Chapter 6 Elasticity PDF

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Chapter 6: Elasticity Saturday, August 8, 2020

4:20 PM

CHAPTER 6 (Overview)

6.1 Price Elasticity of Demand ○ Price elasticity of demand - a measure of the responsiveness of buyers to a change in the price of a product. ○ Elastic Demand - modest price changes cause very large changes in the quantity demanded ○ Inelastic Demand - substantial price changes cause only small changes in the amount purchased.

Chapter 6 Sections ✓ Section 6.1 ✓ Section 6.2 Quick Review 6.1 ✓ The price elasticity of demand coefficient Ed is the ratio of the % change in Qd to the % change in price. The averages of the two price and two quantities are used as the base reference in calculating the % changes.

The Price-Elasticity Coefficient and Formula • Economists measure the degree to which demand is price elastic or inelastic with the coefficient Ed, defined as

✓ When Ed > 1, demand is elastic; when Ed < 1, demand is inelastic; when Ed = 1, demand is of unit elasticity. ✓ When price changes, total revenue will change in the opposite direction if demand is price-elastic, in the same direction if demand is price-inelastic, and not at all if demand is unit-elastic.

• Using Averages An price change from $4 to $5 along a demand curve is 25% increase ($1/$4) A price change from $5 to $4 along the same curve is 20% ($1/$5)

✓ Demand is typically elastic in the high-price (low-quantity) range of the demand curve and inelastic in the low-price (high-quantity) range of the demand curve.

○ Which one should we use in the denominator? ▪ The simplest solution is to use the mid-point formula for calculating elasticity.

✓ Price elasticity of demand is greater (a) the larger the number of substitutes available; (b) the higher the price ofCONCEPTS a product relative to one's budget; (c) the KEY greater the extent to which the product a luxury; (d) theCoefficient longer theand time period Formula - TheisPrice-Elasticity involved. - Interpretations of Ed - Total-Revenue Test - Elastic Demand DEFINITIONS - Inelastic Demand ✓ Price elasticity of demand - Unit Elasticity ✓ Elastic Demand - Price Elasticity along a Linear Demand Curve ✓ Inelastic Demand - Determinants of Price Elasticity of Demand ✓ Unit Elasticity ✓ Perfectly inelastic ✓ Perfectly elastic ✓ Total Revenue ✓ Total-Revenue Test

For the same $5-$4 price range, the price reference is $4.50 [= ($5 + $4)/2], and for the same 10-20 quantity range, the quantity reference is 15 units [= (10+20)/2]. The percentage change in price is now $1/$4.50, or about 22%, and the percentage change in quantity is 10/15, or about 67%. So Ed is about 3. ○ This solution eliminates the "up versus down" problem. ○ All the price-elasticity coefficients that follow are calculated using this midpoint formula

• Using Percentages ○ If we use absolute changes, the choice of units will arbitrarily affect our impression of buyer and responsiveness ○ i.e. if price of a bag of popcorn reduced from $3 to $2, consumers increase purchase from 60 to 100 bags ▪ It seems consumers are sensitive to price changes and therefore demand is elastic ▪ But if we change the monetary unit, i.e. pennies, we find that a price change of 100units (pennies) causes a quantity change of 40 units. This may falsely lead us to believe that demand is inelastic.

Quick Review 6.2 ✓ Price elasticity of supply measures the sensitivity of suppliers to changes in the price of a product. The price-elasticity-of-supply coefficient Es is the ratio of the % change in Qs to the % change in price. The elasticity of supply varies directly with the amount of time producers have to respond to the price change.

○ By using %, we can more sensibly compare the consumer responsiveness to price increases by using some common percentage increase in price for both. • Elimination of Minus Sign ○ Price & quantity demanded are inversely related → price-elasticity coefficient of demand Ed will always be negative ○ Economists usually ignore the minus sign and simply present the absolute value of E d to avoid confusion (i.e. saying that Ed of -4 is greater than -2). So we ignore the minus sign and show only the absolute. ○ Elasticity of supply coefficients therefore are positive numbers.

Interpretations of Ed  We can interpret the coefficient of price elasticity of demand as follows: • Elastic Demand (Ed > 1) ○ % change in price results in a larger % change in quantity demanded (%

Qd > %

P)

• Inelastic Demand (Ed < 1) ○ % change in price produces a smaller % change in quantit • Unit Elasticity (Ed = 1) ○ A % change in price and resulting % change in quantity de % P) • Extreme Cases ○ When we say demand is "inelastic", we do not mean consumers are completely unresponsive to a price change. ○ Perfectly inelastic - when a price change results in no change in quantity demanded. Ed =0 ▪ i.e. acute diabetic's demand for insulin

○ Pe

✓ The cross-elasticity-of-demand coefficient Exy is computed as the % change in the Qd of product X divided by the % change in the price of product Y. If the crosselasticity coefficient is positive,KEY the CONCEPTS two products are substitutes; if negative, they - The Immediate Market Period are complements. - The Short Run computed as the % change in Qd divided by ✓ The income-elasticity coefficient E-i isThe Long Run the % change in income. A positive-coefficient indicates a normal or superior good. Cross Elasticity of Demand The coefficient is negative for an inferior good. - Income Elasticity of Demand DEFINITIONS ✓ Elastic Supply ✓ Inelastic Supply ✓ Price elasticity of supply ✓ Immediate market period ✓ Short run ✓ Long run ✓ Cross elasticity of demand ✓ Income elasticity of demand

Learning Objectives 1. Discuss price elasticity demand and how it is calculated. d

=

- Price elasticity of demand measures consumer response to price changes. If consumers are relatively sensitive to price changes, demand is elastic. If they are relatively unresponsive to price changes, demand is inelastic.

- The price-elasticity coefficient Ed measures the degree of elasticity or inelasticity of demand. The coefficient is found by the formula - Economist use the averages of prices and quantities under consideration as reference points in determining % change in price and quantity. If Ed > 1, demand is elastic. If Ed < 1, demand is inelastic. Unit elasticity is the special case in which Ed = 1 - Perfectly inelastic demand is graphed as a line parallel to the vertical axis; perfectly elastic demand is shown by a line above and parallel to the horizontal axis.

The Total-R • The importance of elasticity for firms relates to the effect of price change on profits.

• Total Revenue (TR) - the total amount the seller receives from the sale of a product in a particular time period. Calculated by multiplying product price (P) by the quantity sold (Q). • TR = PxQ

- Elasticity varies at different price ranges on a demand curve, tending to be elastic in the upper-left segment and inelastic in the lower-right segment. Elasticity cannot be judged by the steepness or flatness of a demand curve. 2. Explain the usefulness of the total-revenue test for price elasticity of demand. - If total revenue changes in the opposite direction from prices, demand is elastic. If price and total revenue change in the same direction, demand is inelastic. Where demand is of unit elasticity, a change in price leaves the total revenue unchanged.

3. List the factors that affect price elasticity of demand and describe some applications of Ed. - The number of available substitutes, the size of an item's price relative to

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3. List the factors that affect price elasticity of demand and describe some applications of Ed.

• Total-Revenue Test ○ If total revenue change in opposite direction from price → demand is elastic TR ↑ ○ If total revenue change in same direction as price → demand is inelastic TR ↓ ○ If total revenue does not change when price changes → demand is unit elastic

- The number of available substitutes, the size of an item's price relative to one's budget, whether the product is a luxury or a necessity, and length of time to adjust are all determinants of Ed. P↓

P↑

- The elasticity concept also applies to supply. The coefficient of price

elasticity of supply is found by the formula

 Elastic Demand ○ ↑Price will ↓Total Revenue ▪ Revenue gained on the higher price unit will be more than offset by the revenue lost from lower quantity sold. ○ ↓Price will ↑Total Revenue ▪ Even if lesser price is receive, additional units are sold to more than make up for the lower price  Inelastic Demand ○ ↑Price will ↑Total Revenue ○ ↓Price will ↓Total Revenue ▪ Increase in sales will not fully offset the decline in revenue per unit

 Unit Elasticity ○ Change in price does not change total revenue ▪ The loss in revenue from a lower unit price is exactly offset by the revenue loss associated with accompanying decline in the amount demanded. ▪ i.e. for the price of $3, 10 units are sold, TR = $30, for the price of $1, 30 units are sold, TR = $30.  Price Elasticity along a Linear Demand Curve ○ Elasticity typically varies over different price ranges of the same demand curve *exception is Figure 6.2c*

- The averages of the prices and quantities under consideration are used as reference points for computing % changes. Elasticity of supply depends on the ease of shifting resources between alternative uses, which varies directly with the time producers have to adjust to a price change.

5. Apply cross elasticity of demand and income elasticity of demand. - Cross elasticity of demand indicates how sensitive the purchase of one product is to changes in the price of another product. The coefficient of cross elasticity of demand is found by the formula

- Income elasticity of demand indicates the responsiveness if consumer purchases to a change in income. The coefficient of income elasticity of demand is found by the formula

- The coefficient is positive for normal goods and negative for inferior goods.

- Industries that sells products that have high income-elasticity-of-demand coefficients are particularly hard hit by recessions. Those with products that have low or negative Ei fare much better.

• Table 6.1 ○ Plotting column 1 and 2 gives us a linear demand curve ○ From column 3, the price elasticity coefficient ↓ as we move from higher to lower price

○ For all downsloping straight-line and most other demand curves, demand is more price-elastic toward the upper left than toward the lower right. This is the consequence of the arithmetic properties of the elasticity measure ▪ % change in quantity is large on upper left because original reference quantity is small ▪ % change in price is small because original reference price is large

is

○ Slope of the curve (Figure 6.3a) is computed from absolute changes in price and quantity, while elasticity involves relative or percentage changes in price and quantity. ○ The demand curve in Figure 6.3a is linear → slope is constant ○ But it is demonstrated such a curve is elastic in its high price ($8-$5) range and inelastic in its low price ($4-$1) range

 Price Elasticity along a Linear Demand Curve ○ In Figure 6.3b we plot the Total Revenue per week that correspond to each pricequantity combination indicated along the demand curve D in Figure 6.3a. ○ Comparison of curves D and TR sharply focuses on the relationship between elasticity and total revenue. ▪ In the elastic range ($8-$5), lowering ticket price increases TR, increasing ticket price decreases TR. ▪ In the unit elasticity range, when price decrease from $5-$4 or increase $4-$5, TR remains $20,000 ▪ In the inelastic range ($5-$1), lowering price decreases TR, raising price increases TR

Determinants of Price Elasticity of Demand • Substitutability ○ Larger the number of substitute goods, greater the price elasticity of demand (Ed) ○ i.e. Candy bars are generally substitutable, highly elastic. Tooth repairs are inelastic, no close substitutes • Proportion of income ○ Higher the price of a good relative to consumers' income, greater the price elasticity of demand (Ed) ○ i.e. 10% increase in low-priced pencils Qd will probably only decrease slightly (Ed is low) 10% increase in high-priced items (automobile or housing), Qd will likely diminish significantly (Ed tend to be high)

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4. Describe price elasticity of supply and how it can be applied.

• Luxuries vs. Necessities ○ The more of a good is considered to be a "luxury", the greater the price elasticity of demand (Ed) ○ i.e. Electricity (necessity), price increase will not significantly reduce Qd Vacation travel and jewelry, people can live without them when price rises • Time ○ Product demand is more elastic the longer the time period under consideration ○ i.e. when the price of a product rises, time is needed to find, experiment, and accept other products. ○ Consumers may not immediately reduce their purchase very much, but in time they may shift to other substitutes.

 Applications of Price Elasticity of Demand ○ Large Crop Yields ▪ The demand for most farm products is highly inelastic; Ed is perhaps 0.20 or 0.25 ▪ Increase in supply of farm products tend to depress both price and total revenues □ For farmers as a group, the inelastic demand means large crop yield may not be desirable. ○ Excise Taxes ▪ Government pays attention to elasticity to levy excise taxes on goods and services. □ If a $1 tax is levied on a product and 10,000 units are sold, tax revenue will be Es is never negative $10,000 □ If the tax is raised to $1.50, but higher price results reduces sale to 4,000 tax revenue will be $6,000 ▪ Higher tax on a product with elastic demand will bring in less tax revenue ▪ Legislatures tend to seek out inelastic demand products (liquor, gasoline, cigarettes) when levying excises.

○ Decriminalization of Illegal Drugs ▪ Proponents argued that cost (enlarged police forces, prison construction, overburdened court system) increased. Legalization would allegedly reduce drug trafficking by taking profit out of it. □ Because demand of addicts is highly inelastic, amounts consumed at lower prices would increase only modestly. Addicts total expenditures will decline, so would street crimes. ▪ Opponents say that overall demand for drugs is far more elastic □ In addition to inelastic demand of addicts, there is another market segment consist of occasional users or "dabblers" whose demand is relatively elastic. □ They use hard drugs when the price are low, but substitute (alcohol) when prices are high □ Lower price would increase consumption by dabblers, and removal of legal prohibitions might make drug use more socially acceptable, increasing demand. □ The overall result would be higher social cost.

6.2 Price Elasticity of Supply ○ Elastic Supply - quantity supplied by producers is relative responsive to price changes. ○ Inelastic Supply - quantity supplied is relatively insensitive to price changes.

○ i.e. an increase in price of a good from $4 to $6 increases the quantity supplied from 10 units to 14 units. The % change in price would be 2/5, or 40%, and the % change in quantity would be 4/12, or 33%.

▪ Es > 1 supply is elastic ▪ Es < 1 supply is inelastic ▪ Es = 1 supply is unit elastic ○ The degree of Es depends on how easily producers can shift resources between alternative uses. ▪ The easier or more rapidly → the greater the elasticity of supply. ▪ Shifting resources takes time, the longer the time, greater the "shiftability", greater response, greater Es ○ In analyzing the impact of time on elasticity, economists distinguish among: ▪ immediate market period, the short run, and the long run.

Price Elasticity of Supply: The Immediate Market Period • Immediate market period - length of time over which producers are unable to respond to change in price with a change in Qs. • In the immediate market period, both the supply of product and the quantity of product supplied are fixed. ○ A farmer offers only one truckload of tomatoes no matter how high or low the price. ○ Supply curve is perfectly inelastic because farmer do not have time to respond to a change in demand.

Price Elasticity of Supply: The Short Run • Short run - a period of time too short to change plant capacity but enough to use the fixedsize plant more or less intensively. ○ i.e. in the short run, farmer's plant (land and farm machinery) is fixed, but he have time to cultivate tomatoes more intensively by applying more labour and more fertilizer and pesticides to the crop. • The result is a somewhat greater output in response to a presumed increase in demand, reflected in more elastic supply. • The equilibrium price is lower in the short run than in the immediate market period.

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○ Because the increase in demand from D1 to D2 is met by an increase in quantity from Q0 to Qs.

Price Elasticity of Supply: The Long Run • Long run - a time period long enough for firms to adjust their plant size and for firms to enter (or leave) the industry.

○ i.e. the tomato farmer has the time to acquire additional land and buy more machinery and equipment. Furthermore, other farmer might be attracted to tomato farming by the increase demand and higher price. ○ Such adjustments create a larger supply response • Outcome is a smaller price rise (Po to P1) and a larger output increase (Qo to Q1) in response to the increase in demand (D1 to D2) • There is no total-revenue test for elasticity of supply. ○ Since supply shows direct relationship between price and amount supplied, then price and TR always move together

Applications of Price Elasticity of Supply  Antiques and Reproductions ○ High price of an antique results from strong demand and limited, highly inelastic supply. ○ For one-of-a-kind antiques, the supply is perfectly inelastic.  Volatile Gold Prices ○ The price of gold is quite volatile (shooting upward one period and plummeting downward the next)

○ Main sources of these fluctuations are shifts in demand interacting with highly inelastic supply, ▪ Gold production is time consuming: exploration, mining, refining ▪ Physical ability of gold is highly limited. ○ Increase in gold prices do not elicit substantial increases in quantity supplied. ○ Gold mining is costly to shut down, gold bars are expensive to store ▪ Price decreases therefore do not product large drops in quantity of gold supplied, ▪ Supply of gold is inelastic ○ Because of gold supply is inelastic, even relatively small changes in demand produce relatively large changes in price.

Cross Elasticity and Income Elasticity of Demand  Consumption of good is also affected by a change in the price of a related product or by a change in income. Cross Elasticity of Demand • Cro ac

se a product X are to

• Co

• Thi stand substitute and com • We allow the coefficient of cross elasticity of demand to be either positive or negative.  Substitute Goods ○ Exy is positive (sales of X move in same direction as a change in price of Y) ○ X and Y are substitute goods ○ The larger the positive Exy, the greater the substitutability between the two products.  Complementary Goods ○ Exy is negative (an increase in price of one decreases the demand for the other) ○ X and Y are complementary goods ○ The larger the negative Exy, the greater is the complementarity between the two goods.

 Independent Goods ○ A zero or near-zero elasticity suggests that X and Y are independent goods ○ A change in price of X does not affect demand for Y.  Application ○ The degree of substitutability of products is important to business and government. ○ Government assess whethe...