spent on a good, the more elastic is its demand. A change in these products' price will be highly noticeable as  they affect consumers' budget with a bigger magnitude. Consumers will respond by cutting back more on these product when price increases. On the other hand, the smaller the percentage of income spent on a good, the less elastic is its demand. 4. Time lag: The longer the time after the price change, the more elastic will be the demand. It is because consumers are given more time to carry out their actions. A 1-day sale usually generate less sales change per day as a sale lasted for 2 weeks.

Total Revenue Test Total revenue (TR) is calculated by multiplying price (P) per unit and quantity (Q) of the good sold. TR = P x Q The total revenue test is a method of estimating the price elasticity of demand. As Ed will impact the total revenue, we can estimate the Ed by looking at the movement of the total revenue. Total Revenue Test Ed > 1, total revenue will decrease as price increases. P and TR moves in opposite directions. Producers can increase total revenue ( TR = Price x Quantity) by lowering the price. Therefore, most department stores will have sales to attract customers. Apparel's demand is elastic. Ed < 1, total revenue will increase as price increases. P and TR moves in the same direction. Producers can increase total revenue by raising the price. Inelastic demand for agricultural products helps to explain why bumper crops depress the prices and total revenues for farmers. You may look at the movement of TR in the example below. It demonstrated the relationship described above.

TR Test Example DEMAND FUNCTION FOR PRODUCT X: P = 2.5-0.01Q
P = PRICE; Q = QUANTITY, TR = TOTAL REVENUE Ed = PRICE ELASTICITY OF DEMAND           A      B       C       D       E        F        G        H         I        J Q:       0     50        150     200    250    300   350   400   450 P:       4.5    4     3.5       3        2.5       2       1.5      1      0.5      0 TR:      0    200    350     450      500    500    450   350    200     0 Ed:         17     5      2.6      1.57       1     0.64    0.38    0.2    0.06 ELASTICITY OF DEMAND; FROM A TO E Ed >1     TR increases FROM E TO F Ed =1      TR remains same. FROM F TO J Ed <1       TR decreases.

Price Elasticity of Supply
Definition: Law of supply tells us that producers will respond to a price drop by producing less, but it does not tell us how much less. The degree of sensitivity of producers to a change in price is measured by the concept of price elasticity of supply. Price elasticity formula: Es = percentage change in Qs / percentage change in Price. If the percentage change is not given in a problem, it can be computed using the following formula: Q2-Q1) /P2-P1)X (P1 + P2)/(Q1+Q2)= Because of the direct relationship between Qs and Price, the Es coefficient will always be a positive number. Examples: 1.  If the price of Product A  increased by 10%,  the quantity supplied increases by 5%. Then the coefficient for  price elasticity of the supply of Product A is: Es = percentage change in Qs / percentage change in Price = (5%) / (10%) = 0.5 2. If the quantity supplied of Product B has decreased from 1000 units to 200 units as price decreases from \$4 to \$2 per unit, the coefficient for Es is: Es Q2-Q1) /P2-P1)X (P1 + P2)/(Q1+Q2)= = 2

Characteristics & Determinants
Es approaches infinity, supply is perfectly elastic. Producers are very sensitive to price change. Es > 1, supply is elastic. Producers are relatively responsive to price changes. Es = 1, supply is unit elastic. Producers’ response and price change are in same proportion. Es < 1, supply is inelastic. Producers are relatively unresponsive to price changes. Es approaches 0, supply is perfectly inelastic. Producers are very insensitive to price change. It is impossible to judge elasticity of a supply curve by its flatness or steepness. Along a linear supply curve, its elasticity changes. Determinants: 1. Time lag: How soon the cost of increasing production rises and the time elapsed since the price change influence the Es. The more rapidly the production cost rises and the less time elapses since a price change, the more inelastic the supply. The longer the time elapses, more adjustments can be made to the production process, the more elastic the supply. 2. Storage possibilities: Products that cannot be stored will have a less elastic supply. For example, produces usually have inelastic supply due to the limited shelf life of the vegetables and fruits.

Cross Elasticity of Demand
Definition: Cross elasticity (Exy) tells us the relationship between two products. it measures the sensitivity of quantity demand change of product X to a change in the price of product Y. Formula: Exy = percentage change in Quantity demanded of X / percentage change in Price of Y. Characteristics: Exy > 0,  Qd of X and Price of Y are directly related. X and Y are substitutes. Exy approaches 0, Qd of X  stays the same as the Price of Y changes. X and Y are not related. Exy < 0, Qd of X and Price of Y are inversely related. X and Y are complements. Examples: 1. If the price of Product A  increased by 10%,  the quantity demanded of B increases by 15 %. Then the coefficient for the cross  elasticity of the A and B is : Exy = percentage change in Qx / percentage change in Py = (15%) / (10%) = 1.5 > 0, indicating A and B are substitutes. 2. If the price of Product A  increased by 10%,  the quantity demanded of B decreases by 15 %. Then the coefficient for the cross  elasticity of the A and B is : Exy = percentage change in Qx / percentage change in Py = (- 15%) / (10%) = < 0, indicating A and B are complements.

Income Elasticity of Demand
Definition: Income elasticity of demand (Ey, here y stands for income) tells us the relationship a product's quantity demanded and income. It measures the sensitivity of quantity demand change of product X to a change in income. Price elasticity formula: Ey = percentage change in Quantity demanded / percentage change in Income If the percentage change is not given in a problem, it can be computed using the following formula: Percentage change in Qx where Q1 = initial Qd, and Q2 =  new Qd. Percentage change in Y where Y1 = initial Income, and Y2 = New income. Putting the two above equations together: Ey = {(Q1-Q2) / (Y1-Y2) X (Y1 + Y2/Q1+Q2)] Characteristics: Ey > 1,  Qd and income are directly related. This is a normal good and it is income elastic. 0< Ey<1,  Qd and income are directly related. This is a normal good and it is income inelastic. Ey < 0, Qd and income are inversely related. This is an inferior good. Ey approaches 0, Qd   stays the same as income changes, indicating a necessity. Example: If income  increased by 10%,  the quantity demanded of a product increases by 5 %. Then the coefficient for the income  elasticity of demand for this product is:: Ey = percentage change in Qx / percentage change in Y = (5%) / (10%) = 0.5 > 0, indicating this is a normal good and it is income inelastic.

ELASTICITIES OF SUPPLY AND DEMAND
2.4 ELASTICITIES OF SUPPLY AND DEMAND elasticity Percentage change in one variable resulting from a 1-percent increase in another. Price Elasticity of Demand price elasticity of demand Percentage change in quantity demanded of a good resulting from a 1-percent increase in its price. (2.

ELASTICITIES OF SUPPLY AND DEMAND
2.4 ELASTICITIES OF SUPPLY AND DEMAND Linear Demand Curve linear demand curve Demand curve that is a straight line. Figure 2.11 Linear Demand Curve The price elasticity of demand depends not only on the slope of the demand curve but also on the price and quantity. The elasticity, therefore, varies along the curve as price and quantity change. Slope is constant for this linear demand curve. Near the top, because price is high and quantity is small, the elasticity is large in magnitude. The elasticity becomes smaller as we move down the curve.

ELASTICITIES OF SUPPLY AND DEMAND
2.4 ELASTICITIES OF SUPPLY AND DEMAND Linear Demand Curve Figure 2.12 (a) Infinitely Elastic Demand For a horizontal demand curve, ΔQ/ΔP is infinite. Because a tiny change in price leads to an enormous change in demand, the elasticity of demand is infinite. infinitely elastic demand Principle that consumers will buy as much of a good as they can get at a single price, but for any higher price the quantity demanded drops to zero, while for any lower price the quantity demanded increases without limit.

ELASTICITIES OF SUPPLY AND DEMAND
2.4 ELASTICITIES OF SUPPLY AND DEMAND Linear Demand Curve Figure 2.12 (b) Completely Inelastic Demand For a vertical demand curve, ΔQ/ΔP is zero. Because the quantity demanded is the same no matter what the price, the elasticity of demand is zero. completely inelastic demand Principle that consumers will buy a fixed quantity of a good regardless of its price.

ELASTICITIES OF SUPPLY AND DEMAND
2.4 ELASTICITIES OF SUPPLY AND DEMAND Other Demand Elasticities income elasticity of demand Percentage change in the quantity demanded resulting from a 1-percent increase in income. (2.2) cross-price elasticity of demand Percentage change in the quantity demanded of one good resulting from a 1-percent increase in the price of another. (2.3) Elasticities of Supply price elasticity of supply Percentage change in quantity supplied resulting from a 1-percent increase in price.

ELASTICITIES OF SUPPLY AND DEMAND
2.4 ELASTICITIES OF SUPPLY AND DEMAND Point versus Arc Elasticities point elasticity of demand Price elasticity at a particular point on the demand curve. Arc Elasticity of Demand arc elasticity of demand Price elasticity calculated over a range of prices. (2.4)

ELASTICITIES OF SUPPLY AND DEMAND
2.4 ELASTICITIES OF SUPPLY AND DEMAND For a few decades, changes in the wheat market had major implications for both American farmers and U.S. agricultural policy. To understand what happened, let’s examine the behavior of supply and demand beginning in 1981. By setting the quantity supplied equal to the quantity demanded, we can determine the market-clearing price of wheat for 1981:

ELASTICITIES OF SUPPLY AND DEMAND
2.4 ELASTICITIES OF SUPPLY AND DEMAND Substituting into the supply curve equation, we get We use the demand curve to find the price elasticity of demand: Thus demand is inelastic. We can likewise calculate the price elasticity of supply: Because these supply and demand curves are linear, the price elasticities will vary as we move along the curves.

SHORT-RUN VERSUS LONG-RUN ELASTICITIES
2.5 SHORT-RUN VERSUS LONG-RUN ELASTICITIES Demand Demand Figure 2.13 (b) Automobiles: Short-Run and Long-Run Demand Curves . If price increases, consumers initially defer buying new cars; thus annual quantity demanded falls sharply. In the longer run, however, old cars wear out and must be replaced; thus annual quantity demanded picks up. Demand, therefore, is less elastic in the long run than in the short run.

SHORT-RUN VERSUS LONG-RUN ELASTICITIES
2.5 SHORT-RUN VERSUS LONG-RUN ELASTICITIES Demand Income Elasticities Income elasticities also differ from the short run to the long run. For most goods and services—foods, beverages, fuel, entertainment, etc.— the income elasticity of demand is larger in the long run than in the short run. For a durable good, the opposite is true. The short-run income elasticity of demand will be much larger than the long-run elasticity.

SHORT-RUN VERSUS LONG-RUN ELASTICITIES
2.5 SHORT-RUN VERSUS LONG-RUN ELASTICITIES Demand Cyclical Industries cyclical industries Industries in which sales tend to magnify cyclical changes in gross domestic product and national income. Figure 2.14 GDP and Investment in Durable Equipment Annual growth rates are compared for GDP and investment in durable equipment. Because the short-run GDP elasticity of demand is larger than the long-run elasticity for long-lived capital equipment, changes in investment in equipment magnify changes in GDP. Thus capital goods industries are considered “cyclical.”

SHORT-RUN VERSUS LONG-RUN ELASTICITIES
2.5 SHORT-RUN VERSUS LONG-RUN ELASTICITIES Demand Cyclical Industries Figure 2.15 Consumption of Durables versus Nondurables Annual growth rates are compared for GDP, consumer expenditures on durable goods (automobiles, appliances, furniture, etc.), and consumer expenditures on nondurable goods (food, clothing, services, etc.). Because the stock of durables is large compared with annual demand, short-run demand elasticities are larger than long-run elasticities. Like capital equipment, industries that produce consumer durables are “cyclical” (i.e., changes in GDP are magnified). This is not true for producers of nondurables.

SHORT-RUN VERSUS LONG-RUN ELASTICITIES
2.5 SHORT-RUN VERSUS LONG-RUN ELASTICITIES Demand TABLE Demand for Gasoline Number of Years Allowed to Pass Following a Price or Income Change Elasticity Price −0.2 −0.3 −0.4 −0.5 −0.8 Income TABLE Demand for Automobiles Number of Years Allowed to Pass Following a Price or Income Change Elasticity Price − − − − −0.4 Income

SHORT-RUN VERSUS LONG-RUN ELASTICITIES
2.5 SHORT-RUN VERSUS LONG-RUN ELASTICITIES Supply Supply Figure 2.16 Copper: Short-Run and Long-Run Supply Curves Like that of most goods, the supply of primary copper, shown in part (a), is more elastic in the long run. If price increases, firms would like to produce more but are limited by capacity constraints in the short run. In the longer run, they can add to capacity and produce more.

SHORT-RUN VERSUS LONG-RUN ELASTICITIES
2.5 SHORT-RUN VERSUS LONG-RUN ELASTICITIES Figure 2.17 Price of Brazilian Coffee When droughts or freezes damage Brazil’s coffee trees, the price of coffee can soar. The price usually falls again after a few years, as demand and supply adjust.

SHORT-RUN VERSUS LONG-RUN ELASTICITIES
2.5 SHORT-RUN VERSUS LONG-RUN ELASTICITIES Figure 2.18 Supply and Demand for Coffee (c) In the long run, supply is extremely elastic; because new coffee trees will have had time to mature, the effect of the freeze will have disappeared. Price returns to P0.

UNDERSTANDING AND PREDICTING THE EFFECTS OF CHANGING MARKET CONDITIONS
2.6 UNDERSTANDING AND PREDICTING THE EFFECTS OF CHANGING MARKET CONDITIONS Figure 2.19 Fitting Linear Supply and Demand Curves to Data Linear supply and demand curves provide a convenient tool for analysis. Given data for the equilibrium price and quantity P* and Q*, as well as estimates of the elasticities of demand and supply ED and ES, we can calculate the parameters c and d for the supply curve and a and b for the demand curve. (In the case drawn here, c < 0.) The curves can then be used to analyze the behavior of the market quantitatively.

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