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?