1. 1 Civil Systems Planning Benefit/Cost Analysis Scott Matthews 12-706/19-702 / 73-359 Lecture 7

2. 12-706 and 73-3592 Efficiency Definitions/Metrics  Allocative - resources are used at highest value possible  But welfare economics uses another:  An allocation of goods is Pareto efficient if no alternative allocation can make at least one person better off without making anyone else worse off.  Inefficient if can re-allocate to make better without making anyone else worse  Assumed that decisions made with this in mind?

3. 12-706 and 73-3593 A Pareto Example  Try splitting $ between 2 people  Get total ($100) if agree on how to split  No agreement, each gets only $25  Pareto efficiency assumptions:  More is better than less  Resources are scarce  Initial allocation matters

4. 12-706 and 73-3594 $100 0 Given this graph, how can We describe the ‘set of all Possible splits between 2 people That allocates the entire $100? ?

5. 12-706 and 73-3595 $100 0 Line is the ‘set of all possible splits that allocates the entire $100, Also called the potential pareto frontier. Is the line pareto efficient?

6. 12-706 and 73-3596 $100 0 No. Could at least get the ‘status quo’ result of (25,25) if they do not agree on splitting. So neither person would accept a split giving them less than $25. Is status quo pareto efficient? $25

7. 12-706 and 73-3597 $100 0 No. They could agree on splits of (25, 30) or (30, 25) if they wanted to - all the way to (25,75) or (75,25). All would be pareto improvements. Which are pareto efficient? $25 $75

8. 12-706 and 73-3598 $100 0 The ‘pareto frontier’ is the set of allocations that are pareto efficent. Try improving on (25,75) or (50,50) or (75,25)… We said initial alloc. mattered - e.g. (100,0)? $25

9. 12-706 and 73-3599 Pareto Efficiency and CBA  If a policy has NB > 0, then it is possible to transfer value to make some party better off without making another worse off.  To fully appreciate this, we need to understand willingness to pay and opportunity cost in light of CBA.

10. 12-706 and 73-35910 Willingness to Pay  Example: how much would everyone pay to build a mall ‘in middle of class’  Near middle may not want traffic costs  Further away might enjoy benefits  Ask questions to find indifference pts.  Relative to status quo (no mall)  E.g. middle WTP -$2 M, edges +$3 M  Edges could ‘pay off’ middle to build  Only works if Net Benefits positive!

11. 12-706 and 73-35911 Opportunity Cost  Def: The opportunity cost of using an input to implement a policy is its value in its best alternative use.  Measures value society must give up  What if mall costs $2 M?  Total net WTP = $1M, costs $2M  Not enough benefits to pay opp. cost  Can’t make side payments to do it

12. 12-706 and 73-35912 Wrap Up  As long as benefits found by WTP and costs by OC then sign of net benefits indicated whether side payments can make pareto improvements  Kaldor-Hicks criterion  A policy should be adopted if and only if gainers could fully compensate losers and still be better off  Potential Pareto Efficiency (line on Fig 2.1)

13. 12-706 and 73-35913 Three Legs to Stand On  Pareto Efficiency  Make some better / make none worse  Kaldor-Hicks  Program adopted (NB > 0) if winners COULD compensate losers, still be better  Fundamental Principle of CBA  Amongst choices, select option with highest ‘net’ benefit

14. 12-706 and 73-35914 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.

15. 12-706 and 73-35915 Discussion - WTP  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

16. 12-706 and 73-35916 (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* 0 1 2 3 4 Q* A B Actually an inverse demand curve (where P = f(Q) instead).

17. 12-706 and 73-35917 Market Demand Price P* 0 1 2 3 4 Q A B  If above graphs show two (groups of) consumer demands, what is social demand curve? P* 0 1 2 3 4 5 Q A B

18. 12-706 and 73-35918 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

19. 12-706 and 73-35919 Social WTP (i.e. market demand) Price Quantity P* 0 1 2 3 4 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

20. 12-706 and 73-35920 Total/Gross/User Benefits Price Quantity P* 0 1 2 3 4 Q* A B  Benefits received are related to WTP - and approximated by the shaded rectangles  Approximated by whole area under demand: triangle AP*B + rectangle 0P*BQ* P1

21. 12-706 and 73-35921 Benefits with WTP Price Quantity P* 0 1 2 3 4 Q* A B  Total/Gross/User Benefits = area under curve or willingness to pay for all people = Social WTP = their benefit from consuming = sum of all WTP values  Receive benefits from consuming this much regardless of how much they pay to get it

22. 12-706 and 73-35922 Net Benefits Price Quantity P* 0 1 2 3 4 Q* A B A B  Amount ‘paid’ by society at Q* is P*, so total payment is B to receive (A+B) total benefit  Net benefits = (A+B) - B = A = consumer surplus (benefit received - price paid)

23. 12-706 and 73-35923 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.  = (p  q) / (q  p)

24. 12-706 and 73-35924 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

25. 12-706 and 73-35925 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

26. 12-706 and 73-35926 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

27. 12-706 and 73-35927 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.

28. 12-706 and 73-35928 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

29. 12-706 and 73-35929 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.

30. 12-706 and 73-35930 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 value)  Change to Revenue = 1*21,000 - 1.2*20,000 = 21,000 - 24,000 = -3,000.  Change CS = 0.5*(0.2)*(20,000+21,000)= 4,100  Change to TWtP = (21,000-20,000)*1 + (1.2-1)*(21,000- 20,000)/2 = 1,100.

31. 12-706 and 73-35931 Estimating Linear Demand Functions zAs above, sometimes we don’t know demand zFocus on demand (care more about CS) but can use similar methods to estimate costs (supply) zOrdinary least squares regression used yminimize the sum of squared deviations between estimated line and p,q 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). zCan have multiple linear terms

32. 12-706 and 73-35932 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 (see Chap 12) yE.g., ln q = ln a + b ln(p) + c ln(hh)..

33. 12-706 and 73-35933 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.

34. 12-706 and 73-35934 Maglev Log-Linear Function  q = a*p b - From above, b = -0.3, so if p = 1.2 and q = 20,000; so 20,000 = a*(1.2) -0.3 ; a = 21,124.  If p becomes 1.0 then q = 21,124*(1) -0.3 = 21,124.  Linear model - 21,000  Remaining revenue, TWtP values similar but NOT EQUAL.

35. 12-706 and 73-35935 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

36. 12-706 and 73-35936 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

37. 12-706 and 73-35937 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

38. 12-706 and 73-35938 Monopoly - the real game  One producer of good w/o substitute  Not example of perfect comp!  Deviation that results in DWL  There tend to be barriers to entry  Monopolist is a price setter not taker  Monopolist is only firm in market  Thus it can set prices based on output

39. 12-706 and 73-35939 Monopoly - the real game (2)  Could have shown that in perf. comp. Profit maximized where p=MR=MC (why?)  Same is true for a monopolist -> she can make the most money where additional revenue = added cost  But unlike perf comp, p not equal to MR

40. 12-706 and 73-35940 Monopoly Analysis MR D MC Qc Pc In perfect competition, Equilibrium was at (Pc,Qc) - where S=D. But a monopolist has a Function of MR that Does not equal Demand So where does he supply?

41. 12-706 and 73-35941 Monopoly Analysis (cont.) MR D MC Qc Pc Monopolist supplies where MR=MC for quantity to max. profits (at Qm) But at Qm, consumers are willing to pay Pm! What is social surplus, Is it maximized? Qm Pm

42. 12-706 and 73-35942 Monopoly Analysis (cont.) MR D MC Qc Pc What is social surplus? Orange = CS Yellow = PS (bigger!) Grey = DWL (from not Producing at Pc,Qc) thus Soc. Surplus is not maximized Breaking monopoly Would transfer DWL to Social Surplus Qm Pm

43. 12-706 and 73-35943 Natural Monopoly  Fixed costs very large relative to variable costs  Ex: public utilities (gas, power, water)  Average costs high at low output  AC usually higher than MC  One firm can provide good or service cheaper than 2+ firms  In this case, government allows monopoly but usually regulates it

44. 12-706 and 73-35944 Natural Monopoly MR D Q* P* Faced with these curves Normal monop would Produce at Qm and Charge Pm. We would have same Social surplus. But natural monopolies Are regulated. What are options? Qm Pm MC AC a b c d e

45. 12-706 and 73-35945 Natural Monopoly MR D Q* P* Forcing the price P* Means that the social surplus is increased. DWL decreases from abc to dec Society gains adeb Qm Pm MC AC a b c d e Q0

46. 12-706 and 73-35946 Monopoly  Other options - set P = MC  But then the firm loses money  Subsidies needed to keep in business  Give away good for free (e.g. road)  Free rider problems  Also new deadweight loss from cost exceeding WTP

47. 12-706 and 73-35947 Pricing Strategies  Highway pricing  If price set equal to AC (which is assumed to be TC/q then at q, total costs covered  p ~ AVC: manages usage of highway  p = f(fares, fees, travel times, discomfort)  Price increase=> less users (BCA)  MC pricing: more users, higher price  What about social/external costs?  Might want to set p=MSC