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CU-Boulder ECON 2010 - How responsive are you?

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How responsive are you?Edward Morey: draft October 14, 2014The more one reacts to an outside in‡uence, the more responsive you are tothat in‡uence.For example, if, in the next election the addition of Paul Ryan to the Repub-lication presidential ticket causes you to switch from being a die-hard Democratto a stanch Republican, you are responsive to that exogenous in‡uence.If you go from wanting nothing to do with Wanda but then marry her be-cause one day she wore a blue dress, you are very responsive to blue dresses,particularly on Wanda.Or if an increase of 1% in the catch rates for bass at your favorite …shinghole causes you to increase your trips there by 10%, then you are responsive tothat change.Besides blue dresses and bass, many people are a¤ected by price changes:when the price changes some respond by buying more or less of the product;those who do not buy more or less are unresponsive to the price change.Most of us do not respond to most price changes. (For example, most of uswould not change our behavior if the rental rates for commercial property inParis increases by 1%, or if the price of …rst-class plane tickets to Syria dropped10%)How much the quantity purchased changes depends on: (1) how much theprice changes, (2) from what level the price changes, (3) one’s preferences, (4)one’s income, and lot of other things.11 How response are you to a change in the priceof gasoline?With recent dramatic rises and falls in the price of gasoline, the answer isimportant. For example, how much will a run-up in the price of gas decreasehow many miles we drive, and/or what we drive.If the price increase reduces demand a lot, much less gas will be burned andwe won’t pollute as much or have to import as much oil from countries that donot necessarily like us. But these e¤ects will be small if the price increase haslittle e¤ect on demand.Before what’s his name, the foreigner, got elected President, Hillary Clintonand John McCann, both running for their party’s nomination, both proposeda summer vacation from the Federal gas tax due to the high price of gasoline?What would that have done to the demand for gasoline? How much?2What factors in‡uence the amount of gas an individual buys in a week1if they own a carwhere they livewhere they worktype of carnumber of kids and where they go to schoolhow much they enjoy drivingthe availability of alternative forms of transportation (buses, trains, bikes,feet, etc.) and what they cost. Alternative forms of transportation are substi-tutes.level of physical …tness?how they shop (number of trips, whether you buy on or o¤-line)where their friends livewhere their signi…cant other lives. I know a number of couples who livethousands of miles from one another.how much you like to ski, …sh, party in Vegastheir incomeAre their compliments to driving? Name one or two? How would theyin‡uence how much gas you buy?etc.1Alternatively, we could discuss the factors that determine ho w much gasoline a …rm buys.3A change in any of these will likely in‡uence their demand for gas. A changein any of these would cause a shift in their demand function (quantity as afunction of price).How could you reduce the amount of gas you consume?4List at least …ve things in your notes1. quit your job2. dump the girlfriend in Kansas or boyfriend in Wiggins CO.3. take the bus4. buy a bike, and use it for trips that were previously made by car5. shop online6. lose weight so you can walk to work without dying7. tune up the car8. move closer to work59. get a job closer to where you live2 Consider Wilbur’s per-week demand functionfor gasoline. He commutes 25 miles a day andlikes to go to the mountains on weekends, a100-mile round-trip. Assume his current carget 25 m.p.g.His demand function might look as follows:GWD= 18  :75p1:8G- at a zero price Wilbur would buy 18 gallons a week(about one tank), and the quantity he buys decrease, at an increasing rate, atthe price increases.20 1 2 3 4 524681012141618Pg = price of gasgallonsWilbur’s weekly demand for gas as a function of the priceWhy did I pick (makeup) a mathematical function with a graph like this?Note that gallons are on the vertical axis.2Economists spend a lot of e¤ort est imating demand functions for gasoline, but I just madethis one up, a simple one so things do not get too complicated.6I wanted it to re‡ect reasonable behavior given Wilbur’s commuting con-straints, Wilbur’s preference for trips to the mountains, and the current priceof gas.With gas at $4 a gallon, Wilbur buys only 18:75(4)1:8= 8: 905 7, enough toget him to work and one trip to the mountains, but no errands or other drivingto fun places.What will happen if the price rises to $5 gallon? Wilbur buys only 18 :75(5)1:8= 4: 410 4, enough only to drive to work four days a week (will need totake the bus the other day) and no trips to the mountains.Alternatively, if we drill for oil everywhere and the price drops to $1 gallon,unlikely, Wilbur goes wild and buys 18  :75(1)1:8= 17: 25 gallons a week,enough to drive wherever he wants to go.I chose a mathematical function that got steeper and as the price of gasolinerises.7Note that my chosen demand function implies that Wilbur will be takingthe bus or walking to work when the price is around $6=gallon.2.1 So, given his demand function for gasoline, how re-sponsive is Wilbur to an increase in the price of gaso-line?It depends on the current price and on h ow one measures responsiveness.We might be interested in how much Wilbur’s demand for gasoline willchange if the price increases by, for example, $1.2.1.1 The slope/steepness of his demand function:One possible measure of responsiveness is4GWD4pG: the change in Wilbur’s quantitydemand divided by the change in price, 4 is a symbol for change.Steepness as a measure of responsiveness.Would you expect this measure of responsiveness to b e p ositive or negative?8For example if the price increases from $4 to $5, Wilbur’s demand for gasolinedrops from 8: 905 7 gallons to 4: 410 4, a drop of 4: 495 3 gallons.In this case,4GWD4pG=4: 410 48: 905 754= 4: 495 3 gallons, which is the slope ofhis demand curve between $5 and $4Alternatively, if the price rises from $2 to $4 demand would decrease from15: 388 gallons to 8: 905 7 gallons.In this case,4GWD4pG=8: 905 715: 38842= 3: 241 2 gallons, the slope betweenthese two prices.9Note that4GWD4pGis the slope of the Wilbur’s demand function between thelower


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