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26 Fig. XXIV When two straight tine demand curves intersect, ttie flatter curve is more elastic ferent elasticities. And we could go on. We urge you, therefore, not to conftrse slope with elasticit). THE ELASTICITY OF SUPPLY The elasticity of supply measures the responsiveness of the quantity supplied to a change in price along a supply curve and is defined analogously in the point formula as: Percentage Change in Quantit) Supplied Percentage Change in Price (AQ/Q) (AQ P) (AP/P) ( Q) The concept presents no new difficulties. Except that were now moving along a supply curve rather than a demand curve, both the arc and point formulas are identical. (Well skip repriiuing the arc formula.) Moreover, as with vertical demand curves, vertical .supply curves, such as the one depicted in Figure XXVlll are perfectly inelastic, while horizontal ones, such a.s Figure XXIX, are perfectly elasdc. Similarly, uirie tends to increase the elasticity of supply. For example, it may not be possible for producers to adjust production much in a short period of time, but large supply responses are often possible, given enough reacdon time. Figure XXX models the situation. With no reaction time, supply is given by Sj; but as reaction dme increases, die supply curve rotates through Sj to reach S3, a more elastic curve. Expectations on the part of producers may also play a part; for example, supply i more likely to be elastic if producers expect a price; increase to be permanent rather than temporar); This is only common sense. Elasdcity of supply nie sures the supply responsiveness to a change in 1 price. If suppliers believe a price increase is here stay, they will want to expand the size of their plan hire more labor, buy more inputs, and expand duction considerably so that e, will be large. A prio rise lasting only a day or two would clearly not warran] so strong a reaction. Consequendy, would in case be small. In Figure XXX, S) is the response temporary increase in price, while S3 is the response t a permanent one. However, some significant differences betweei demand and supply elasticity do emerge. Fiisi because .supply curves slope upward, the percen change in the quantit) supplied must have the sa: Fig. XXV Fig. XXVI Fig. XXVII Pounds Kilos
Fig. XXVIi Fig. XXiX Perfectly Inelastic Supply Perfectly Elastic Supply Rising Supply Elasticity ;n as die percentage change in price, i.e., raising the price by some percent or anotiier raises tiie quandty by percent. Second, any straight line supply curve passing through the origin is unit elasuc at all prices; lie only reason weve included the point elasticity JFoimula is so we could prove our point; the formula Itself is not important for this book.) Consider Figure CXXI, where we calculate the at the arbitrary price From the graph we know quandt) will be Q*. loreover, from high school algebra, the slope of the hir\e, the rise over the run {AP/AQ), at P* is P*/Q*. lipping this over gi\es the run over the rise, AQ/ = */ *. Substitudiig on the right in formula (5) and icelling gives: Percentage Change in Quandty Percentage Change in Income p* Q* Our discussion in Section II implies that iid will be positive for normal goods and negative for inferior goods. If, for example, your income rises by a few percent, you will buy a greater quantity of normal goods, i.e., your purchases will rise by some percent. Since both numerator and denominator in (6) are positive, so is •fid. Likewise, if your income falls by some percent, your purchases of normal goods will also fall by some percent or another. Again because both numerator and denominator have the same sign, ] is positive. If, however, the good is inferior a percentage increase in income will mean a percentage decrease in the pur lally, the suppliers total revenue (TR) always pcreases with supply price, whatever the elasticity of ipply. This too is oiil) common sense. A percentage increase in the suppl) price does not decrea.se the quantity supplied. Therefore, imlike elasticity of iemand, the resulting percentage change in the quality supplied never opposes the percentage change in IjPrice and usually reinforces it. Hence total revenue f (and price always mo\e together along a supph curve, whatever the elasdcit) of supply i" ,OTHER ELASTICITIES ii; The income elasticity of demand measures the tojresponsiveness of demand to a change in consumers mconies and is defined as: Fig. XXXI       / Ed = 1 lor any straight line supply curve passing Ihrougti the origin.     0 « 
ELASTICITY Demand Supply Income Cross CRITICAL POINT none 0 EFFECT If e<i < 1.0, TR & P price move in same direction If Ed > 1.0, TR & P move in opposite directions !f > 0, good is normal 11 < 0, good is Inferior If > 0, goods are substitutes If cj < 0, goods are complements chases ofthe good. Hence in this case, the numerator and denominator in (6) have opposite signs so that is negative. Finally, the cross elasdcit) of demand refers to the responsiveness of demand for a particular good (x) to the change in price of another good (y). This is defined as: X Percentage Change in Quantity of Good X (/) £ y~~ Percentage Change in Price of Good Y Cross elasticit) is closefy related to the concepts of substitutes and complements. If the goods "x" and "y" are complements, for example, tennis balls and rackets, then the cross elasticity will be negative. This is again only common sense: for example, as the price of tennis balls (good y) rises by some percent in formula (7), the percentage change in the quantit) of tennis rackets purchased (good x) ivill be negative became people will want to play less tennis. Therefore E in (7) must also be negative. Moreover, Ey will remain negative if the price of balls were to fall. In this case, people will want to play tennis more, so the the percentage change in the numerator will be positive. With opposite signs in the munerator and denominator, Ey nnjst again Ix negative. Similarly, if goods are substitutes, such as racket ball and tennis rackets, the cross elasticity will be positive. This is likewise common sense. For example, if the price ot racket ball rackets (good y) rises by some percent, the percentage change in the quantit) of tennis rackets purchased (good x) will likewise be positive because people will wish to switch out of racket ball and into tennis. Hence Ey in (7) is also positr Naiinally. luuelated goods tend to have cross elasti lies close to zero. While any type of elasticit) is considered ela if, ignoring the sign, its value is greater than one : inelastic if its value is le.ss than one, the critical bou ary points of the various elasticity types differ and ; summarized in Table III. However, we do not necessarily advise comrij ting these critical poinui to memory." Perhaps the 1 way to handle problems is to recall the defmition ; to work duough the iniderlying logic. EMPIRICAL CALCULATION OF DEMAND SUPPLY ELASTICITIES Since neither demand nor supply curves be directlv observed, how can real world elasticides calcidated? Empirical calculation of elasticities, i calculation based upon real word obserxation experience, begins with curve shifts of the sort int duced at the .start ofthis .section. Suppos< we have reason to believe that the suj ply cvnve of widgets is stable, but that the demar curve is unstable. That is to sav. imagine that over certain lime period the forces which shift the widgi supph cuive are roughh constant, but that one more of the (iemaiid shifters varies. Then in Figu XXXIl. we woidd get a movement from P to P and to Q along ihe supplv curve. .Although we caniio einpiricall) detect die whole demand and supp cinves. we ran, howevei, capture the two supply curv points shown in the right hand panel of the figure, such, we haw enough information to calculate Ixid the percentage change in quaniit\ and die perceiiWg
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