Conclusion of “tools” chapters Today: More on welfare economics Market failure Various tools of cost-benefit analysis

Today Conclusion of our “tools” chapters More on Chapter 3 Production economy Two fundamental theorems of welfare economics Market failure Chapter 8: Cost-benefit analysis Present value Internal rate of return Discount rates and valuing public projects Other issues

More on welfare economics Production economy Production possibilities curve Efficiency Two fundamental theorems of welfare economics Market failure

Recall linear production possibility curve Becky has a given number of hours per day Feasible bundles: t, v, w, x, y, z Point t does not use up her time allotment Point u is infeasible

Efficiency Efficient points are on the line connecting (0,4) and (20,0) Examples of efficient points: v, w, x, y, and z

Efficiency At efficient points, increasing production of one good must result in another good having decreased production We will typically assume efficient points are chosen No satiation: More is better See Figure 3.8, p. 39

Marginal Rate of Transformation MRTaf = Marginal rate of transformation of apples for fig leaves MRTaf = MCa/MCf

Efficiency condition With apple and fig leaf supply variable, we need the following to get efficiency MRTaf = MRSaf = MRSaf MCa/MCf = MRSaf = MRSaf Adam Eve Adam Eve

Efficiency condition Assume that the efficiency condition is not met Someone could trade to improve utility Trade will continue to occur until efficiency condition is met

First Fundamental Theorem With competition and open markets for all commodities, efficiency can occur This idea is conveyed in the First Fundamental Theorem of Welfare Economics “All producers and consumers act as perfect competitors” (R/G p. 40) No market power “A market exists for each and every commodity” (R/G p. 40) Does not happen in real life (No market for the air we breathe)

Sketch of efficiency conditions Consumer side: MRSaf = Pa/Pf MRSaf = Pa/Pf MRSaf = MRSaf Producer side: MC = MB implies MCa/MCf = Pa/Pf MRTaf = Pa/Pf Adam Eve Adam Eve Efficiency conditions met Each line wipes right after click

Second Fundamental Theorem We return to fairness Two efficient points are the origins Although these points are efficient, are they “fair?” Government can play a role in fairness Lump-sum taxes act in the same way as changing endowments

Efficiency versus equity A utility possibilities curve can show all of the Pareto efficient points See Figure 3.10, p. 43 Notice that from any point on a utility possibilities curve, an increase of one person’s utility must cause another’s utility to decrease Points inside the curve are not Pareto efficient See Figure 3.9, p. 42, for more on efficiency versus equity

Determining a social welfare function Determining a social welfare function can differ from person to person Examples Additive Multiplicative Which one is “right?” Hard to say Most economists do not try to address this issue See Figure 3.11, p. 44, for an example of social indifference curves

Maximizing the social welfare function In order to maximize the social welfare function, find the indifference curve with highest utility that is indifferent to utility possibilities curve See Figure 3.12, p. 44, for an example

Market failure There are instances in which market efficiency cannot be achieved Market power Many ways to control price Nonexistence of markets Asymmetric information Important in health care and retirement: Chapters 9-11 Externalities: Chapter 5 Public goods: Chapter 4

Market failure due to market power How Do Firms Gain Market Power? Exclusive control over important inputs Patents and copyrights Government licenses or franchises Economies of scale  Natural monopoly Networks

Exclusive control over important inputs If a company controls a significant portion of the important inputs to a product, it can have significant influence on price

Exclusive control over important inputs Example: De Beers Rough diamond explorer Around 40% of world diamond production by value Sales and marketing through the Diamond Trading Company This company sells almost half of the world’s rough diamonds by value (Information from http://en.wikipedia.org/wiki/De_Beers, checked Feb. 3, 2008)

De Beers Such large control over the market makes De Beers able to act similarly to a monopolist Marketing of diamond jewelry does not have to be brand specific "A Diamond is Forever" attempts to prevent old jewelry from entering the market De Beers does have some control over world prices

Patents and copyrights Patents and copyrights prohibit others from copying private work and discoveries Example: Copying songs and movies that are copyrighted are typically prohibited by law

Government licenses or franchises Government owned property often allows exclusive operation of the property for various uses This is to prevent competition that could deteriorate a natural destination

Government licenses or franchises Example: Yosemite National Park Limited parking Tasteful hotels Most of the park is undeveloped Most of park development is in only 7 square miles Park is 1,200 square miles Bridal Veil Falls

Economies of scale Some technologies are such that as the quantity produced increases, ATC decreases for all reasonable quantities produced This is due to increasing returns to scale This happens when ALL inputs double and production MORE THAN doubles Often happens with large fixed costs and nearly-linear variable costs

One firm could gain market power When a firm gains market control with economies of scale, it is called a natural monopoly There are problems with natural monopolies if left uncontrolled Price ($) D ATC Q

Network economies What do the following products have in common? Skype Sony IVE Microsoft's MSN Messenger Ojo

Network economies They are all trying to become the leader in video calling programs This technology has improved since the PicturePhone was unveiled in 1964

Market failure & government intervention In some of the topics this quarter, government intervention will be justified by market failure Governments can fail, too More in Chapter 6

Summary: More on welfare economics Production possibilities Efficiency First Fundamental Theorem Second Fundamental Theorem Efficiency versus fairness Market failure: Market power and nonexistence of markets

Cost-benefit analysis We now move on to Chapter 8 for the last “tools” chapter Cost-benefit analysis Present value Internal rate of return Benefit-cost ratio Discount rates and valuing public projects Valuing intangibles Tactics used to make a project look more or less desirable Distribution and uncertainty Certainty equivalent value

Present value Present value shows how much future payments are worth today Example: $100 paid today is not worth the same as $100 paid a year from now Lost interest in safe investments

Using future value to derive present value Suppose we put $1,000 into the bank today, earning 1% per year on it Value today: $1,000 Value 1 year from now: $1,010 $1,000 * (1 + 0.01) Value 2 years from now: $1,020.10 $1,000 * (1 + 0.01)2 $1,010 * (1 + 0.01)

Projecting Future Dollars into the Present If we multiply to get future value, we divide to find present value of a future payment R0 = $1000 R1 = $1000*(1+.01) = $1010 R2 = $1010*(1+.01) = $1020.10 R2 = $1000*(1+.01)2 = $1020.10 RT = R0*(1+r)T 5 lines visible 1st click – 6th line 7th click – “Present Value” 8th click – “discount rate” 9th click ‘ discount rate arrow disappears, bracket appears, “discount factor” Present Value R0 = RT/(1+r)T discount rate discount factor

Present Value of a Stream of Money

Present value, permanent annual payment Special case Present value of an annual payment of R every year forever (starting today), when the annual interest rate is r :

Cost-benefit analysis Welfare economic theory framework Find present value of benefits and costs If benefits exceed costs, the project should be done Information for cost-benefit analysis is often difficult to obtain

Cost-benefit analysis Present value criteria When there are two mutually exclusive projects, the preferred project is the one with the highest net present value (assuming it is positive) What about “fairness?”

Factoring in inflation Unless otherwise mentioned, we assume costs and benefits are in real terms Real costs and benefits account for inflation When costs and benefits are in nominal terms, inflation must be factored in Note that we get same result, once we cancel inflation terms

Private Sector Project Evaluation Comparing two projects R&D project Advertising project Choice depends on interest rate (see bolded #s) Annual Net Return PV Year R&D Advertising r = -$1,000 $150 $200 1 600 0.01 $128 $165 2 0.03 $86 $98 3 550 1,200 0.05 $46 $37 0.07 $10 -$21

Internal rate of return The internal rate of return is the discount rate needed to make the present value of a project equal to zero

Internal rate of return versus NPV Note that internal rate of return does not necessarily imply which project to do Project X has the higher internal rate of return Project Y has the higher present value  Do Y Project Year 0 Year 1 ρ Profit PV X -$100 $110 10% $4 3.77 Y -$1,000 $1,080 8% $20 18.87 Assume 6 percent interest rate in calculating profit

Benefit-cost ratio Benefit-cost ratio is simply B / C If this ratio is greater than one, then benefits exceed costs The project is worth considering when the benefit-cost ratio exceeds one We should only use benefit-cost ratios to determine if a project is worth considering Use present value criteria to determine which project gets done

Public projects What should public discount rate be? Example Depends on how much private sector consumption and investment change Example One-fifth of funds come at the expense of consumption, with discount rate of 10 percent Four-fifths of funds come at the expense of investment, with discount rate of 15 percent Public sector discount rate is one-fifth of 10 percent, plus four-fifths of 15 percent, or 14 percent

Public projects in practice Government conducts two separate analyses to determine costs and benefits 7 percent More in line with example on previous slide 3 percent Lower investment rate used to increase concern for: Future generations Individuals with discount rates that are “too high” Externalities of R&D

Valuing public benefits and costs There are many ways to value public benefits and costs Market prices Adjusted market prices and shadow prices Problems due to monopoly Problems due to taxes Problems due to unemployment Consumer surplus Economic behavior Value of time Value of life

Market prices Market price is a good measure of marginal social cost if the market is perfectly competitive with no government intervention Problem: Many markets have market power

Adjusted market prices There are instances in which social marginal cost is not clear Underlying social MC is known as shadow price Examples where social MC is not clear Monopoly: Market power controls price Taxes: Taxes change price Unemployment: Lack of employment makes valuing a worker’s skills difficult

Consumer surplus Decisions by a single firm typically have minimal consequences on a market Prices often change substantially with some government projects Consumer surplus can also change substantially with the implementation of government projects Pounds of avocados per year Price per pound of avocados Increased CS when price drops from $2.89 to $1.35 per pound e b d Sa $2.89 c g Sa’ 1st click – left-hand side text line-by-line 2nd click - axes and labels, D, S, A, d, and g 3rd click – S’, A1 $1.35 Da A0 A1

Economic behavior Some things that are valuable are not formally traded Time “Time is money” for each person Convenience Driving versus public transit Life How much is a life worth? Lost earnings and value of leisure time Probability of death versus wages in dangerous industries

Valuing intangibles Some consumption is very hard to put a value on Space exploration Beautiful views National security Fireworks shows Although benefits are difficult to measure, costs can still be minimized given a set of goals

Games cost-benefit analysts play The Chain-Reaction Game Secondary benefits counted Secondary costs not counted The Labor Game Some politicians count job creation as a benefit Wages are costs, not benefits The Double-Counting Game Example: Value of land plus rent from land Only one can be counted as a benefit, since land can either be sold or rented

Distribution and “fairness” Hicks-Kaldor criterion A project should be undertaken if it has positive net present value, regardless of distributional consequences Social welfare criterion A project should be undertaken if it improves overall social welfare Bill Gates example Bill Gates example: What if a public project benefits Bill Gates by $1 billion, but every other person in the US loses $1? Social welfare is probably lower. How do we solve this? Do the public project, and have Bill Gates give every other person in the US $2.

Uncertainty Actual results of a public project are not certain Errors can occur Mars orbiter disaster in 1999, due to conversion failure “Earthquake-safe” technology The benefits are often not known until tested by a big earthquake Benefits are also uncertain if we don’t know when the next “big one” is

Certainty equivalent If people were risk neutral, utility would be linear Most people are risk averse Concave utility function Expected utility of a gamble is less than the utility of the expected value More on uncertainty in Chapter 9

Calculating the Certainty Equivalent Value 75% probability of gaining y

Summary: Cost-benefit analysis Cost-benefit analysis is used to determine which projects have higher costs than benefits With limited resources, we do projects with highest net present values Costs and benefits are not always easy to calculate Uncertainty is important when people are risk averse