1. 1 Civil Systems Planning Benefit/Cost Analysis Chapters 3 and 4 Scott Matthews Courses: 12-706 and 73-359 Lecture 5 - 9/15/2004

2. 12-706 and 73-3592 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)

3. 12-706 and 73-3593 Recap: 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)

4. 12-706 and 73-3594 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.

5. 12-706 and 73-3595 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

6. 12-706 and 73-3596 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

7. 12-706 and 73-3597 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

8. 12-706 and 73-3598 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

9. 12-706 and 73-3599 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)

10. 12-706 and 73-35910 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?

11. 12-706 and 73-35911 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

12. 12-706 and 73-35912 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

13. 12-706 and 73-35913 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

14. 12-706 and 73-35914 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

15. 12-706 and 73-35915 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!

16. 12-706 and 73-35916 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

17. 12-706 and 73-35917 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

18. 12-706 and 73-35918 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.

19. 12-706 and 73-35919 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?

20. 12-706 and 73-35920 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?

21. 12-706 and 73-35921 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?

22. 12-706 and 73-35922 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

23. 12-706 and 73-35923 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?

24. 12-706 and 73-35924 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

25. 12-706 and 73-35925 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

26. 12-706 and 73-35926 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

27. 12-706 and 73-35927 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

28. 12-706 and 73-35928 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

29. 12-706 and 73-35929 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

30. 12-706 and 73-35930 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

31. 12-706 and 73-35931 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

32. 12-706 and 73-35932 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

33. 12-706 and 73-35933 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

34. 12-706 and 73-35934 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

35. 12-706 and 73-35935 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?

36. 12-706 and 73-35936 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

37. 12-706 and 73-35937 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

38. 12-706 and 73-35938 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

39. 12-706 and 73-35939 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

40. 12-706 and 73-35940 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

41. 12-706 and 73-35941 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

42. 12-706 and 73-35942 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