INTERMED MICROECON ECON 301
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Ms. Ari Lesch
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This 14 page Class Notes was uploaded by Ms. Ari Lesch on Saturday September 26, 2015. The Class Notes belongs to ECON 301 at Iowa State University taught by Staff in Fall. Since its upload, it has received 6 views. For similar materials see /class/214446/econ-301-iowa-state-university in Economcs at Iowa State University.
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Date Created: 09/26/15
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umtmyelastx mm 21421512 5 WM rPcHuc yc mc 2 a n 4 0 mm 4 mm mm Pedech mm a m 3258 a mum w m quotmum Wmuyummcmua mPsmmwnasncDmam mmmmmmmm a u g mm Mm d cmssemmy 5 7quot 17 5a Egg ltn cam zmzms pm llama 9mm 5 Imamammeg WE K dY 777m marmalng n ltu Infenmgwd Taxlrmdlma mwsarm sum pm pGfp 1Gp Wm Wham Um ax p my pism xfgvv39tcallzc axfmmpmdvcexs psmp p Ifgvv39tcallzc axfmmcansnmexs ISDSN G mmmuum or 0 zzn a Muhmkn mpwkprwgr I dnemquot mamnfthz m 15 callzctzdfmm cansumzxs axpmducexs Tumwwszmg39mmm mpxg39rmm 8 7 1w 4 Clip Cunsluner Clmim Timuxy mgmm z pmfzmzs cammms mmhvny mm 15 bum Indm exence Curve A Lhzbnndhs an 1c pmvldz cansllmzxs wnhsamz ame u same mhiy Davan slam d MRSW gm m mxxmum ammlm afydm an cansumzns wdhng m gm up mgetam max mtan Apmpmzs 1 Dawnwmd slaying 2Damtcmssmyathlec 3 Fanhzxfmmangmlsbemx ClnsexJawzxmLth A Em thmugh mxypmm 0mm Camex Dmnlshmg ms 5mm cases magnum Smgh mdm exeme Perfec cam zmzms Rummy shapd 1c 111 m1 WWW S w W Wm M 1 mm 5mm 6 i m WWW y 2 3 W Linnqu mm m mdm exence curve fax um funicular 1m du Rzlananshpbemenn nyandMRS MRSW m 4 Cowman m pyy Y MRTW amp Ta gm mm nmmfy cmmmm gm up 74m m A In ammwcme mmquot A m r m an um m y Mm mm m mm a punMt Wm 50 m 1 mu m umauu 25 5 z mmpysmmm Wm MRS MRTW Kay mm mm ammlms thznwe have an m emxsahma Itquotth exmsa zasmm afnzgmve apnmahmnnm thznwe have Camrsah mn m MRS ltMRTM 20me 01 In m MRSW WRTW xmxo m Inlay mm 5 2mm mm mm h nm N w z m WWW CALCULATIONS OF DERIVATIVES In economics we often use mathematical equations to quantify or specify the relationship between the variables These equations are often referred to as specific functions In these equations it is common to denote a dependent variable as y independent variables as XI x1 etc and constants as a or a 31 or b etc Mathematical rules enable us to determine the partial derivative for different functions Note if y is a function of only one variable x the partial derivative and the total derivative ie dydx are the same A few common examples follow FUNCTION y DERIVATIVE y l Power function Power rule gt y axquot EX rzax39 l dx Special case dy n0gt a gtoax l0 y dx 2 Sum of functions Sum of derivatives rule dy dU dW gtyuw dx 1X dX where U gx w hx 3 Product of functions V Product mic UW dy U dW W du gt y gt A dx dx dx where U gx W h x 4 Chain function Chain rule gt yfz Z bl 1195 J dx where Z gx dx d7 ECON 301 CLASS REVIEW Chp 5Chp 7 June 23 2004 SUMMER 2004 XUE QIAO Ch deter 5 Aggllging Consumer Th ear V Deriving demand curve For any given price we can apply consumer constrained choice to derive the optimal consumption bundle Find the combination of prx and plot it then we derive the demand curve To derive it numerically use formula MRS MRT which can also be rewritten as M U X PX M U Y PY The above formula will derive a equation about optimal consumption bundle then put this equation back into budget constraint then we can nd xii V Income change cause Budget constraint to shift optimal consumption Incomeconsumption curve Engle curve upward sloping implies normal good Income elasticity 77 downward sloping inferior good DQ gt0 then normal good DY Q lt0 then inferior good V Price change Total effect substitution effect income effect Decompose TE into SE and IE Step 1 draw a budget line BL parallel to the new BL and tangent to Initial indifference curve then we have a new tangent point e Step 2 The movement from eo the tangent point between initial IC and Initial budget constraint to 6 measures the SE Step 3 The movement from e to e1 the tangent point between new BC And new IC measures the IE Note Be careful about the direction SE 6 eo IE 61 6 TE 61 eo Consider the case when price of good X drops Normal good SE DQ gt 0 IE DQ gt 0 Then TE gt0 Inferior good SE DQ gt 0 IE DQlt0 ThenTEgt0 iflSElgtlIEl TE lt 0 if l SE lltl IEl Giffen good V Derive Labor supply curve Derive leisure demand curve by applying consumer constrained choice Labor supply 24demand curve of leisure Properties of leisure decides the shape of labor supply curve When wage is low people view leisure as an inferior good W increases labor supply increase When wage is high people view leisure as a normal good W increases labor supply decrease So labor supply will increase rst then start to decrease ie upward Sloping rst then downward sloping Ch deter 6 Firm and Qroductitm V Production function is de ned as the maximum output by using existing inputs so this de nition implies ef cient production process shortrun capital is xed longrun labor and capital can both be varied V Shortrun production TP MPL AP the shapes of these three de nitions properties of these three de nitions and how to show them graphically Diminishing marginal returns MPL is decreasing when L increases V Longrun production isoquant q fLK MP slope of1soquant MRTS L and MRTS 1s decreas1ng MPK shape of isoquant straight line perfect substitutes rightangle perfect complement convex imperfect substitutes V Return to scales ftKtL gt rfKL IRS Def ftKtL rfKL 3 CRS ftKtL lt rfKL DRS Tell the return to scales from graph given several isoquants and corresponding inputs bundles Return to scales can be varied across rm s size IRS for small CRS for moderate DRS for large Chapter 7 Costs V Measuring cost economical costexplicit cost opportunity cost V Shortrun cost capital is xed so we have a nonzero FC 7 Defs FC VC TC AFC AVC AC MC TCVCFC ACAVCAFC AFCFCQ AVCVCQ Properties of these 7 curves and relationship among them Be able to show them graphically Effect on cost of a government speci c tax amp franchise fee V Longrun cost FC0 isocost line C wL rK w slope of1socost r derive the costminimizing bundles of inputs MRTS K r or Lowest isocost line or Last dollar rule Shape of Longrun costLRC Longrun Average costLRAC MC depends on return to scales CRS LRC upwardsloping straight line LRAC amp MC constant IRS LRC increasing but slope is decreasing LRAC amp MC decreasing DRS LRC increasing but slope is increasing LRAC amp MC increasing the part where LRAC is decreasing is called economies of scale increasing diseconomies Constant no economies Longrun expansion path and shortrun expansion path Read practice IV Chapter 3 Applying the Supply and Delnand Model Shape matters How responsive are the consumers How responsive are the producers Tax incidence 7 who is paying for the tax Shape matters 0 How much more will the quantity demanded increase if we reduce the price by 10 Pictorial analyses are not enough here We nee a quantitative analysis The information is all on the demand curve the task is to extract it Let s see some different shapes of the demand curve cf Figure 31 Show a steep and a at demand curves The atter the curve is the more responsive the quantity is to a change in price How responsive are the consumers How to summarize the information we need 7 Elasticity It is definition as the percentage change in quantity over that in price 8 AQQAPP Why define it this way 1 We knew that slope APAQ but it changes with the choice of units We want to know the ratio of their percentage changes 2 Usually we control price to in uence quantity So we want to know the response of quantity to price Relate elasticity to slope s AQQAPP AQ AP P Q The inverse slope times the ratio Example If the demand curve is Q a 7 bP Then the elasticity is s bPQ Review Figure 32 Upper part 8 lt l elastic Middle point 8 l unitary elastic Lower part 8 gt 1 inelastic It is easy to see why it is more elastic when you move up the demand curve and it is more inelastic when you move down the curve Show two movements along the curve Why is it equal to 7l in the middle Example Q a 7 bP Intercepts a and ab Slope b Middle point is a2 a2b So 8 b a2bb2 1 Some extreme demand curves Figure 33 Horizontal perfectly elastic The good can be perfectly substitute by another same kind of apples from different states Vertical perfectly inelastic Example Essential goods for survival daily drug versus the price for a surgery or gene therapy Application Should we have a sale to boost revenue Schnuck s has bought 10001b of strawberries Note that these are perishable and cannot be resold The got a fixed stock The price of strawberries are set at 499 lb The revenue is steady but can they do better The manager is now thinking about a 5 off sale Yes managers do think sometimes especially those who went to business schools Can the sale increase their revenue The only information we have is strawberries price elasticity s 08 But this is enough to help us make a decision TR PQ The sale has two effects gain from a quantity increase and loss from a price drop ATR APQ AQP The first one is a negative and the second is a positive change to the total revenue When APQ AQP gt 0 we should have a sale This is because the gain form a quantity t increase dominates the loss from a price drop That is AQP gt APQ AQAP lt QP AQ APP Q lt l s lt 1 Conclusion When 8 lt l a sale can increase the total revenue Gain from quantity increase dominates When 8 gt 1 a sale will decrease the total revenue Loss from price drop dominates Application Sometimes farmers destroy their crop to prevent loss Why If they sell the crop won t they get more money The reason is that food is a necessity this means it the demand for food is in elastic They cannot sell all their crop at a high price If they sell the remaining at a lower price they market price will go down and the total revenue goes down 7 The effect of a price drop dominates the effect of a quantity increase Consumers response to other factors Other factors affect the quantity demanded as well like we saw in the demand function Their elasticities are defined in the same way 0 Income Elasticity you can use SY amp AQQAYY AQAYXYQ Percentage change of quantity demanded over that of income Example Q 171720P 20 Pb 3Pc 2Y When Q 220 and Y 125 calculate the income elasticity A Y 5 2 125220 0114 Application How to predict the demand in ten years Many companies need to tell their stockholders about their business prospect 3 to 5 years into the future When most companies do long term predictions the most reliable variable is people s income Since other factors are varying all the time they will take it as fixed Suppose the economists predict that the economy has a growth rate of 2 per year from 2003 to 2006 We know that our product faces an income elasticity SY 15 How much should we expand our capacity in 2006 3 year into the future SY AQQAYY 15 AQQ 6 15 AQ Q 9 o Crossprice elasticity 8C AQQAPOP0 AQAPOP0Q When 8C lt 0 the other good is a complement of this good When SC gt 0 the other good is a substitute of this good Example How to calculate this Q 171720P 20 Pb 3Pc 2Y For good b a substitute AQ 20APb SC AQAPbPb Q 20PbQ When Q 220 and Pb 4 we have crossprice elasticity 0364 For good c a complement AQ 3APc 8C AQAPcPcQ 3PcQ When Q 220 and Pc 10 we have crossprice elasticity 0136 How responsive are the producers The information on the supply curve can be summarized concisely in the same way We de ne the price elasticity of supply as SS AQQAPP AQAPXPQ Note that it has the same formula as the elasticity of demand But it is calculated along the supply curve It is the percentage change in quantity supplied over that in price Example Q 88 40P AQ 40AP So when Q 220 and P 33 SS AQAPXPQ 4033220 06 The same we call SS lt l inelastic SS l unitary elastic SS gt 1 elastic Example A vertical supply curve perfectly inelastic the supply of land
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