Civil Systems Planning Benefit/Cost Analysis Scott Matthews 12-706 / 19-702

Admin Issues Please try to install Decision Tools Suite ASAP (in case there are problems) Installation in CEE cluster continues (Group) Project 1 due Friday Quick demo/recap of TopRank plugin 12-706 and 73-359

Why these Lectures? Very important to know who the benefits, costs accrue to in public (policy) analysis Benefit-cost analysis a simple and useful framework to assist with this 12-706 and 73-359

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? 12-706 and 73-359

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 12-706 and 73-359

? Given this graph, how can We describe the ‘set of all $100 Given this graph, how can We describe the ‘set of all Possible splits between 2 people That allocates the entire $100? ? $100 12-706 and 73-359

$100 Line is the ‘set of all possible splits that allocates the entire $100, Also called the potential pareto frontier. Is the line pareto efficient? $100 12-706 and 73-359

$100 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 $100 $25 12-706 and 73-359

$100 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? $75 $25 $25 $75 $100 12-706 and 73-359

We said initial alloc. mattered - e.g. (100,0)? $100 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 $100 $25 12-706 and 73-359

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. 12-706 and 73-359

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 ‘pay off’ middle , still better off Only works if Net Benefits positive! 12-706 and 73-359

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 12-706 and 73-359

Wrap Up As long as benefits found by WTP and costs by OC then sign of net benefits indicated whether transfers 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 Figure) 12-706 and 73-359

Three Legs to Stand On Pareto Efficiency Kaldor-Hicks 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 12-706 and 73-359

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. 12-706 and 73-359

(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). 12-706 and 73-359

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 12-706 and 73-359

Total/Gross/User Benefits Price Quantity P* 0 1 2 3 4 Q* A B P1 Benefits received are related to WTP - and approximated by the shaded rectangles Approximated by whole area under demand: triangle AP*B + rectangle 0P*BQ* 12-706 and 73-359

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 12-706 and 73-359

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) 12-706 and 73-359

Consumer Surplus Changes Price CS1 A P* B P1 0 1 2 Q* Q1 Quantity New graph - assume CS1 is original consumer surplus at P*, Q* and price reduced to P1 Changes in CS approximate WTP for policies 12-706 and 73-359

Consumer Surplus Changes Price A CS2 P* B P1 0 1 2 Q* Q1 Quantity CS2 is new cons. surplus as price decreases to (P1, Q1); consumers gain from lower price Change in CS = P*ABP1 -> net benefits Area : trapezoid = (1/2)(height)(sum of bases) 12-706 and 73-359

Consumer Surplus Changes Price A CS2 P* B P1 0 1 2 Q* Q1 Quantity Same thing in reverse. If original price is P1, then increase price moves back to CS1 12-706 and 73-359

Consumer Surplus Changes Price A CS1 P* B P1 0 1 2 Q* Q1 Quantity If original price is P1, then increase price moves back to CS1 - Trapezoid is loss in CS, negative net benefit 12-706 and 73-359

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 12-706 and 73-359

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. 12-706 and 73-359

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 12-706 and 73-359

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. 12-706 and 73-359

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. 12-706 and 73-359

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. Price At any given price, determines how much output to produce to maximize profit Supply=MC AVC Quantity 12-706 and 73-359

Market Supply Curves Producer surplus is similar to CS -- the amount over and Above cost required to produce a given output level Changes in PS found the same way as before Supply=MC Price P* PS* P1 PS1 TVC* TVC1 Quantity Q1 Q* Producer Surplus = Economic Profit 12-706 and 73-359

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 CS = (0.5)*(8/9)*(4-1.33) = 1.19 PS = (0.5)*(8/9)*(4/3) = 0.6 12-706 and 73-359

Social Surplus Social Surplus = consumer surplus + producer surplus Is difference between areas under D and S from 0 to Q* Losses in Social Surplus are Dead-Weight Losses! P S P* D Q* Q 12-706 and 73-359

Allocative Efficiency Allocative efficiency occurs when MC = MB (or S = D) Equilibrium is max social surplus - prove by considering Q1,Q2 Price S = MC b P* D = MB a Q1 Q* Q2 Quantity Is the market equilibrium Pareto efficient? Yes - if increase CS, decrease PS and vice versa. 12-706 and 73-359

Further Analysis Assume price increase is because of tax Old NB: CS2 New NB: CS1 Change:P2ABP* A CS1 P2 B C P* 0 1 2 Q2 Q* Quantity Assume price increase is because of tax Tax is P2-P* per unit, tax revenue =(P2-P*)Q2 Tax revenue is transfer from consumers to gov’t To society overall , no effect Pay taxes to gov’t, get same amount back But we only get yellow part.. 12-706 and 73-359

Deadweight Loss Yellow paid to gov’t as tax Price A CS1 P2 B P* 0 1 2 Q* Q1 Quantity 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!) - loss of CS There will always be DWL when tax imposed 12-706 and 73-359

Net Social Benefit Accounting Change in CS: P2ABP* (loss) Government Spending: P2ACP* (gain) Gain because society gets it back Net Benefit: Triangle ABC (loss) Because we don’t get all of CS loss back OR.. NSB= (-P2ABP*)+ P2ACP* = -ABC 12-706 and 73-359