Since $1987,$ airlines have been required to report to the Department of Transportation $($DOT$)$ the scheduled and

actual arrival times of their domestic flights. Although the DOT collects detailed data about the actual minutes of

delay incurred on each flight, it only counts a flight as being $$late$$ if it arrives $15$ minutes or more behind

schedule. The DOT issues monthly reports that rank airlines based

on the percentage of their flights that are late under this definition

and excerpts from these rankings are frequently reported in the

media $($TV$,$ magazines, etc$).$

In $1996,$ TWA implemented employee bonus programs based

explicitly on the TWA$$s performance in the government$$s

ranking of on$-$time performance. Under this program, each TWA

employee would receive a payment of between $$65$ and $$100$ in

any month in which TWA is placed at or near the top of the DOT

ranking. Figure A shows the distribution of delay time $($negative

value indicates arriving earlier than scheduled time, and positive

value indicates arriving later than scheduled time$)$ for TWA flights

during $19871995.($Vertical lines in the figures indicate $15$ minute

delay time$).$

$3-1.(1$ points$)$ Draw the distribution of delay time of TWA flights after

the incentive plan $($bonus$)$ is introduced in $1996$ in Figure B $($For

example, the dotted line shows when there is no change in the

distribution$).$

$3-2.(1$ point$)$ The pattern in Figure B is most likely driven by gaming

$(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_)$ behavior.

a$.$ threshold b$.$ rachet c$.$ adverse selection d$.$ loss$-$aversion

$00\mathrm{.}511\mathrm{.}52$

$0$

$0\mathrm{.}5$

$1$

$1\mathrm{.}5$

$2$

DEBT VALUE

COMPANY REVENUE $($$MILLION$)$

DEBT VALUE $($$MILLION$)$

$00\mathrm{.}511\mathrm{.}52$

$0$

$0\mathrm{.}5$

$1$

$1\mathrm{.}5$

$2$

EQUITY VALUE

COMPANY REVENUE $($$MILLION$)$

EQUITY VALUE $($$MILLION$)$

$00\mathrm{.}511\mathrm{.}52$

$0$

$0\mathrm{.}5$

$1$

$1\mathrm{.}5$

$2$

COMPANY VALUE

COMPANY REVENUE $($$MILLION$)$

COMPANY VALUE $($$MILLION$)$

$4.$ Ownership structure Consider an ownership structure $($involving two firms A and B$)$ where Company A owns

$50\%$ of Company B$$s shares, and Company B owns $25\%$ of Company A$$s shares. The controlling family owns $1\%$

of Company A$$s shares, $1\%$ of Company B$$s shares, and manages Company A and B by holding the CEO position

in these companies. If you need, the formula for infinite sum is: $(1+$x$+$x$2+$ x$3+$ x$4+$ x$5+$ x$6+....)=1/(1-$x$).$

$4\mathrm{.}1.(2$ points$)$ Estimate the cash flow rights of the controlling family. To be more specific, if Company B makes

$$200,$ how much is the legal amount that the controlling family should receive?

$4\mathrm{.}2.(1$point$)$ What is the control rights of the controlling family on Firm B$.$