MIT Civil Engineering 1.011 -- Project Evaluation Spring Term 2003Carl D. Martland Page 11.011 Project EvaluationCost & Revenue FunctionsTopicsBreakeven volume for making a profit (if prices are known and you are a "price taker")Identifying a range of prices for which you can make a profit (assuming that demand varies with price)Choosing prices to maximizing profitSupply/demand/equilibrium - an overviewPresent economyConditions for Profitability-Simple Linear Cost & Revenue Functions Cost = a + bV Price = P Revenue = PV Profit = PV - a - bV = (P-b)V - aBreakeven Volume = a/(P-b)Conditions for Positive Profits:Price > variable costVolume greater than breakeven volume Breakeven Volume for ProfitabilityBreakeven point P is where TR = TCRevenue = 1.5 V TC = 50 + V P10 20 30 40 50 60 70 80 90 100 110 120Volume050100150200CostTotal Cost RevenueProfitsLossIn General, Volume Varies With Price:The lower the price, the higher the volumeVolume0250PriceTotal Revenue Also Varies With Price:Revenue Declines if Price is Too High or Too Low1234567891011121314Volume (Demand) for the Given Price0500Price or RevenueRevenuePrice1234567891011121314Volume (Demand) for the Given Price0500$RevenueCostMaximizing Profit is not the Same asMaximizing RevenueMax Profit Max RevenueMIT Civil Engineering 1.011 -- Project Evaluation Spring Term 2003Carl D. Martland Page 2Maximizing Profit is not the Same as Maximizing RevenueMax Profit When V = 3Max Revenue When V = 41234567891911121314Volume (Demand) for the Given Price0100200300400500$RevenueCostProfitA Company Will Produce Only if its Expected Market Share Will Allow It to Make a Profit for Some Range of Prices1234567891011121314Volume (Demand) for the Given Price0500$RevenueCostPotentially ProfitableIf costs are very high, then a company will be unable to make a profit for any range of pricesCostRevenue1234567891011121314Volume (Demand) for the Given Price01000$RevenueCostTotal cost always exceeds total revenuePrices Reflect an Equilibrium Between Supply and DemandDemandSupply 1 2 3 4 5 6 7 8 9 10 11 12 13 14Volume (Demand or Supply for the Given Price)0PriceSupply DemandEquil. PriceInvestment may allow suppliers to offer lower prices,increasing volume (a movement along the demand curve)New SupplyDemandSupply 1234567891011121314Volume (Demand or Supply for the Given Price)0PriceSupply DemandNew SupplyNew Equilibrium PricePopulation Growth, Advertising, Higher Incomes, or other Factors May Cause an Increase in Demand(a shift in the demand curve) New DemandSupply 1234567891011121314Volume (Demand or Supply for the Given Price)0500PriceSupply DemandNew DemandEquil. PriceMIT Civil Engineering 1.011 -- Project Evaluation Spring Term 2003Carl D. Martland Page 3How Does the Equilibration Work?If demand increases, and there isn't enough supply, then prices rise (or, in the case of some types of infrastructure, congestion and service delays get worse)If prices rise, then suppliers make more profits and are willing to increase productionIf production increases, then there may be some producers willing to cut prices to get more market share If demand declines, then prices drop and inefficient producers leave the businessPrices Reflect an Equilibrium Between Supply and Demand1234567891011121314Volume (Demand or Supply for the Given Price)0PriceSupply DemandWe probably only know a little about supply & demand"Present" EconomyA "present economy" study seeks to change the supply function by improving the production capabilities of the organizationThe term "Present" is used to indicate that we don't have to worry about expenditures over a long time horizonAll costs and revenues are therefore in the same "current" dollars With a better supply function, we may be able to underprice competitors or create a new, profitable serviceCost Driven OptimizationA basic design question may arise when some costs vary directly and others vary inversely with a particular, important design parameter (which is known as a "cost driver")Example 2-9 in Eng. Economy:How fast should a scheduled aircraft fly?Time is inversely proportional to speedCost increases with speed raised to the 3/2 powerCreate an equation of total cost (actually, just consider the costs that vary with speed)Use calculus to find the optimumHow Fast to Fly?Cost Operations = k v 1.5, where v is speed in mph = $300/mile @ 400 mph so that k = $300/(4001.5) = $0.0375If passenger time is $300,000/hr, then Pax time cost/flight = $300,000 (miles/v)TC = $0.0375(miles)v1.5+ 300,000 (miles/v)d(TC)/dv = 0 when 1.5 (0.0375) v0.5= 300,000/v2V* = 491 mph How Fast to Fly?We are willing to spend more money to fly faster so long as the incremental value of time saved (and therefore the incremental price that we can charge the passengers) is higher)We can express our result as an equation:v* = [(Pax Time Value/hr)/k]2/5MIT Civil Engineering 1.011 -- Project Evaluation Spring Term 2003Carl D. Martland Page 4Complicating Factors for ProjectsLong livesDemand can change substantiallyCompetition from other suppliers and new technologies can be expectedThe time value of money becomes criticalExternalities are important Unique projectsDifficult to test supply & demand Equilibration takes place through what may be slowly evolving changes in land use and location decisions by firms and
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