1. 1 Civil Systems Planning Benefit/Cost Analysis Scott Matthews Courses: 12-706 and 73-359 Lecture 3 - 9/4/2002

2. 12-706 and 73-3592 What about Other Goals, non- Efficiency?  Multigoal Analysis  Economic performance  Social performance  Environmental performance  Technological performance  Flexibility  We’ll come back to this later in course

3. 12-706 and 73-3593 Welfare Economics Concepts  Perfect Competition  Homogeneous goods.  No agent affects prices.  Perfect information.  No transaction costs /entry issues  No transportation costs.  No externalities:  Private benefits = social benefits.  Private costs = social costs.

4. 12-706 and 73-3594 Demand Curves  Downward Sloping is a result of diminishing marginal utility of each additional unit. Price Quantity P* 0 1 2 3 4 Q* A B

5. 12-706 and 73-3595 Social WTP Price Quantity P* 0 1 2 3 4 Q* A B  An ‘aggregate’ demand function: how all potential consumers in society value the good or service (i.e. there is someone willing to pay every price…)

6. 12-706 and 73-3596 Gross Benefits Price Quantity P* 0 1 2 3 4 Q* A B  Benefits received are related to WTP - and equal to the shaded rectangles  Approximated by whole area under demand: triangle AP*B + rectangle 0P*BQ* P1

7. 12-706 and 73-3597 Gross Benefits with WTP Price Quantity P* 0 1 2 3 4 Q* A B  Total/Gross Benefits = area under curve or willingness to pay for all people = Social WTP = their benefit from consuming

8. 12-706 and 73-3598 Price Quantity P* 0 1 2 3 4 Q* A B A “price discriminator” could collect A0Q*B for output level Q*. But only one price is charged in the market, so consumers pay P*0Q*B. Price Discrimination

9. 12-706 and 73-3599 Net Benefits Price Quantity P* 0 1 2 3 4 Q* A B A B  Amount ‘paid’ by society at Q* is P*, so the total payment is B to get A+B benefit  Net benefits = (A+B) - B = A = consumer surplus (benefit received - price paid)

10. 12-706 and 73-35910 Consumer Surplus Changes Price Quantity P* 0 1 2 Q* Q1 A B P1 CS1  New graph  Assume CS1 is the original consumer surplus at P*, Q*

11. 12-706 and 73-35911 Consumer Surplus Changes Price Quantity P* 0 1 2 Q* Q1 A B P1 CS2  CS2 is the new consumer surplus when price decreases to (P1, Q1)  Change in CS = Trapezoid P*ABP1 = gain = positive net benefits

12. 12-706 and 73-35912 Consumer Surplus Changes Price Quantity P* 0 1 2 Q* Q1 A B P1 CS2  Same thing in reverse. If original price is P1, then increase price moves back to CS1

13. 12-706 and 73-35913 Consumer Surplus Changes Price Quantity P* 0 1 2 Q* Q1 A B P1 CS1  If original price is P1, then increase price moves back to CS1 - Trapezoid is loss in CS, negative net benefit

14. 12-706 and 73-35914 Further Analysis  Assume price increase is because of tax  Tax is P*-P1 per unit, revenue (P*-P1)Q*  Is a transfer from consumers to gov’t  To society, no effect (we get taxes back)  Pay taxes to gov’t, get same amount back  But we only get yellow part.. Price Quantity P* 0 1 2 Q* Q1 A B P1 CS1

15. 12-706 and 73-35915 Deadweight Loss  Yellow paid to gov’t as tax  Green is pure cost (no offsetting benefit)  Called deadweight loss  Consumers buy less than they would w/o tax (exceeds some people’s WTP!)  There will always be DWL when tax imposed Price Quantity P* 0 1 2 Q* Q1 A B P1 CS1

16. 12-706 and 73-35916 Market Demand Price P* 0 1 2 3 4 Q A B  If the above graphs show the two groups of consumers’ demands, what is social demand curve? P* 0 1 2 3 4 5 Q A B

17. 12-706 and 73-35917 Market Demand  Found by calculating the horizontal sum of individual demand curves  Market demand then measures ‘total consumer surplus of entire market’ P* 0 1 2 3 4 5 6 7 8 9 Q

18. 12-706 and 73-35918 Commentary  It is trivial to do this math when demand curves, preferences, etc. are known. Without this information we have big problems.  Unfortunately, most of the ‘hard problems’ out there have unknown demand functions. Thus the advanced methods in this course

19. 12-706 and 73-35919 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.  = (p  q) / (q  p)

20. 12-706 and 73-35920 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

21. 12-706 and 73-35921 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

22. 12-706 and 73-35922 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

23. 12-706 and 73-35923 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 riders at average fare of $ 1.20. Estimate Total Willingness to Pay.

24. 12-706 and 73-35924 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 = -0.0002 or 2.0 x 10^-4

25. 12-706 and 73-35925 Demand Example (cont)  Maglev Demand Function:  p = 5.2 - 0.0002*q  Revenue: 1.2*20,000 = $ 24,000 per day  TWtP = Revenue + Consumer Surplus  TWtP = pq + (a-p)q/2 = 1.2*20,000 + (5.2- 1.2)*20,000/2 = 24,000 + 40,000 = $ 64,000 per day.

26. 12-706 and 73-35926 Change in Fare to $ 1.00  From demand curve: 1.0 = 5.2 - 0.0002q, so q becomes 21,000.  Using elasticity: 16.7% fare change (1.2- 1/1.2), so q would change by -0.3*16.7 = 5.001% to 21,002 - slightly different result.  Change to TWtP = (21,000-20,000)*1 + (1.2-1)*(21,000-20,000)/2 = 1,100.  Change to Revenue = 1*21,000 - 1.2*20,000 = 21,000 - 24,000 = -3,000.

27. 12-706 and 73-35927 Estimating Linear Demand Functions zOrdinary least squares regression used yminimize the sum of squared deviations between estimated line and observations- p = a + bq + e yStandard algorithms to compute parameter estimates - spreadsheets, Minitab, S, etc. yEstimates of uncertainty of estimates are obtained (based upon assumption of identically normally distributed error terms). zUse Excel/other software to do the hard work zCan have multiple linear terms.

28. 12-706 and 73-35928 User cost versus Price zSome circumstances - better to estimate demand function and willingness-to-pay versus user cost rather than just price. zPrice is only one component of user cost. zClassic example: travel demand, in which travel time is major user cost. zSecond example: equipment requirements, such as computers for AOL.

29. 12-706 and 73-35929 User Cost Versus Price zFor travel, can define demand function and performance functions with respect to travel time. zAlternative: can value all aspects of user cost in $ amounts. For example, what is value of time for congestion delays?

30. 12-706 and 73-35930 Log-linear Function zq = a(p) b (hh) c ….. zConditions: a positive, b negative, c positive,... zIf q = a(p) b : Elasticity interesting = (dq/dp)*(p/q) = abp (b-1) *(p/q) = b*(ap b /ap b ) = b. yconstant elasticity at all points. zEasiest way to estimate: linearize and use ordinary least squares regression

31. 12-706 and 73-35931 Log-linear Function  q = a*p^b and taking log of each side gives: ln q = ln a + b ln p which can be re-written as q’ = a’ + b p’, linear in the parameters and amenable to ols regression.  This violates error term assumptions of OLS regression.  Alternative is maximum likelihood - select parameters to max. chance of seeing obs.

32. 12-706 and 73-35932 Maglev Log-Linear Function  Q = ap^b. From above, b = -0.3, so if p = 1.2 and q = 20,000, then 20,000 = a*(1.2)^-0.3 and a = 21,124.  If p becomes 1.0 then q = 21,124*(1)^-0.3 = 21,124.  Linear model - 21,000

33. 12-706 and 73-35933 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

34. 12-706 and 73-35934 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

35. 12-706 and 73-35935 Commentary - Externalities zExternal costs SHOULD be included zMeasurement difficult, maybe impossible zTypically no market transactions to use zProxy: cost of eliminating hazard created zBeware transfers / double counting! zExample: Construction disrupts commerce ybusiness not lost - just relocated in interim

36. 12-706 and 73-35936 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