Civil Systems Planning Benefit/Cost Analysis

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

2. Unifying Cost and Supply • Economists learn Supply and Demand • Equilibrium: where S=D • In our case, substitute cost for supply • Econ: S = MC under perfect competition • Perfect competition => no profits • Thus market price = cost of producing • Why cost? Need to trade-off Demand • Using MC is a standard method 12-706 and 73-359

3. Meaning of Cost Curves • Highway pricing • p = f(fares, fees, travel times, discomfort) • p ~ AVC: manages usage of highway • Price increase=> less users (BCA) • MC pricing: more users, higher price 12-706 and 73-359

4. Welfare Economics Continued The upper segment of a firm’s marginal cost curve corresponds to the firm’s supply curve. Again, diminishing returns occur. Supply=MC Price At any given price, determines how much output to produce to maximize profit Quantity 12-706 and 73-359

5. Supply/Marginal Cost Notes Demand: WTP for each additional unit Supply: additional cost incurred for each additional unit Supply=MC Price At any given price, determines how much output to produce to maximize profit P* Q1 Q* Q2 Quantity 12-706 and 73-359

6. Supply/Marginal Cost Notes We always want to be considering opportunity costs (total asset value to society) and not accounting costs Supply=MC Price Area under MC is TVC - why? P* Q1 Q* Q2 Quantity 12-706 and 73-359

7. Supply/Marginal Cost Notes  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 Quantity Q1 Q* 12-706 and 73-359

8. Equilibrium Example • Demand Function: p=4-3q • Supply function: p=1.5q • Assume equilibrium, what is p,q? • Eq=> S=D; 4-3q=1.5q ; 4.5q=4 ; q=8/9 • P=1.5q=1.5*(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

9. Allocative Efficiency Allocative efficiency occurs when MC = MB S = MC Price b P* D = MB a Q1 Q* Q2 Quantity 12-706 and 73-359

10. Social Surplus = consumer surplus + producer surplus Losses in Social Surplus are Dead-Weight Losses! P S P* D Q* Q Social Surplus 12-706 and 73-359

11. Subsidies/Target Pricing Allocative efficiency can only be achieved when P=MC. Assume market for corn, in initial eq’m -> what happens when government guarantees PT to farmers? S Price a d PT b P* D c Q* QT Quantity 12-706 and 73-359

12. Subsidies/Target Pricing At PT, farmers want to supply QT units. But at QT , consumers only want to pay PD . This is effective market price. So PT-PD is subsidized by government policy. What is change in CS, PS? S Price a d PT b P* PD e D c Q* QT Quantity 12-706 and 73-359

13. Subsidies/Target Pricing CS increases from aP*b (yellow) to aPDe (yellow+orange). What about PS? S Price a d PT b P* PD e D c Q* QT Quantity 12-706 and 73-359

14. Subsidies/Target Pricing PS also increases, from P*bc to PTdc. Is overall net benefit to society then positive (since PS and CS both increase)? S Price a d PT b P* PD e D c c Q* QT Quantity 12-706 and 73-359

15. Subsidies/Target Pricing The cost to society (taxpayers) is the government subsidy - So what is the overall net benefit to society? S Price a d PT b P* PD e D c Q* QT Quantity 12-706 and 73-359

16. Subsidies/Target Pricing Overall net benefit to society is (Increased CS + Increased PS) - Costs = Orange + Yellow - Grey = Triangle bde (loss!). This is a DWL, orange and yellow areas are transfers! Leakage of program is Area bde/Area PTdePD S Price a d PT b P* PD e D c Q* QT Quantity 12-706 and 73-359

17. 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 D • If something other than price changes (e.g. demand more of good) • Then entire demand curve shifts • Same things true for supply 12-706 and 73-359

18. 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 12-706 and 73-359

19. Benefits in Efficient Market • NSB=DCS+ DPS + 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 • See related problems on p. 73 12-706 and 73-359

20. Surplus Food Example Initial equilibrium at P0, Q0 New eq’m at (lower)P1, (higher) Q1 What is change in CS? S P S+q’ a P0 b P1 D Q Q2 Q0 Q1 12-706 and 73-359

21. Surplus Food Example Change in CS is P0abP1 (gain) What about PS? S P S+q’ a P0 b P1 D Q Q2 Q0 Q1 12-706 and 73-359

22. Surplus Food Example Change in PS is P0acP1 (loss) for the ‘original suppliers’ since they still Operate on supply curve ‘S’ What is social surplus? S P S+q’ a P0 b P1 c D Q Q2 Q0 Q1 12-706 and 73-359

23. Surplus Food Example Social surplus is net gain of CS+PS, Or the triangle abc - what is Net Social Benefit? S P S+q’ a P0 b P1 c D Q Q2 Q0 Q1 12-706 and 73-359

24. Surplus Food Example Government gains revenue Q2cbQ1, so NSB =Q2cabQ1 S P S+q’ a P0 b P1 c D Q Q2 Q0 Q1 12-706 and 73-359

25. 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 12-706 and 73-359

26. Monopoly - the real game (2) • Could have shown that in perf. comp. Profit maximized where p=MR=MC • 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 12-706 and 73-359

27. Monopoly Analysis 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? MC Pc Qc MR D 12-706 and 73-359

28. Monopoly Analysis (cont.) 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? MC Pm Pc Qm Qc D MR 12-706 and 73-359

29. Monopoly Analysis (cont.) 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 MC Pm Pc Qm Qc D MR 12-706 and 73-359

30. 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 12-706 and 73-359

31. Natural Monopoly Faced with these curves Normal monop would Produce at Qm and Charge Pm. We would have same Social surplus. But natural monopolies Are regulated, usually Produce where D=AC Why? a Pm d P* AC b e MC c Qm Q* D MR 12-706 and 73-359

32. Natural Monopoly Forcing the price P* Means that the social surplus is increased. DWL decreases from abc to dec Society gains adeb a Pm d P* AC b e MC c Qm Q* D MR 12-706 and 73-359