1. 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

2. 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:
Percentage change in Qd = (Q1-Q2) / [1/2 (Q1+Q2)] where Q1 = initial Qd, and Q2 =  new Qd.
Percentage change in P = (P1-P2) / [1/2 (P1 + P2)] where P1 = initial Price, and P2 = New Price.
Putting the two above equations together:
Ed = {(Q1-Q2) / [1/2 (Q1+Q2)] } / {(P1-P2) / [1/2 (P1 + P2)]}
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 = {(Q1-Q2) / [1/2 (Q1+Q2)] } / {(P1-P2) / [1/2 (P1 + P2)]} = {( ) / 1/2( )} / {(2 - 4) / 1/2 (2+4)} =
Take the absolute value of , Ed = 0.16

3. 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:

4. 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

5. 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.

6. 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.

7. 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.

8. 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:
Percentage change in Qs = (Q1-Q2) / [1/2 (Q1+Q2)] where Q1 = initial Qs, and Q2 =  new Qs.
Percentage change in P = (P1-P2) / [1/2 (P1 + P2)] where P1 = initial Price, and P2 = New Price.
Putting the two above equations together:
Es = {(Q1-Q2) / [1/2 (Q1+Q2)] } / {(P1-P2) / [1/2 (P1 + P2)]}
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 = {(Q1-Q2) / [1/2 (Q1+Q2)] } / {(P1-P2) / [1/2 (P1 + P2)]} = {( ) / 1/2( )} / {(4-2) / 1/2 (4+2)} = 2

9. 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.

10. 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.
If the percentage change is not given in a problem, it can be computed using the following formula:
Percentage change in Qx = (Q1-Q2) / [1/2 (Q1+Q2)] where Q1 = initial Qd of X, and Q2 =  new Qd of X.
Percentage change in Py = (P1-P2) / [1/2 (P1 + P2)] where P1 = initial Price of Y, and P2 = New Price of Y.
Putting the two above equations together:
Exy = {(Q1-Q2) / [1/2 (Q1+Q2)] } / {(P1-P2) / [1/2 (P1 + P2)]}
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.

11. 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 = (Q1-Q2) / [1/2 (Q1+Q2)] where Q1 = initial Qd, and Q2 =  new Qd.
Percentage change in Y = (Y1-Y2) / [1/2 (Y1 + Y2)] where Y1 = initial Income, and Y2 = New income.
Putting the two above equations together:
Ey = {(Q1-Q2) / [1/2 (Q1+Q2)] } / (Y1-Y2) / [1/2 (Y1 + Y2)]
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.