1 Civil Systems Planning Benefit/Cost Analysis Chapters 3 and 4 Scott Matthews Courses: and Lecture 5 - 9/15/2004

and Office Hours  Reminder: TA Office Hours (Paulina)  Wednesdays 3-5 every week  Mon/Wed 3-5 before HWs due (e.g. today for next Monday’s HW)

and Recap: Net Benefits Price Quantity P* 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)

and 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.

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 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

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 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 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 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 Market Supply Curves Quantity Price Supply=MC P1 Q1 Q*  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 P* PS 1 PS* TVC 1 TVC* Producer Surplus = Economic Profit

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  CS = (0.5)*(8/9)*(4-1.33) = 1.19  PS = (0.5)*(8/9)*(4/3) = 0.6

and 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! Q P Q* P* S D

and Allocative Efficiency Allocative efficiency occurs when MC = MB (or S = D) Equilibrium is max social surplus - prove by considering Q1,Q2 Q* P* S D = MB = MC Q1Q1 Q2Q2 a b Price Quantity Is the market equilibrium Pareto efficient? Yes - if increase CS, decrease PS and vice versa.

and Subsidies/Target Pricing Q* P* S D QTQT a b d c PTPT Price Quantity Allocative efficiency only achieved when P = social MC. Assume market for corn below in initial eq’m -> what happens when government guarantees P T to farmers? Social surplus?

and Subsidies/Target Pricing Q* P* S D QTQT a b d e c PDPD PTPT Price Quantity At P T, farmers want to supply Q T units. At Q T, consumers only want to pay P D. This is effective market price. So P T -P D must be subsidized by government policy. What is change in CS, PS?

and Subsidies/Target Pricing Q* P* S D QTQT a b d e c PDPD PTPT Price Quantity CS increases from aP*b (yellow) to aP D e (yellow+orange). What about PS?

and Subsidies/Target Pricing Q* P* S D QTQT a b d e c PDPD PTPT Price Quantity PS also increases, from P*bc to P T dc. So is overall net benefit to society then positive (since PS and CS both increase)? c

and Subsidies/Target Pricing Q* P* S D QTQT a b d e c PDPD PTPT Price Quantity A cost to society (taxpayers) is the government subsidy - So what is the overall net benefit to society?

and Subsidies/Target Pricing Q* P* S D QTQT a b d e c PDPD PTPT Price Quantity Overall net benefit to society is (Increased CS + Increased PS) - Costs = Orange + Yellow - Grey = Triangle bde (loss!). This is a DWL, increases in CS, PS are transfers! Efficiency Measure: Leakage = Area bde/Area P T deP D

and Changes in Demand  There is a difference in ‘change in quantity demanded’ and a ‘change in demand’.  If (only) the price of good changes  Change in qty demanded - move along existing D  If something other than price changes (e.g. demand more of good due to advertising)  Then entire demand curve shifts (all p,q points)  Same things true for supply

and Types of Markets  Primary: directly affected by policy  Secondary: indirectly affected  Example: new highway  Primary: commuting, traffic, pollution  Secondary: change in repairs, gas  Efficient markets (as discussed)  Distorted markets: when external effects occur as a result of market  Could be positive or negative

and Benefits in Efficient Market  NSB=  CS+  PS + Net Gov’t Revenues  Government adds large quantity of good to market to reduce price  Example: surplus food programs  Government intervenes by supplying q’ units into the market  Supply curve moves out (right) - more supplied at each price point

and Surplus Food Example Q P Q0 P0 S+q’ D S P1 Q1 Initial equilibrium at P0, Q0 New eq’m at (lower)P1, (higher) Q1 What is change in CS? a b Q2

and Surplus Food Example Q P Q0 P0 S+q’ D S P1 Q1 Change in CS is P 0 abP 1 (gain) What about PS? a b Q2

and Surplus Food Example Q P Q0 P0 S+q’ D S P1 Q1 Change in PS is P 0 acP 1 (loss) for the ‘original suppliers’ since they still Operate on supply curve ‘S’ What is social surplus? a b c Q2

and Surplus Food Example Q P Q0 P0 S+q’ D S P1 Q1 Social surplus is net gain of CS+PS, Or the triangle abc - what is Net Social Benefit? a b c Q2

and Surplus Food Example Q P Q0 P0 S+q’ D S P1 Q1 Government gains revenue Q 2 cbQ 1, so NSB = Q 2 cabQ 1 a b c Q2

and 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

and 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

and 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?

and 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

and 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

and 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

and 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

and 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

and 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

and 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