1 Civil Systems Planning Benefit/Cost Analysis Scott Matthews /19-702

and Discussion - “willingness to pay”  Survey of students of WTP for beer  How much for 1 beer? 2 beers? Etc.  Does similar form hold for all goods?  What types of goods different?  Economists also refer to this as demand

and (Individual) Demand Curves  Downward Sloping is a result of diminishing marginal utility of each additional unit (also consider as WTP)  Presumes that at some point you have enough to make you happy and do not value additional units Price Quantity P* Q* A B Actually an inverse demand curve (where P = f(Q) instead).

and Market Demand Price P* Q A B  If above graphs show two (groups of) consumer demands, what is social demand curve? P* Q A B

and Market Demand  Found by calculating the horizontal sum of individual demand curves  Market demand then measures ‘total consumer surplus of entire market’ P* Q

and Social WTP (i.e. market demand) Price Quantity P* Q* A B  ‘Aggregate’ demand function: how all potential consumers in society value the good or service (i.e., someone willing to pay every price…)  This is the kind of demand curves we care about

and Demand Curve Shifts  Difference between change in demand and change in quantity demanded  Change in just the price, all else equal, will just move along same demand curve  If other things change, eg preferences for eating meat, demand curve shifts.  Could also happen from income changes, etc.

and First: Elasticities of Demand  Measurement of how “responsive” demand is to some change in price or income.  Slope of demand curve =  p/  q.  Elasticity of demand, , is defined to be the percent change in quantity divided by the percent change in price.

and Elasticities of Demand Elastic demand:  > 1. If P inc. by 1%, demand dec. by more than 1%. Unit elasticity:  = 1. If P inc. by 1%, demand dec. by 1%. Inelastic demand:  < 1 If P inc. by 1%, demand dec. by less than 1%. Q P Q P

and Elasticities of Demand Q P Q P Perfectly Inelastic Perfectly Elastic A change in price causes Demand to go to zero (no easy examples) Necessities, demand is Completely insensitive To price

and Elasticity - Some Formulas  Point elasticity = dq/dp * (p/q)  For linear curve, q = (p-a)/b so dq/dp = 1/b  Linear curve point elasticity =(1/b) *p/q = (1/b)*(a+bq)/q =(a/bq) + 1

and Sorta Timely Analysis zHow sensitive is gasoline demand to price changes? zHistorically, we have seen relatively little change in demand. Recently? zNew AAA report: higher gasoline prices have caused a 3 percent reduction in demand from a year ago.  What was  p?  q?  ? zWhat does that tell us about gasoline?

and Maglev System Example  Maglev - downtown, tech center, UPMC, CMU  20,000 riders per day forecast by developers.  Let’s assume:  price elasticity -0.3;  linear demand;  20,000 average fare of $  Estimate Total Willingness to Pay.

and Example calculations  We have one point on demand curve:  1.2 = a + b*(20,000)  We know an elasticity value:  elasticity for linear curve = 1 + a/bq  -0.3 = 1 + a/b*(20,000)  Solve with two simultaneous equations:  a = 5.2  b = or 2.0 x 10^-4

and Types of Costs zPrivate - paid by consumers zSocial - paid by all of society zOpportunity - cost of foregone options zFixed - do not vary with usage zVariable - vary directly with usage zExternal - imposed by users on non-users ye.g. traffic, pollution, health risks yPrivate decisions usually ignore external

and Making Cost Functions zFundamental to analysis and policies zThree stages: y Technical knowledge of alternatives y Apply input (material) prices to options y Relate price to cost zObvious need for engineering/economics zMain point: consider cost of all parties zIncluded: labor, materials, hazard costs

and Functional Forms  TC(q) = F+ VC(q)  Use TC eq’n to generate unit costs  Average Total: ATC = TC/q  Variable: AVC = VC/q  Marginal: MC =  [TC]/  q =  TC  q  but  F/  q = 0, so MC =  [VC]/  q

and Short Run vs. Long Run Cost  Short term / short run - some costs fixed  In long run, “all costs variable”  Difference is in ‘degree of control of plans’  Generally say we are ‘constrained in the short run but not the long run’  So TC(q) < = SRTC(q)

and From Cost to Supply  Given knowledge of costs to produce, producers decide how much to produce  As price to sell at increases, incentivizes producers to make more  Also leads to more opportunities/methods to pay costs required to produce  (e.g., we would mine a lot more coal if the price were $100 rather than $20 a ton)

and BCA Part 2: Cost Welfare Economics Continued The upper segment of a firm’s marginal cost curve corresponds to the firm’s SR supply curve. Again, diminishing returns occur. Quantity Price Supply=MC At any given price, determines how much output to produce to maximize profit AVC

and Supply/Marginal Cost Notes Quantity Price Supply=MC At any given price, determines how much output to produce to maximize profit P* Q1 Q* Q2 Demand: WTP for each additional unit Supply: cost incurred for each additional unit

and Supply/Marginal Cost Notes Quantity Price Supply=MC Area under MC is TVC - why? P* Q1 Q* Q2 Recall: We always want to be considering opportunity costs (total asset value to society) and not accounting costs

and Firm Production Functions MC Q P What do marginal, Average cost curves Tell us? AVC Variable cost shows Non-fixed components Of producing the good Marginal costs show us Cost of producing one Additional good Where would firm produce?

and Unifying Cost and Supply  Economists learn “Supply and Demand”  Equilibrium (meeting point): where S = D  In our case, substitute ‘cost’ for supply  Why cost? Need to trade-off Demand  Using MC is a standard method  Recall this is a perfectly competitive world!

and Example  Demand Function: p = 4 - 3q  Supply function: p = 1.5q  Assume equilibrium, what is p,q?  In eq: S=D; 4-3q=1.5q ; 4.5q=4 ; q=8/9  P=1.5q=(3/2)*(8/9)= 4/3