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Econ 1000 lecture 4: Elasticity

Econ 1000 lecture 4: Elasticity. C.L. Mattoli. This week. Mod 2, part 3 Chapter 5: Elasticity. Learning objectives: Mod 2. On successful completion of this module (lecture 3 of the module), you should be able to: Explain the concept of elasticity

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Econ 1000 lecture 4: Elasticity

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  1. Econ 1000 lecture 4:Elasticity C.L. Mattoli (C) Red Hill Capital Corp, Delaware USA 2008

  2. This week • Mod 2, part 3 • Chapter 5: Elasticity (C) Red Hill Capital Corp, Delaware USA 2008

  3. Learning objectives: Mod 2 On successful completion of this module (lecture 3 of the module), you should be able to: • Explain the concept of elasticity • Calculate and interpret price, income and cross-price elasticity of demand • Calculate and interpret price elasticity of supply. (C) Red Hill Capital Corp, Delaware USA 2008

  4. Introduction • We have talked, in general terms, about demand and supply schedules and curves. • We have discussed opportunity costs: • When a consumer buys one thing, he will not have money for others. • When a producer decides to produce one thing, he will forego the opportunity to produce other things. • The real question is how important is one thing versus the other opportunities. (C) Red Hill Capital Corp, Delaware USA 2008

  5. Producer motivations • Producers (suppliers) are in business to make a profit. • In that regard, they would like to get as high a price as they can for a good or service. • On the other hand, they know what minimum price they can offer goods in certain quantities and still make a profit. • They need to understand how consumers will react to different prices, in order to arrive at proper prices for marketing their wares. (C) Red Hill Capital Corp, Delaware USA 2008

  6. Psychology & Logic of Econ • Think about how things affect each other, how they interact. • Think about how people are. • For example, if the price of coca cola goes up, some people will just switch to Pepsi, if it’s price didn’t change … it’s just human nature. • Thus, the availability of substitutes will affect how demand will change as prices go up and down. (C) Red Hill Capital Corp, Delaware USA 2008

  7. Psychology & Logic of Econ • You don’t have much of a choice about who will supply your electricity, if you live in a city … you can’t get by on batteries. • If there are barriers to entry for an industry, high prices will be charged, until other people break into the market and compete and lower the excess profits. • A change in the price of one vegetable will affect the supply of other vegetables. There is only so much farming land, and farmers will allocate according to their profit expectations. (C) Red Hill Capital Corp, Delaware USA 2008

  8. Psychology & Logic of Econ • With a lot of things, the more you do it, the less pleasure you get out of it. You eat out, and you eventually get saturated with eating out. But if the price was lowered, you might go back for more. • You only have so much money, and you have to allocate it according to your needs and desires. (C) Red Hill Capital Corp, Delaware USA 2008

  9. Revenue and how is it shown in the market model What happens to revenue when demand changes? Price S0 P0 Revenue goes up when demand goes up P1 D0 D1 Q1 Q0 Quantity (C) Red Hill Capital Corp, Delaware USA 2008

  10. Revenue and how is it shown in the market model? What happens to revenue when supply changes? Price S0 S1 Not as clear P0 P1 D0 Q0 Q1 Quantity (C) Red Hill Capital Corp, Delaware USA 2008

  11. The importance of percentages • Often, in finance and economics, we are more concerned with percentages and percentage changes than with raw numbers or absolute number changes. • That is because percentages give us a better basis for comparison, in many cases. (C) Red Hill Capital Corp, Delaware USA 2008

  12. The importance of percentages • For example, it is not so important that someone made $100 on an investment. What is more important is to ask how much did she invest to earn the $100. If she invested $100 to earn $100, then the return on investment was Income/investment = $100/$100 = 100%. If the investment was $10,000, the return on investment was $100/$10,000 = 1%. The percentage number was much more interesting. (C) Red Hill Capital Corp, Delaware USA 2008

  13. The importance of percentages • The same is true about growth in GDP (gross domestic product). If one country’s GDP growth was $100 million last year and another country's growth $1 trillion, the next question to ask is how much total did the countries have in GDP. Then, we can compute a percentage growth rate, and we will better be able to compare the growth rates in GDP of the two economies. (C) Red Hill Capital Corp, Delaware USA 2008

  14. The importance of percentages • We looked at the general concepts of supply and demand: quantity demanded should be a decreasing function of price, while quantity supplied should be an increasing function of price. • But how will those quantities vary exactly with price: that is an important question. (C) Red Hill Capital Corp, Delaware USA 2008

  15. The importance of percentages • To begin our next stage of economic analysis, elasticity, we will look, more precisely, at how quantities vary with. To do that, in a meaningful way, we will …. You guessed it…. Use percentages. • Elasticities look at percentage change of one variable with respect to percentage change of another. (C) Red Hill Capital Corp, Delaware USA 2008

  16. Elasticity of Demand (C) Red Hill Capital Corp, Delaware USA 2008

  17. Price Elasticity of demand • The law of demand says that the quantity demanded, QD(P), is a function of price, P, and QD(P) is decreasing with increasing price. • The question is: how much will QD change when price changes. That will be a valuable piece of information for suppliers to know. Then, they can pick up their own pencils, and figure out whether or not production should be done, at what price, quantity, and what cost. (C) Red Hill Capital Corp, Delaware USA 2008

  18. Price Elasticity of demand • Instead of using the ordinary variation of QD with P, i.e., ΔQD/Δ P,consider the percentage change of quantity, ΔQD/ QD, versus the percentage change in price, Δ P/P. ED = Elasticity of demand = [percentage change in quantity demanded ]/ [percentage change in price] (C) Red Hill Capital Corp, Delaware USA 2008

  19. Price Elasticity of demand = [ΔQD/ QD ]/[Δ P/P] • In that regard, we are looking at percentage change in the number of units purchased caused by a one percent change in price. (C) Red Hill Capital Corp, Delaware USA 2008

  20. Elasticity of demand exampled • Suppose that we made observations that found that Kangda college’s enrollment will drop by 20%, if the price of tuition increases by 10%. • Then, we could calculate the elasticity coefficient of demand =[percentage change in quantity demanded ]/ [percentage change in price] = [ΔQD/ QD ]/[Δ P/P] = %ΔQD/%ΔP = (-20%)/(10%) = -2. (C) Red Hill Capital Corp, Delaware USA 2008

  21. Elasticity of demand exampled • It will always be a negative number since, if price goes up, quantity demanded goes down, and vice versa. • That’s just human nature. • So, we usually just say that the elasticity coefficient is equal to 2. (C) Red Hill Capital Corp, Delaware USA 2008

  22. What it means to a supplier • What that means to the supplier is that, if he increases or decreases the price by 1%, he will experience a an opposite change of 2% in the number of units that he will be able to sell. • That will affect his total revenues, which are equal to QxP = Total Revenue = RT. • For example, assume that the price for tuition at Kangda is currently $50,000 per year = P0, and that there are 5,000 students = Q0. Then, RT0= Q0xP0 = $50,000x5,000 = $250 million. (C) Red Hill Capital Corp, Delaware USA 2008

  23. What it means to a supplier • Next, suppose that we try to increase the price by 1% = $50,000 x 0.01 = $500 to P1 = $50,500. • Then, according to the elasticity coefficient of 2, enrollment will decrease by 2% = 100 to 4,900. • In that case total revenue will be RT = $50,500x4,900 = $247,450,000, which means that the supplier has lost revenue of about $2.5 million, which is no small amount of money. (C) Red Hill Capital Corp, Delaware USA 2008

  24. What it means to a supplier • What that means is that, in order to be ahead of the game by raising prices, he will also have to raise his profit margin enough to more than compensate for his loss in revenue. • For example, assume that he had a profit margin of 10%, originally. Profit margin = PM = profit/revenue = 10%. Then, his original profit would be profit = E0 = RTxPM = $250,000,000x10% = $25,000,000. (C) Red Hill Capital Corp, Delaware USA 2008

  25. What it means to a supplier • For the supplier to break even on profits, his new profit margin needs to be $25,000,000/$247,450,000 = 10.1%. • Therefore, the supplier will have to look at his pro-forma profit margin before he can make a decision to raise or lower prices. • In the end, it will be his own internal costs and marginal cost considerations that will allow him to make a decision about what price he should charge to maximize his profits (C) Red Hill Capital Corp, Delaware USA 2008

  26. Mathematically: total revenue change • Total revenue equals price time quantity demanded: RT0 = Q0xP0 • Q1 = Q0 + ΔQ ; P1 = P0 – ΔP since price and quantity demanded will have opposite signs. • The variation of total revenues with respect to price is given by: Δ RT /ΔP = P x[ΔQ/ΔP] + QxΔP/ΔP = P x[ΔQ/ΔP] • And Δ RT /ΔP = [Q0xP0 – Q0xΔP – ΔQxΔP + ΔQxP0 – Q0xP0]/ΔP = – Q0 – ΔQ + ΔQxP0/ΔP = – Q1 + P0x ED. So what?... (C) Red Hill Capital Corp, Delaware USA 2008

  27. Mathematically: total revenue & elasticity • If we want to find the condition for increasing total revenue, that means that the change in revenue should always be a positive number. In algebra, we require: Δ RT /ΔP > 0. • So, Δ RT /ΔP = P x[ΔQ/ΔP] + Q >0 • Rearranging the symbols in the equation, we get ΔQ/(ΔP/P) > – Q (C) Red Hill Capital Corp, Delaware USA 2008

  28. Mathematically: total revenue • Or, (ΔQ/Q)/(ΔP/P) = %ΔQ/%ΔP = ED> – 1 • Thus, in order for R to increase with increasing P, E must be less than 1 in size. • Demand must be price inelastic. • We shall take a closer look at revenues, in the next module. (C) Red Hill Capital Corp, Delaware USA 2008

  29. The problem with elasticity calculations • When we actually do calculations, we are not dealing in abstract equations or perfect continuous curves. We will usually deal with a finite number of pairs of quantity and price, (Qi,Pi), in a demand schedule or a table. • Suppose we know two points in the demand schedule between which we want to calculate elasticity: (Q1,P1) = (400,$10) and (Q2,P2) = (440,$9.50). (C) Red Hill Capital Corp, Delaware USA 2008

  30. The problem with elasticity calculations • Then, we can calculate the percentages two different ways. • If we assume that prices fall and we want to know how much demand will rise, we quite naturally choose the starting points as (Q1,P1) = (400, $10) and calculate the percentages changes from those starting points of price and quantity, so elasticity = ED = [(440 – 400)/400]/[($9.50 – $10)/$10] = 2. (C) Red Hill Capital Corp, Delaware USA 2008

  31. The problem with elasticity calculations • If, on the other hand, we want to look at what would happen to a price increase from $9.50 to $10, we would naturally use starting point of (Q2,P2) = (440,$9.50). Elasticity is, then, [(400 – 440)/440]/[($10 – 9.50)/$9.50] = 1.72. • So, we get two different answers, depending on how we calculate: which point we start at. (C) Red Hill Capital Corp, Delaware USA 2008

  32. Elasticity: Mid-point approximation • The simple cure to this problem, in economics, is to use an average of some sort, • After all, right now we are imagining that we do not care if price goes up or if price goes down by 1%, we want one number for the percentage quantity that will either be retracted from or added to demand, as a general result. (C) Red Hill Capital Corp, Delaware USA 2008

  33. Elasticity: Mid-point approximation • Moreover, since we are using 2 discrete, separate points, not even in a real curve, what we are really doing in our actual calculation of elasticity is to measure an approximate value at the mid-point on the actual curve that would exist, if we had mounds of minutely-detailed data for quantity and price. • Thus, economics, as done in this course, will use a mid-point average value that is calculated in the following manner:……. (C) Red Hill Capital Corp, Delaware USA 2008

  34. Elasticity: Mid-point approximation • Take the mid points for both quantity and for price, which are simple averages ΔQD/ [(Q1D + Q2D)/2] and ΔP/ [(P1 + P2)/2]. • Then, use percentages based on the mid-point as: mid-point elasticity approximation:%ΔQD/%ΔP= {ΔQD/ [(Q1D + Q2D)/2]}/{ ΔP/ [(P1 + P2)/2]} ={ΔQD/ (Q1D + Q2D)}/{ ΔP/ (P1 + P2)} because the 2’s on top and bottom cancel. • We demonstrate some of these concepts, pictorially, in the next slide (C) Red Hill Capital Corp, Delaware USA 2008

  35. Graphical Approximations • First, look at elasticity along the dashed line. • That is actually what we are using to calculate the approximate elasticity. • It is approximately the same line as the dotted line that is tangent to the actual curve at the mid-point, more or less, so we use the mid-point to calculate it. • Notice, also, that on a real demand curve the elasticity will change at different points o the line. Demand Curve P $10.50 $10 $9.50 $9 QD 400 440 480 520 (C) Red Hill Capital Corp, Delaware USA 2008

  36. Graphical Approximations • For example, if we calculate mid-point Elasticities between $9.50 and $10, we get E = [(440-400)/ ((440+400)/2)]/[($9.5-$10)/ ((9.5+10)/2)] = 1.86 • If we calculate between $9 and $9.5, we get E = [(520-440)/((530+440)/2)]/ [(9-9.5)/((9.5+9)/2)] = 3.08. • So, demand is more responsive to changes in price as price decreases, in this case. Demand Curve P $10.50 $10 $9.50 $9 QD (C) Red Hill Capital Corp, Delaware USA 2008 400 440 480 520

  37. Elasticity classifications • We classify elasticity into 3 basic categories: • Elastic demand, ED > 1, means that the percentage change in quantity demandedchanges more than the percentage change in price. Thus, a reduction in price will cause total revenues to increase; a rise in price will cause total revenues to fall. • So, if elasticity of demand for Kangda college is 1.5, enrollment is 5000, and the price increases by 10% from $50,000/year to $55,000, then, enrollment will decrease by 1.5x10% = 15%. (C) Red Hill Capital Corp, Delaware USA 2008

  38. Elasticity classifications • Enrollment will fall to 5000x85% = 4250, and total revenues will fall to from 5,000x$50,000 = $250 million to 4250x%55,000 = $233,750,000. • Unitary elasticity, ED = 1, is a special case in which the percentage change in quantity exactly equals the percentage change in price. In this special case, total revenues are completely insensitive to changes in price. • Total revenue for Kangda will remain at $250 million, no matter what price is charged for tuition. (C) Red Hill Capital Corp, Delaware USA 2008

  39. Elasticity classifications • Inelastic demand, ED < 1, means that the percentage change in quantity demanded will be less than the percentage change in price. That means that total revenues will increase when price increases but will decrease when price decreases. • In this case, if Kangda has an elasticity of 0.75, and it decides to raise its tuition from $50,000 to $60,000, a 20% price hike, it will only lose 15% (=0,75x20%) in enrollment, from 5000 to 4250, and total revenues will rise to $255 million. • We show graphical examples of the three cases in the next 2 slides. (C) Red Hill Capital Corp, Delaware USA 2008

  40. How does the relative elasticity affect changes in producer revenue? Inelastic = revenue increase with price increase & vice versa Price ($) 90 70 D0 Quantity/wk 1400 1000 (C) Red Hill Capital Corp, Delaware USA 2008

  41. 3 Types of elasticity • The general shapes of elasticity graphs (see page 120 of the textbook) and their causal chains. Total Revenues Increase Total Revenues unchanged Total Revenues decrease Price decrease Price decrease Price decrease Elastic Unitary Elastic Inelastic (C) Red Hill Capital Corp, Delaware USA 2008

  42. Elasticity extremes • There are also extreme cases for elasticity: perfectly inelastic, ED = 0, and perfectly elastic, ED = ∞. These are limiting cases for the index. • Perfectly elastic demand corresponds to a demand curve that is perfectly horizontal (slope of Q(P) = ∞). So, if tuition is $50,000 and is perfectly inelastic, a change in tuition to $50,000.01 will result in zero enrollment. • Perfectly elastic is the limiting case in which an infinitesimally small change in price will result in an infinite change in quantity demanded. (C) Red Hill Capital Corp, Delaware USA 2008

  43. Elasticity extremes • Perfect inelasticity is the opposite extreme. In that case a change in price results in no change in quantity demanded. The demand curve is totally vertical (slope of Q(P) = 0), and demand is limited to an exact quantity. • Perfect inelasticity is the limiting case in which a change in price causes no change at all in quantity demanded. • We show example graphical representations of these extremes, in the next slide. (C) Red Hill Capital Corp, Delaware USA 2008

  44. Graphical Perfect elasticity • Perfect elasticity can be represented by a flat demand curve. Then, change in price results in an infinite change in demand. • There is only one price • ED = ∞ (C) Red Hill Capital Corp, Delaware USA 2008

  45. Graphical Perfect inelasticity • Perfect inelasticity can be represented by a vertical demand curve. Then, change in price results in no change in demand. • There is only one quantity • ED = 0 (C) Red Hill Capital Corp, Delaware USA 2008

  46. Elasticity variations on a line • Since elasticity is percentage change versus percentage change, it is different from the slope of a line, and elasticity may vary along demand curves. • Thinking at the extremes, when price is very high and quantity demanded is small. Then, a change of one unit of quantity demanded is a large percentage change, while a change of price by $1 will be a small percentage change, so that demand is very elastic. (C) Red Hill Capital Corp, Delaware USA 2008

  47. Elasticity variations on a line • When price is low and the quantity demanded is already large numbers of units, a $1 change in price is a large percentage change, while a unit change in quantity demanded is a small percentage change. Thus, demand at that end of the curve will be very inelastic. • In between those extremes will come a turning point at which elasticity of demand will be unitary. (C) Red Hill Capital Corp, Delaware USA 2008

  48. Elasticity variations on a line • Actually, it will, in particular, vary along a straight-line demand curve. • We show this varying type of elasticity for a line, in the next slide. • In the slide we show demand for DVD’s from a street vendor. • In the upper region, it is elastic; in the lower, inelastic (C) Red Hill Capital Corp, Delaware USA 2008

  49. Elasticity variations on a line Demand Schedule Demand for DVD’s Elastic: E>1 Unitary elastic: E=1 Inelastic: E<1 Total Revenues (C) Red Hill Capital Corp, Delaware USA 2008

  50. Break time • Please take a 10 minute break. • Come up and ask questions, if you have any. (C) Red Hill Capital Corp, Delaware USA 2008

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