# Study Questions Chapter 2. Energy Lessons From The Past .

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Study QuestionsChapter 2. Energy Lessons from the Past and Modeling the FutureStudy Question 2.1. Suppose that you have estimated the following time series model forworld oil pricePt 0:9Pt-1 - 0:8Pt-2 0:0002Yt 0:0001Yt-1You have the starting values for price per barrel and world income in billions of dollars for2009, 2010, and 2011 as 79.4561.922012 47.5116195.04YtYt-1730457889773045837067889779.45 85825.0383706In Excel create a simple forecasting model to forecast oil price from 2012 to 2013 in thecolumn under Pt. Note I have included the forecasts for 2012 so you can check if you are doingthe problem correctly.2.1a. First assume that income grows by 2.5 % per year with continuous growth rate.(i.e. Yt Yt-1e0.025) Fill the column under Yt using this formula. Create the values in thecolumn for Yt-1. What is income in 2100?2.1b. What is income in 2100, if you use discrete annual compounding. (i.e. Yt Yt-1(1 0.025))?2.1c. Create your columns for forecasted Pt, Pt-1, Pt-2. Graph Pt-1 against time.Study Question 2.2 A firm owns a coal mine (X1) and an electricity generator (X2) 0.23 ofcoal is required per dollar of coal, and 0.25 of electricity is required per dollar of coal. 0.30 ofelectricity is required per dollar of electricity and 0.15 of coal is required per dollar ofelectricity. End-use demand for coal is 700 and end-use demand for electricity is 2000. Howmuch coal and electricity have to be produced?Study Question 2.3 You live in an economy with three industries - non-energy basic resources(B), manufacturing (M), and energy (E). The following A matrix represents the input-outputcoefficients for this economy. The matrix is represented in input/ .3a. Explain the coefficients 0.05 and 0.07.

2.3b. What is value added in each of the three industries?2.3c. If end use demand for (B, M, E) (2,3,8), how much total B, M, E must beproduced?2.3d. For the solution in 2.3c what are the direct purchases of energy for the productionof B?2.3e. What is the cradle to grave use of E in the production of one unit of B?2.3f. Suppose that the production of each of these products generates carbon dioxide. Thepounds of carbon dioxide per of B, M, E are: 0.02, 0.03, 0.04, respectively. Compute the totalamount of CO2 generated by the total output vector you found in part 2.3c.2.4. The following is an input output coefficient matrix for a five sector economy.FoodBasicHousing materials EnergyManufactured 00.060.050.030.20Basic ervices0.040.020.020.050.060.252.4a. In Excel, solve the model for end use demands of Food 25, Housing 50, Basicmaterials 34, Energy 10, Manufactured Goods 20, and Services 15. 5b. For asummary of matrix computation in .2.4b. How much does each sector buys from another?2.5c. What is the total cradle to grave use of each sector in another.Chapter 3. Perfect Competition and the Coal Industry KeywordsStudy Question 3.1 In the text, we observed that if price was above equilibrium in acompetitive market, excess quantity demanded would put pressure down on price. Orequilibrium was stable from above. Is equilibrium stable from below?Study Question 3.2 Take the following model from the text:Qd 100 2Pc 3Psb 4Pcm 0.10Y (3.6)Qs 6 Pc 1Pk 0.2Pl 0.8Pnr 1.5Psm (3.7)wherePc is the price of coalPcm is a complement to coal consumption such as a boiler, set 10

Pk is the price of capital, set 2Pl is the price of labor, set 3Pnr is the price of other natural resources used in production of coal, set 5Psb is the price of a substitute to coal, such as natural gas, set 6Psm is the price of similar products which a coal producer could produce, set 4Y is a measure of economic activity, set 954 Change the ceteris paribus value for theprice of a substitute from 6 to 2. Resolve the model for price and quantity.Study Question 3.3 Graph what happens in the world coal market given the following events.Note what happens to equilibrium price and quantity. Has there been a change in demand or insupply? Has there been a change in quantity demanded or in quantity supplied? Note one is ashift of the curve and the other is a shift along the curve.3.3a Exxon develops large coal deposits in Colombia.3.3b Combined cycle gas turbines increase natural gas eﬃciencies for the generation ofelectricity.3.3c A ﬁnancial crisis causes recession in Asia.3.3d The end of apartheid removes trade embargoes on South Africa.3.3e Interest rates increase making it more expensive to borrow money. (note that coalconsumption tends to be more capital intensive than the consumption of other fossilfuels and that often such capital is ﬁnanced by borrowing money at the interest rate.Recent U.S. DOE data suggests that capital costs for cheaper coal plants are near 3000/kwh while for conventional gas they are nearer to 1000/kwh.) http://www.eia.gov/oiaf/beck plantcosts/Study Question 3.4 What do you predict would happen to price and quantity if both c and d inStudy Question 3.3 occurred? Support your answer with diagrams.Study Question 3.5 For the demand model in Study Question 3.2 after the price of thesubstitute changed, compute the demand elasticity at equilibrium P & Q with respect to (a)price, (b) income, and (c) price of a substitute. (d) Compute price elasticity of demand at a priceof 0, 20, 40, 60 and 80. (e) What happens to the elasticity as we move up the linear demandfunction? Compute the supply elasticity at equibrium P & Q with respect to (f) price, (g)priceof capital, and (h) price of a similar good. (i) Compute price elasticity of supply at a price of 0,20, 40, 60 and 80. (j) What happens to the elasticity as we move up the linear supply function?Study Question 3.6 South Africa coal consumption is about 140 million metric tonnes. If coalprice goes from 100 a tonne to 120 per tonn and the short run elasticity is -0.25, what wouldthe percentage change in coal consumption be? What would the change in coal consumptionbe? What would new coal consumption be? You can check your in answers ch03m.xlsx,worksheet HW0305.Study Question 3.7 Revenues and elasticity:3.7a Explain what happens to revenues for a price decrease with an elastic demand.

3.7b Explain what happens to revenues if price increases with inelastic demand, ( 1 εp 0).Study Question 3.8 Income elasticities can be used in the same way as price elasticities toshow how much product consumption will change when income changes. Suppose that inChina, the largest coal consumer, income elasticity of coal demand is 0.8, current coalconsumption is 2500 million tonnes, and income will grow at 5% per year.3.8a What would you forecast next year’s coal consumption to be?3.8b If the price elasticity is -0.7, what price increase would be required to offset theincome increase?Study Question 3.9 Cross-price elasticities:3.9a What does a negative cross price elasticity of demand imply? Give an energy example oftwo goods that might have a negative cross price elasticity of demand.3.9b What does a positive cross price elasticity of demand imply? Give an energy example oftwo goods that might have a positive cross price elasticity of demand.3.9c What does a negative cross price elasticity of supply imply? Give an energy example oftwo goods that might have a negative cross price elasticity of supply.3.9d What does a positive cross price elasticity of supply imply? Give an energy example oftwo goods that might have a positive cross price elasticity of supply.Study Question 3.10 Compute the price elasticities for the following functions:3.10a Q α βlnP δlnY3.10b. lnQ α βP δY3.10c Q exp(α βP δY )3.10d Q α βP δY γP YStudy Question 3.11 Create a log linear demand for coal demand in India if coal consumptionis 350 million tonnes, coal price is 100 per tonne, income is 4 trillion dollars, price ofimported LNG is 10/MCF, and price, income, and cross price elasticities are -0.2, 0.75, and 0.3.Study Question 3.12 Your task is to forecast carbon dioxide emissions coming from the consumption of coal, oil, and natural gas. You have used historical data and econometric techniques to estimate own price, cross price, and income elasticities for coal, oil, and natural gasdemand. Which are as tural Gas0.14-0.250.170.50Coal0.070.08-0.300.90You get 161 lbs of CO2 per million Btus of oil, 205 from coal, and 117 from natural gas.

with a minimal burden to the State’s own residents, especially if the taxed resources areexported to customers in other States. Based on the above discussion, do you agree or disagree?Study Question 4.9 Suppose that demand and supply of Chinese coal are𝑄𝑑 60 0.5𝑃.𝑄𝑠 2 2𝑃.4.9a What are equilibrium price and quantity in the Chinese coal market?4.9b What happens to price and quantity if a subsidy of 10 is paid on Chinese coal?4.9c What are the costs to the government of a subsidy?4.9d What are the gains in consumer surplus from the subsidy?4.9e What are the gains in producer surplus from the subsidy?4.9f What are the dead weight losses of the subsidy (Government cost - gain inproducer surplus minus gain in consumer surplus)?4.9g Show the costs, gains in consumer surplus, gains in producer surplus anddeadweight losses from a subsidy on a graph.

Study Question 4.10 Suppose the demand equation for shale gas is Qd 10P 1.8and the0.2supply equation Qs 2P.4.10a What is the price elasticity of demand?4.10b What is the price elasticity of supply?4.10c What is the incidence of a 2 tax?Chapter 5. Natural Monopoly and Electricity GenerationStudy Question 5.1 Suppose that a 500 megawatt hydro power plant including the dam hasupfront or overnight cost of 2500 per kilowatt of capacity.5.1a What is the total cost of building the plant?5.1b What is the maximum amount of electricity in kilowatt hours this plant couldproduce in 40 years if it could operate 24 hours a day, 365 days a year for 40 years?5.1c If capital is paid for upfront, it takes 2 years to build the plant, it then operates for40 years at 80% of capacity, and the interest rate is 10%, what is the levelized cost ofcapital? Assume all capital is paid for up-front at time 0, electricity is all paid for at theend of the year. Thus, payments start at the end of year 3 and commence for 40 years.5.1d How would your answer to 5.1c change if the half of the cost of the plant was paidat year 0 and the balance was paid at the end of the first year?Study Question 5.2 Suppose the electricity generation industry in a region has the followingdemand and cost curves:Q 40 – 0.5PTC 60Q - 0:6Q2Q is measured in megawatt hours, price is measured in dollars per megawatt hour, and totalcosts are measured in dollars.5.2a. What is the socially optimal price and quantity in this market? What are profits atthis level of price and quantity? (Remember to invert demand curve so you can set P MC.)5.2b. What are the economies of scale at the price and quantity in part a? (Checkwhether ATC/ Q 0 indicating diseconomies, economies, or constant economiesof scale. (Note: Industries with these properties can be called increasing, decreasing ofconstant cost industries.)5.2c. Should this market be treated as a natural monopoly? Why or Why not?5.2d. What would you expect to happen in this industry, if the industry was allowed todevelop with no interference? What would price and quantity be? Would there be sociallosses compared with case a? Why or why not? If there are social losses what wouldthey be?5.2e. What would happen if a 2 tax were places on electricity? Be sure to be able to dothis for a subsidy as well.

Study Question 5.3 Now suppose that this utility is connected to a power grid and people arefree to choose any supplier. Power can be wheeled for 17 dollars per megawatt hour. Thus, anybuyer would not buy from this utility if they charged a price higher than 17 dollars but wouldbuy off of the grid. This makes this utility's demand curve at 17 dollars and above but they facetheir downward sloping demand at prices below 17 dollars.5.3a D the utility's new demand curve?5.3b What is marginal revenue for the flat area of the demand curve?5.3c What is the marginal revenue curve for the downward sloping portion of theirdemand curve?5.3d What price and quantity would a profit maximizing monopoly choose?Study Question 5.4 Suppose you are on a state utility commission and you have to make adecision on a rate case for Power Galore Utility (PGU). The legally established rate of returnfor the utility is s 10%. PGU sells to two customer classes - residential and business - and isrequesting the following prices for each class in dollars per kilowatt hour ( /kWh). Theyestimate sales in each rate class to be Qi, their rate base is 750,000, they estimate fuel costs in /kWh to be ci and other operating costs in /kWh to be oi.PiQiciOiRBi 10.081,966,6670.020.03750,000i 20.05799,9990.020.015.4a Based on their request summarized in the table would you approve the rates requested?Why or why not?5.4b Now suppose you have hired an independent contractor to estimate the demand equationsfor the two customer classes.Q1 2; 000; 000 - 100; 000P1Q2 900; 000 - 100; 000P2From this new information, what would you predict to be electricity consumption in each rateclass at their requested rates (prices?5.4b Given all the information in parts a and b, would you approve their rate request?Why or why not?Study Question 5.5 Suppose stand alone costs in your market areCx 800 20XCy 700 40YIf one utility provides services to both customers, combined costs are:Cxy 1200 20X 40Y5.5a Are costs sub-additive for this example?5.5b If 75% of fixed costs are allocated to consumer class X and 25% to consumer class

Y, how much of the fixed costs would be charged to X and how much to Y?5.5c. Suppose you have marginal cost pricing. What is the marginal cost of producing aunit for X? a unit for Y?5.5d If you marginal cost price for X and Y and allocated costs as in b, what is the totalcost curve for X? What is the total cost curve for Y?5.5e. If you were a customer in group X would you feel the prices were discriminatory,why or why not? If you were a customer in group Y would you feel the prices werediscriminatory, why or why not?5.5f. If demand for group X were Px 92 - 3X and demand for group Y werePy 120-4Y, would the above fixed cost allocation be efficient?Study Question 5.6 Let off-peak demand be Qopk 10-2Popk, peak demand Qpk 20-Ppk, ck 4and co 2.5.6a What are the socially optimal prices in this market?5.6b How much electricity is consumed peak and off-peak?5.6c How much is consumed in each, market if a price of 5 is charged in each market?5.6d What are the social losses, if a price of 5 is charged in both peak and offpeak? (Toget loss compare the social welfare with optimal situation and remember to check thatutility is covering all of its costs)5.6e Suppose you have been charging 5 and are considering charging optimal peak loadprices for peak and offpeak. The costs to implement peak load pricing are 10 would itbe a good idea to implement peak load pricing or not? Why or why not?5.6f Would your answers to a and b change if capital costs were 6 instead of 4.Study Question 5.7 Suppose a utility owns a coal mine. It sells 100 tons of coal to itself peryear at 29 per ton and produces and sells 222,000 kilowatts of electricity at 0.06 per kilowatthour. Coal mining has a 10% Federal depletion allowance, which allows them to deduct 10% oftheir revenues for tax purposes. Deductible costs are shown in the example below. Taxableincome for the combined mine and utility are 2260 2420 4680.MineSales Revenue 29*100 Operating CostsDepreciation% depletion allowance (10%)Taxable income 2,900 300 50 290 2,260UtilitySales Revenue 0.06*222000 13,320

fuel cost 2,900other operating costs 5,000Depreciation 3,000Taxable income 2,4205.7a What happens to taxable income in the above example if the utility pays its mine 40 per ton?5.7b Explain why taxable income changes ?Chapter 6. Deregulation-Privatization Electricity SectorStudy Question 6.1 The table at http://dahl.mines.edu/T0604.xlsx contains information forcountries electricity sectors. Find one new country or update the information for one countrythat has or is privatizing its electrical sector and note the following information.6.1a Indicate when the privatization was initiated.6.1b Try to determine which of the models from Shuttleworth and Hunt the new modelmost closely resembles.6.1c What sort of dispatch is being used or considered?Study Question 6.2 Many countries are opening up their power sectors to private investmentleading to a boom in electricity projects. The table at http://dahl.mines.edu/T0605.xlsxcontains information for some such projects. Find another example of one such recent project.Note the location, cost, capacity, construction time, completion/expected completio date, andreference. Study Question 6.3 What is the maximum possible efficiency of a light waterreactor that inputs steam at 1000 degrees F and outputs cooling water at 100 degrees F?Read the technology box at http://dahl.mines.edu/tech0501.pdf to answer this question.Input temp1000 F1Output temp100 F2T1 in K 5/9(F1-32) 273 810.7778T2 in K 5/9(F2-32) 273 310.7778Efficiency 1-T2/T1 0.616692Study Question 6.4 A typical 1000 MW light water reactor creates about 3 cubic meters ofwaste every three years. Compute what this implies about how much nuclear waste the averageAmerican who receives all their electricity from nuclear power would generate in 70 years with

and without reprocessing. Indicate all the assumptions you have to make to do yourcomputation.Study Question 6.5 A trade organization for the US electric power industry is the EdisonElectric Institute at www.eei.org. Go to this address and find out what companies belong to thistrade group. Try to find 10 other electricity links.Study Question 6.6 Suppose that during a peak period forecasted demand is 150 and the bidsfrom the original 5 bidders isNational Power bids 0.06 per kWh for 80 kWPower Gen bids 0.065 per kWh for 30 kWScottish Power bids 0.07 per kWh for 50 kWEdF bids 0.075 per kWh for 10 kWNational Grid bids 0.08 per kWh for 50 kWThere is the same transmission constraint of 65 kW from National Power to market.6.6aWhat is SMP for this set of bids? What are the dispatch orders.6.6b Suppose for the next hour, there is a 5% probability of a 10 kW short fall and a 1%probability of a 15 kW short fall. The loss of output from a 10 kW shortfall is estimatedat 15, and the loss of output from a 15 kW shortfall is estimated at 25. What is CC forthis market?6.6c Assume the power dispatched in 5.6a is the amount taken. If 20 of spinningreserve was dispatched but not taken, what is the uplift charge per kWh dispatched.6.6d What is the pool selling price?Study Question 6.7 Regulated utilities that must charge average rather than marginal costssometimes undertake demand side management programs to reduce peak loads and improveload factors. Such activities include free energy audits to advise customers on how to reduceloads, information on energy saving possibilities, loans, subsidies and rebates for energyefficient lighting, appliances and motors.6.7a Explain why a utility would encourage customers to consume less electricity underaverage cost pricing, particularly during peak periods?6.7b What do you think will happen to demand side management programs if a utility isderegulated and moves to marginal cost pricing?Study Question 6.8 If the market interest rate on a bond of similar risk is 8% and the bondholders marginal tax rate is 25%, what interest rate would you expect the tax free bond to pay?Why?Study Question 6.9 Hunt and Shuttleworth present four different models for the electricitysector. Briefly compare and contrast the four models.Study Question 6.10 California's electricity restructuring in the late 1990's and early 2000'swent radically wrong. Outline what happened in the California's market at that time. Indicatewhat you think was the biggest policy mistake the regulators made and suggest a better policy.

Study Question 6.11 The text includes deregulation experiences for 4 countries. Compare andcontrast these four experiences. Be sure to include which model from Hunt and Shuttlewortheach country has as its goal, the type of price regulation if any they are most in favor of, whichsegments of the industry are allowed to compete and which segments are still regulated and thetype of ownership.Chapter 7. Monopoly, Dominant Firm and OPECStudy Question 7.1 Many countries have antimonopoly laws as shown athttp://dahl.mines.edu/T07?. Check information for 1 country in the Table and see if you canfind information for one country not in the Table.Study Question 7.2 Suppose that MC 12 and the demand price elasticity equals -1.8.The monopoly pricing result is P MC/(1-1/ εp )7.2a Using the above expression, what price should the monopolist charge?7.2b If MC goes up what will happen to optimal price?7.2c If the demand becomes more elastic and changes to -2.5, what happens to optimalprice?7.2d Why does the pricing equation imply that the monopolist must be operating in theelastic region of a linear demand curve? (i.e. Where 𝜀𝑝 1 or 𝜀𝑝 1.)Study Question 7.3 Let marginal costs for two OPEC countries be:MC1 5 Q1MC2 5 4Q27.3a What would OPEC price and quantity be, if OPEC inverse demand is P 100-2Q?7.3b How much would each OPEC country produce (Qi)?7.3c What are profits for each OPEC country (pi)?7.3d What are total social losses (DWL)?7.3e What happens if a unit tax of 20 is placed on the supplier to P, Qo, Q1, Q2, p1, p2,DWL.7.3f If the producing country, which adds the tax only sells oil, and the consumingcountry only buys oil is the producing country better off with or without the tax? (Hintdoes the producer country get enough tax revenue to more than offset the loss inproducer surplus.)7.3g What if the consuming instead of the producing country puts on a tax? Is theconsuming country better off with or without the tax?7.3h How much would the monopolist produce if a price control of 80 wereimplemented in case 7.3a (no taxes)?7.3i Can you find a price control for which the monopolist would produce less than incase 7.3a (no taxes)?

7.3j If OPEC started to squabble and the industry became competitive, what wouldhappen to price and quantity for case 7.3a (no price controls of taxes)?Study Question 7.4With an ad valorem tax, profits for the monopoly become:π (1 ta ) p(Q )Q TC (Q )First order conditions are:(1 ta ) MR MC 0Suppose Qd 100 -2PdTC 10Q Q27.4a Show the monopolists optimal price and quantity on a graph.7.4b Solve for the optimal P and Q using the above demand and cost functions.7.4c Does this policy get us to the socially optimal Q?7.5 Two other taxes are a profit tax, 𝑡𝜋 , and a lump sum tax (𝑇). The after tax profit for thesetaxes are as follows:π tπ (1 tπ )( PQ TC (Q ))πT PQ TC (Q ) T𝑑𝜋7.5a. What would be the first order conditions (𝑑𝑄) for each of these functions? Whatare second order conditions? For the lump sum tax π T TC (Q ) P 0 Q Q7.5b. Use the implicit function on the first order condition to show that the tax has noeffect on output in these two cases. π tπ(e.g. use QdQ tπdQto show that 0 π tπdtπdt Q Q TC (Q ) 1( P )dQ( 1)0 Q 02 TC (Q ) sign of slope of MC (usually )dtπ(1 tπ ) Q 2For the tax to not kill the industry (1-tπ) 0. The numerator ( P TC) in the above Q

expression must be 0.For the lump sum tax T,dQ00 02dT TC (Q ) sign of slope of MC (usually ) Q 27.5c. Explain intuitively why these taxes have no effect on output.Study Question 7.6 Now OPEC is a dominant firm facing the demand and costs information in7.3 along with a competitive fringe.7.6a Let fringe supply be Qf -17.5 0.5P. Solve for Qo, Qf, Q1, Q2, P, πo, πf, π1, π2.7.6b Let fringe supply be Qf -37.5 0.5P. Solve for Qo, Qf, Q1, Q2, P, πo, πf, π1, π2.7.6c Let fringe supply be Qf -50 0.5P. Solve for Qo, Qf, Q1, Q2, P, πo, πf, π1, π2.7.6d Compare the solution for the dominant firm model in 7.6a to a competitivesolution. Remember that in a competitive model MC would be the horizontal sum ofOPEC plus the fringe and they would face total world demand. Solve for Qo, Qf, Q1, Q2,P, πo, πf, π1, π2.7.6e For a competitive model for case 7.6a. solve for Qo, Qf, Q1, Q2, P, πo, πf, π1, π2.7.6f Did OPEC or the fringe gain more from OPEC acting as a dominant firm in 7.6acompared to 7.6e?Study Question 7.7 Suppose at optimal output 𝜀𝑤 0.8, 𝜀𝑓 0.3, 𝑄𝑤 67.5, 𝑄𝑜 27.5, 𝑄𝑓 40.7.7a What is the price elasticity of demand for OPEC’s oil?7.7b What happens to the price elasticity of the demand for OPEC’s oil as the world’sdemand gets more price elastic? Why?7.7c What happens to the price elasticity of demand for OPEC’s oil as the fringe supplygets more price elastic? Why?7.7d What happens to the price elasticity of demand for OPEC’s oil, if OPEC’sproduction is a higher percent of world production. Why?7.7e If MC 8, what price should OPEC charge?Study Question 7.8 Suppose inverse export demand for OPEC is Px 53 -4Qx, marginal costis MC 5 (Qx Qd) and inverse domestic demand is Pd 20 – 10Qd. OPEC wants to maximizethe benefits its gets from its oil reserves.7.8a How much will OPEC sell on the domestic and on the export market?7.8b What price will is charge in the domestic and export markets.Study Question 7.9 Daniel Yergin has written a Pullitzer Prize winning book on the history ofthe oil industry. PBS has a nice eight part series based on the book now on youtube. Watch oneepisode of The Prize. For your chosen episode make up and answer one question. Your

(d) Compute price elasticity of demand at a price of 0, 20, 40, 60 and 80. (e) What happens to the elasticity as we move up the linear demand function? Compute the supply elasticity at equibrium P & Q with respect to (f) price, (g)price of capital, and (h) price of a similar good. (i) Compute price elasticity of supply at a price of 0,

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