H FIGURE 14.7 Investor equilibrium. expected rate of return at which the investor
is indifferent between a risky and a risk-free investment. There are, of course,
other portfolios with equivalent riskreturn tradeoffs, such as point H in Figure
14.7, that

for firm A is to charge a low price, which will result in a profit of $250,000,
compared with a profit of $100,000 if it adopts a high-price strategy. Thus, the
final optimal strategy profile for this game is cfw_Low price, (Low price, Low price),
which y

individual is willing to sacrifice is given by the distance CE. Thus, the indifference
curve IH reflects the greater care that an individual takes to avoid a loss,
compared with individuals who are less careful and are willing to sacrifice only AC.
Figure

invest, and if Slumlady Sally does not invest, then it is in Slumlord Larrys best
interest not to invest. Thus, if Slumlord Larry and Slumlady Sally do not cooperate,
the strategy profile cfw_Dont invest, Dont invest, which still constitutes a Nash
equili

If the risk-free discount rate is 10%, then the net present value of this investment
project is Suppose, on the other hand, the investor perceives the project as risky
and uses a risk-adjusted discount rate of 20%. The net present value of the project
is

when the market consists of a high proportion of high-risk individuals, which has
the effect of moving the average-market fair-odds line closer to the fair-odds
Market Uncertainty and Insurance 673 0 S1 S0 B FH FM FL FIGURE 14.27 High-risk,
low-risk, and

Treasury bills and (1 - q) = 0.3333, or 33.33% consists of Lugburz shares. An
alternative solution to this problem is the Lagrange multiplier method. The first
step in the Lagrange multiplier method is to bring all terms to left side of the
constraint. Th

dealer price will fall. This will further exacerbate matters, since it will create an
even greater incentive for plum owners to avoid the used-car market and sell
privately. In the end, only lemons will be available from used-car dealers. In this
case, th

(14.12) where CFt* is the risk-free cash flow and CFt is the actual, risky cash flow
that is considered to be equivalent to CFt*. Since CFt* CFt, then 0 at 1. When
CFt* = CFt, then at = 1, in which case the investment is considered to be risk free.
On the

maximum value of U*. Our discussion of the selection of an optimal portfolio was
very simple. It was restricted to the choice of the optimal combination of a single
risk-free and a single risky asset. A more realistic discussion of the selection of an
opt

95% probability that firm B will charge a high price and a 5% probability that it will
charge a low price. Similarly, firm A believes that a lowprice strategy will result in a
2% probability that firm B will charge a high price and a 98% probability of a

i 25(0.35) 15(0.5) 10(0.15) 14.75 11.34 Strategy 15(0.35) 20(0.5) 5(0.15) 9.5 9.86
15(0.35) 0(0.5) 5(0.15) 6 6.8 Raise price No change Lower price FIGURE 14.15
Decision making under risk: expected values and standard deviations of returns
for each pricing

Figure 14.22 will prefer a consumption level corresponding to point B to any other
point on the fair-odds line. Consumption levels that correspond to points A and C
are found on an indifference curve that is closer to the origin, which yields a lower
leve

650 Risk and Uncertainty State A State B Slumlord Larry $5,000 $1,000 $3,000 $0
Invest Dont invest FIGURE 14.9 The Slumlords Dilemma under alternative states
of nature. GAME TREES In Chapter 13 we introduced the concept of the extensive
form of multistage

000 4 050 000 0 2 250 000 4 050 000 0 8 950 000 0 2 3 800 000 1 900 000 . . . . ., , ,
, . , , , . , . , , Ep Ep 654 Risk and Uncertainty The standard deviation of firm As
expected profits from a low-price strategy is The standard deviations of
expected p

general, risk-averse individuals will purchase full insurance offered at fair odds.
But what if insurance is offered at unfair odds? This situation is depicted in Figure
14.26. Thus far we have assumed that insurance companies operate at zero cost.
This a

Invest will result in a mutually beneficial outcome for both players. But since
there is an obvious incentive for Slumlord Larry and Slumlady Sally to mislead
each other, neither one will be certain whether the other will actually invest in
spite of the a

policy solution to this problem is for local government to exercise the power of
eminent domain and purchase the run-down properties. The government might
redevelop the properties on its own, or sell them to a single developer who will
agree to do so. Thi

is 11.5%. When bi = 0.75, then kc =+ - 7 1 5 10 7 11 5 . .% ( ) = kk k k c rf m rf =+ - i
b ( ) b k k k i c = - m rf Firm Behavior and Risk Aversion 647 b. When krf = 8 and
bi = 1.5, then GAME THEORY AND UNCERTAINTY In Chapter 13 we introduced non
coopera

where Di is the decision index, Mi is the maximum payoff from each strategy, mi is
the minimum payoff from each strategy, and a is the coefficient of optimism. The
optimal strategy using the Hurwicz decision criterion has the highest value for Di.
Definit

management of two firms deciding whether to adopt a high-price or a low-price
strategy. This is a sequential-move game in that firm A must first decide whether
to charge a high price or a low price without having the luxury of knowing how
firm B will resp

free U.S. Treasury bonds and risky Lugburz shares? Solution. From Equation (14.9),
the capital market line is The problem confronting Webb Ungoliant is to create a
portfolio of U.S. Treasury bonds and Lugburz shares that maximizes his investment
utility s

laissez-faire, or nonintervention by government in the marketplace. The
conditions that define perfectly competitive market structures, however, are
rarely satisfied in practice. The output of different firms, for example, are typically
differentiated; bu

prices exhibiting more than the average price fluctuationshave beta coefficients
greater than unity (bi > 1), while stock prices that are less volatile have positive
beta coefficients less than unity (0 < bi < 1). Definition: The capital asset pricing
mod

proprietor of The Floating Log restaurant, which is located on the Delaware River
near Frenchtown. Harry is considering expanding the dining area of his restaurant.
The $150,000 cost of the investment is known with certainty. Harry has estimated
that the

output level. Solution a. A perfectly competitive industry will produce at an output
level at which marginal private cost equals price, MPC = P. Solving the demand
equation for price yields Substituting P* $ = - 200 4 25 100 ( ) = Q* = 25 4 200 4 Q
Q = -