More on the invisible hand Present value Today: Wrap-up of the invisible hand; present value of payments made in the future

What is the invisible hand? Let self-interested actions determine resource allocation Prices help determine how much is allocated for production of each good or service Rationing function Allocative function

Rationing function of price Efficiency cannot be obtained unless goods and services are distributed to those that value these goods and services the most In general, prices can obtain this goal We will examine exceptions in some of the later chapters

Allocative function of price As prices of goods change, some markets become overcrowded, while others get to be underserved Without any government controls or barriers to entry/exit, resources will be redirected in the long run such that economic profits get driven to zero

Regulated markets Sometimes, markets are regulated with public interest in mind However, the invisible hand sometimes leads to results that were not intended Note that this type of regulation may lead to barriers to entry

A regulated market of the past: Airlines Most of you have lived a life without regulation of major commercial airlines in the U.S. However, in the early to mid 1970s, fares were set such that airlines could make economic profits if the airplane was full

Regulation of airlines Airlines were required to use some economic profits of popular routes to pay for routes that had negative economic profits Problem: The invisible hand See p for more on piano bars and elaborate meals Conclusion: Be careful what you regulate

Possible solution: Grant a monopoly This sometimes happens, but it has its own potential set of problems Example: Regulated utilities Regulation may state that economic profits need to be set to zero What if “profits are too high?” Solution: Extravagant office buildings Another example: BC Ferries in British Columbia More on monopolies in Chapter 10

Before we move on… …we need to define and understand present and future value Money can be invested relatively safely in many ways Government debt Savings accounts and CDs in banks Bonds of some corporations

Present and future value Suppose that the rate of return of safe investments is 5% If I invest $100 today, it will be worth $105 in a year Working backwards, I am willing to pay up to $100 for a payment of $105 a year from now

Working backwards We can calculate how much a future payment is by discounting it by interest rate r We calculate the present value of a future payment as follows Payment of M is received T years from now PV represents present value:

Example What is the present value of a $1,210 payment to be received two years from now if the interest rate is 10%? Plug in M = $12,100, r = 0.1, and T = 2 PV = $10,000

Present value of a permanent annual payment What happens if we receive a constant payment every year forever? We can add up all of the discounted payments, or we can use a simple formula to calculate the PV of these payments

Present value of a permanent annual payment Present value of an annual payment of M every year forever, when the interest rate is r :

Question 18 from the practice problems If you won a contest that pays you $100,000 per year forever, how much is its present value if the interest rate is always at 10 percent? Solution: M is $100,000 and r is 10%, or 0.1  PV is M / r, or $100,000 / 0.1 = $1,000,000

Finally, more on equilibrium Remember that equilibrium is not an instantaneous process Sometimes, trial and error is needed to find what equilibrium is By the time this is figured out, a new equilibrium may emerge The bigger the costs of finding equilibrium, the less optimal the market generally is

Finally, more on equilibrium Some people have a good ability to quickly determine what such an equilibrium is These people can earn money from this skill Example: Recognizing the value of a stock before other people

Example: Winning a contest Which is worth more: Winning $50,000 a year forever or $1,000,000 today? Assume that the interest rate is 4% The $50,000 forever has a present value of $50,000 / 0.04, or $1,250,000 Take the $50,000 forever

Example: A stock Suppose that you own a stock that will pay you $1 a year forever with no risk Assume that the annual interest rate is 5% in this example Value is $1 / 0.05, or $20, for the stock

Example: Winning a contest that pays you only 30 years Back to winning a contest, except now the two options are $50,000 a year for 30 years $1,000,000 today Which one is worth more?

Example: Winning a contest that pays you only 30 years This is a perfect example of having to think like an economist to solve this problem quickly You could discount each of the 30 payments appropriately to determine how much the present value of those payments is However, there is another way of solving this

Example: Winning a contest that pays you only 30 years To solve this, we must recognize that this problem is equivalent to the previous contest problem, except that we must take away payments made 30 years or more in the future To calculate this, we must calculate how much this contest is worth today and how much this contest is worth 30 years from now

Example: Winning a contest that pays you only 30 years If you won the contest that paid forever, it would be worth $1,250,000 We already did this calculation How much is this contest worth 30 years from now? We need to discount $1,250,000 by thirty years $1,250,000 / (1.04) 30 = $385398

Example: Winning a contest that pays you only 30 years The present value of 30 yearly payments is $1,250,000 – $385,398, or $864,602 So, if the $50,000-per-year prize is only over 30 years, you should take the $1,000,000 prize today

Summary Today, we have finished our study of the invisible hand We also examined discounting, and ways of summing constant yearly payments made forever