HighFlyer Airlines wants to build new airplanes with greatly increased cabin
space. This will allow HighFlyer Airlines to give passengers more comfort and
sell more tickets at a higher price. However, redesigning the cabin means
rethinking many other elements of the airplane as well, like engine and
luggage placement, and the most efficient shape of the plane for moving
through the air. HighFlyer Airlines has developed a list of possible methods
to increase cabin space, along with estimates of how these approaches would
affect the plane's operating costs and ticket sales. Based on these estimates,
Table 13.5 shows the value of \(\mathrm{R} \& \mathrm{D}\) projects that provide
at least a certain private rate of return. Column 1 = Private Rate of Return.
Column 2 = Value of R\&D Projects that Return at Least the Private Rate of
Return to HighFlyer Airlines. Use the data to answer the following questions.
$$\begin{array}{c|c}\hline \text { Private Rate of Return } & \text { Value of
R\&D } \\\\\hline 12 \% & \$ 100 \\
\hline 10 \% & \$ 200 \\\\\hline 8 \% & \$ 300 \\\\\hline 6 \% & \$ 400
\\\\\hline 4 \% & \$ 500 \\\\\hline\end{array}$$
a. If the opportunity cost of financial capital for HighFlyer Airlines is \(6
\%,\) how much should the firm invest in R\&D?
b. Assume that the social rate of return for \(\mathrm{R} \& \mathrm{D}\) is an
additional \(2 \%\) on top of the private return; that is, an \(\mathrm{R} \&
\mathrm{D}\) investment that had a \(7 \%\) private return to HighFlyer Airlines
would have a \(9 \%\) social return. How much investment is socially optimal at
the \(6 \%\) interest rate?
