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

2. 12-706 and 73-3592 Admin  HW 2 returned. Avg X/X  HW 3 due next Monday.

3. 12-706 and 73-3593 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 Consumer Surplus Changes Price Quantity P* 0 1 2 Q* Q1 A B P1 CS1  New graph - assume CS1 is original consumer surplus at P*, Q* and price reduced to P1  Changes in CS approximate WTP for policies

5. 12-706 and 73-3595 Consumer Surplus Changes Price Quantity P* 0 1 2 Q* Q1 A B P1 CS2  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)

6. 12-706 and 73-3596 Consumer Surplus Changes Price Quantity P* 0 1 2 Q* Q1 A B P1 CS2  Same thing in reverse. If original price is P1, then increase price moves back to CS1

7. 12-706 and 73-3597 Consumer Surplus Changes Price Quantity P* 0 1 2 Q* Q1 A B P1 CS1  If original price is P1, then increase price moves back to CS1 - Trapezoid is loss in CS, negative net benefit

8. 12-706 and 73-3598 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

9. 12-706 and 73-3599 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

10. 12-706 and 73-35910 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

11. 12-706 and 73-35911 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)

12. 12-706 and 73-35912 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?

13. 12-706 and 73-35913 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

14. 12-706 and 73-35914 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

15. 12-706 and 73-35915 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

16. 12-706 and 73-35916 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

17. 12-706 and 73-35917 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!

18. 12-706 and 73-35918 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

19. 12-706 and 73-35919 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

20. 12-706 and 73-35920 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.

21. 12-706 and 73-35921 Further Analysis  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.. Price Quantity P2 0 1 2 Q2 Q* A B P* CS1 C Old NB: CS2 New NB: CS1 Change:P2ABP*

22. 12-706 and 73-35922 Deadweight Loss  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 Price Quantity P2 0 1 2 Q* Q1 A B P* CS1

23. 12-706 and 73-35923 Net Social Benefit Accounting  Change in CS: P 2 ABP* (loss)  Government Spending: P 2 ACP* (gain)  Gain because society gets it back  Net Benefit: Triangle ABC (loss)  Because we don’t get all of CS loss back  OR.. NSB= (-P 2 ABP*)+ P 2 ACP* = -ABC

24. 12-706 and 73-35924 Commentary  It is trivial to do this math when demand curves, preferences, etc. are known. Without this information we have big problems.  Unfortunately, most of the ‘hard problems’ out there have unknown demand functions.  We need advanced methods to find demand

25. 12-706 and 73-35925 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

26. 12-706 and 73-35926 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

27. 12-706 and 73-35927 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?

28. 12-706 and 73-35928 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

29. 12-706 and 73-35929 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

30. 12-706 and 73-35930 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

31. 12-706 and 73-35931 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

32. 12-706 and 73-35932 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

33. 12-706 and 73-35933 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