# ECON 132 Midterm: Practice Questions+Solutions for Midterm #1

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Published on 26 Mar 2019
School
Department
Course
Problem Set 1
Econ 132 Energy Economics, WI15
1. Conversions
a. How many million British Termal Units (MMBtu) are in 310 thousand cubic feet (310 Mcf)
of natural gas?
310 Mcf ×1.035 MMBtu
1Mcf = 320.8500 MMBtu
b. How many million British Termal Units (MMBtu) are in 8,000 pounds of coal?
8,000 pounds ×1short ton
2,000 pounds ×25.0MMBtu
1short ton = 100.0000 MMBtu
c. How many million British Thermal Units (MMBtu) are in 60 blue barrels of oil?
60 bbl ×5.8MMBtu
1bbl = 348.0000 MMBtu
d. How many short tons of coal are equivalent in heat energy content to 700 barrels of oil?
700 bbl ×5.8MMBtu
1bbl ×1short ton
25 MMBtu = 162.4000 short tons
e. How many blue barrels (bbl) of oil are equivalent in heat energy content to 9.4 million
cubic feet (9.4MMcf) of natural gas?
9.4MMcf ×1,000 Mcf
1MMcf ×1.035 MMBtu
1Mcf ×1bbl
5.8MMBtu = 1677.4138 bbl
1
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2. Thermal Eﬃciency
a. The Four Corners Generating Station in Fruitland, New Mexico uses 11,000 Btu of energy to
generate a kilowatt hour of electricity. Find its thermal eﬃciency.
3412 Btu
kW h
11,000 Btu
kW h
= 0.3102
b. The Palomar Energy Center in Escondido, California has a thermal eﬃciency of of 48many
million cubic feet (MMcf) of natural gas are needed to generate 1.4 gigawatt hours of electricity?
1.4GW h×1,000,000kW h
1GW h ×3412 Btu
kW h
0.48 ×1MMBtu
1,000,000Btu×1M cf
1.035MMBtu×1M M cf
1,000Mcf = 9.6151MMcf
3. Elasticities
a. (Point Elasticity) Find the point elasticity of a consumer with demand for gasoline given by
the function q= 60 3p0.25p2when the price is \$2.90 per gallon.
εpoint =
dQ
Q
dP
P
=dQ
dP ×P
Q
P= \$2.90
Q(P) = 60 3P0.25P2
Q(2.90) = 49.1975
dQ
dP =30.5P
=30.5(2.90)
=4.45
εpoint =4.45 2.90
49.1975 =0.2623
2
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b. (Arc Elasticity) Find the arc elasticity of a consumer who uses 15 gallons of gasoline per
week when the price is \$3.50 per gallon and 20 gallons per week when the price is \$2.50 per gallon.
εarc =
Q2Q1
1
2(Q1+Q2)
P2P1
1
2(P1+P2)
=
2015
1
2(15+20)
2.503.50
1
2(3.50+2.50)
=0.8571
c. My home’s heating system is fueled by oil. When the price of home heating oil is \$4 a gallon
and the price of electricity is \$0.08 per kilowatt hour, I use 2 gallons of oil and 323 kilowatt hours
of electricity. When the price of heating oil increases to \$5 a gallon, I lower the thermostat on the
oil heater and use a plug-in electric space heater instead. As a result, I use only 0.5 gallons of oil
but 360 kilowatt hours of electricity. What is my cross-price elasticity of demand for electricity
with respect to the price of heating oil?
εQePh=
Qe2Qe1
1
2(Qe1+Qe2)
Ph2Ph1
1
2(Ph1+Ph2)
=
360323
1
2(323+360)
54
1
2(4+5)
= 0.4876
3
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## Document Summary

Problemset1econ132energyeconomics,wi15answerkey1. conversionsa. howmanymillionbritishtermalunits(mmbtu)arein310thousandcubicfeet(310mcf)ofnaturalgas?310mcf 1. 035mmbtu1mcf=320. 8500mmbtub. howmanymillionbritishtermalunits(mmbtu)arein8,000poundsofcoal?8,000pounds 1shortton2,000pounds 25. 0mmbtu1shortton=100. 0000mmbtuc. howmanymillionbritishthermalunits(mmbtu)arein60bluebarrelsofoil?60bbl 5. 8mmbtu1bbl=348. 0000mmbtud. howmanyshorttonsofcoalareequivalentinheatenergycontentto700barrelsofoil?700bbl 5. 8mmbtu1bbl 1shortton25mmbtu=162. 4000shorttonse. howmanybluebarrels(bbl)ofoilareequivalentinheatenergycontentto9. 4millioncubicfeet(9. 4mmcf)ofnaturalgas?9. 4mmcf 1,000mcf1mmcf 1. 035mmbtu1mcf 1bbl5. 8mmbtu=1677. 4138bbl1 shared via c ourse h ero. co m. 2. thermale ciencya. thefourcornersgeneratingstationinfruitland,newmexicouses11,000btuofenergytogenerateakilowatthourofelectricity. finditsthermale ciency. 3412btukwh11,000btukwh=0. 3102b. thepalomarenergycenterinescondido,californiahasathermale ciencyofof48manymillioncubicfeet(mmcf)ofnaturalgasareneededtogenerate1. 4gigawatthoursofelectricity?1. 4gwh 1,000,000kwh1gwh 3412btukwh0. 48 1mmbtu1,000,000btu 1mcf1. 035mmbtu 1mmcf1,000mcf=9. 6151mmcf3. elasticitiesa. (pointelasticity)findthepointelasticityofaconsumerwithdemandforgasolinegivenbythefunctionq=60 3p 0. 25p2whenthepriceis. 90pergallon. point=dqqdpp=dqdp pqp=. 90q(p)=60 3p 0. 25p2q(2. 90)=49. 1975dqdp= 3 0. 5p= 3 0. 5(2. 90)= 4. 45 point= 4. 45 2. 9049. 1975= 0. 26232 shared via c ourse h ero. co m. T his study resource w as https://www. coursehero. com/file/11056043/problemset1solutions/ b. (arcelasticity)findthearcelasticityofaconsumerwhouses15gallonsofgasolineperweekwhenthepriceis. 50pergallonand20gallonsperweekwhenthepriceis. 50pergallon. arc=q2 q112(q1+q2)p2 p112(p1+p2)=20 1512(15+20)2. 50 3. 5012(3. 50+2. 50)= 0. 8571c. myhome"sheatingsystemisfueledbyoil. whenthepriceofhomeheatingoilisagallonandthepriceofelectricityissh. 08perkilowatthour,iuse2gallonsofoiland323kilowatthoursofelectricity. whenthepriceofheatingoilincreasestoagallon,ilowerthethermostatontheoilheateranduseaplug-inelectricspaceheaterinstead. asaresult,iuseonly0. 5gallonsofoilbut360kilowatthoursofelectricity. whatismycross-priceelasticityofdemandforelectricitywithrespecttothepriceofheatingoil? qeph=qe2 qe112(qe1+qe2)ph2 ph112(ph1+ph2)=360 32312(323+360)5 412(4+5)=0. 48763 shared via c ourse h ero. co m. T his study resource w as https://www. coursehero. com/file/11056043/problemset1solutions/ d. consideringagainmyheatingsituationasinpartcabove,thepriceofheatingoilispergallonandiconsume2gallons. igetapayraisefrom,500permonthto,800permonth. withtheadditionalincome,idecideicana ordtoturnthethermostatonmyhome"soilheateruptothetropicaltemperatureiprefer. asaresult,myheatingoilconsumptionincreasesto5gallonspermonth. whatismyincomeelasticityofdemandforheatingoil? qhi=qh2 qh112(qh1+qh2)i2 i112(i1+i2)=5 212(2+5)1800 150012(1500+1800)=4. 71434. frackingtheunusuallyunscrupulousenergycorporation(uuec)recentlyopenedahydraulicfracturingsitelocated5milesawayfromthewatersupplyofheartland,oklahoma. uuecengineershavecalculatedthat9millioncubicfeet(mmcf)ofnaturalgascanbeextractedfromthesite. however,thefrackingoperationwillcontaminateheartland"swatersupply. basedonpriorexperience,uuecknowsthatitcanextractnaturalgasfor2yearsbeforelocalresidentssuccessfullylobbythestategovernmenttoblockfurtherextraction. thepriceofnaturalgasisknowntobepermcf(notmmcf! )inyear1,andpermcfinyear2. thecostfunctionforextractingnaturalgasinperiod1is:c1(q1)=75+10q1+2q21inperiod2technologicalinnovationcausesthecostfunctiontodropto:c2(q2)=75+8q2+q22uuec"sdiscountrateis0. 4. 4 shared via c ourse h ero. co m. )5 shared via c ourse h ero. co m. = 9,472. 6316sothevalueis 9,472. 6316. inthiscase,ifnotforcedtoextracttheentireamountin2years,theextractioncostsaretoohighrelativetopro ttojustifyextractionofatleastsomeunits. g. howwouldtheoptimalallocationofthenaturalgasextractedinperiods1and2changeundereachofthefollowingscenarios?doq1andq2eachincrease,decreaseornotchange?inonesentenceexplainyourintuition. foreachscenario,assumeeverythingelseisheldcon-stantasdescribedabove(thatis,changesarenotcumulativefromonescenariotothenext). i. thepriceinperiod2increasestopermcf. q1decreases,q2increasesbecauseitisnowrelativelymorepro tabletosellinthesecondperiod,buttheresourceconstraintstillbindssowemustdecreaseq1inordertoincreaseq2. ii. additionalnaturalgasreservesarefoundatthesite,increasingthetotalto9. 5mmcf. bothq1andq2increasebecausetheresourceconstraintishigherbutstillbindsbythethirdfoc,andmaintainingtheequalityofmarginalpro tsineachperiodrequiressplittingtheadditionalproductionbetweenbothperiods,althoughlikelynotequallyiii. technologicalimprovementinthesecondperiodisevenbetterthananticipated,andthesecondperiodcostcurveisc2(q2)=60+6q2+0. 7q22q1decreasesandq2increases. sincepro tineachperiodisrevenue-costs,andthetechnologicalimprovementreducessecondperiodcostsperunit,marginalpro tisrelativelyhigherinthesecondperiodsoweshouldshiftproductionfromthe rstperiodtothesecondperiod. iv. uuec"sdiscountrateincreasesto0. 7. q1increasesandq2decreases. theincreaseindiscountratemeansthatthe rmismoreimpatientthanbeforeandvaluesearlierpro tmorethanlaterpro tbyagreatermarginthanbeforetheincreaseindiscountrate. (amathematicalex-planationisthatlookingbackat(a),thediscountrateisinthedenominatororthepresentvaluecalculationforthesecondperiodpro ts,soifthediscountrateincreases,thesecondperiodvaluationdecreasesv. thepriceinperiod1increasestopermcf. q1increasesandq2decreases,becauseunitssoldinperiod1generaterelativelymorepro tthanbeforethepricechange. 6 shared via c ourse h ero. co m. 5. timberextractionthelincolnlogcompanyjustreceiveda2-yearleasefromthestateofmainetoextracttimberfromoneofmaine"sharvestableforests,whichcontainsenoughtreestoextract150thousandlinearfeetoftimber. inyear1,thepriceoftimberisperthousandlinearfeet. inyear2,thepriceisperthousandlinearfeet. thecostfunctionforextractingtimberinyearst=1andt=2is:ct(qt)=22+8qt+0. 1q2tlincolnlog"sdiscountrateis0. 15. a. writedownthelagrangianrepresentingtheconstrainedoptimizationproblem. l=85q1 (22+8q1+0. 1q21)+11. 15[90q2 (22+8q2+0. 1q22)]+ (150 q1 q2)b. writedownthethree rstorderconditionsthatholdattheoptimum. (q1): =77 0. 2q1(q2): =11. 15(82 0. 2q2)( ):150=q1+q2c. solvefortheoptimalquantityoftimbertobeextractedeachyearaswellasthevalueofbeingabletoextractanotherlinearfootoftimber. q1=85. 0000q2=65. 0000 =60. 0000note:because =60,lincolnlogsshouldbewillingtopayinordertorelaxtheresourceconstraintby1thousandlinearfeetoftimberd. respondinthreesentencesorless:unlikemanyotherextractedenergysources,treescanbeplantedandharvestedoverrelativelyshorttime-spans. treesgrowbestwithgoodloggingpracticesthatlimiterosionandlocalwaterandairpollution. giventhegrowth-rateofthespeciesoftreeloggedinmaineandgoodgrowingconditions,extractionof7 shared via c ourse h ero. co m.

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