Question

A Health Research company faces a cost of borrowing of 7%. If the firm receives only the private benefits of investing in R&D, then we show its demand curve for financial capital by D_Private, as depicted in the table below. Because there are spillover benefits, society would find it optimal to have more investment. If the firm could keep the social benefits of its investment for itself, its demand curve for financial capital would be social and it would willing to borrow more money to do so. With the data below draw the private demand curve and the social demand curve and the borrowing costs as a horizontal line. Now determine both the amount of financial capital that would be invested if the firm were only considering its private benefit and the amount that would be undertaken if the firm took into account the social benefit that would result from the research.

Rate of Return	DPrivate (in millions)	DSocial (in millions)	Borrowing Cost
3%	$92	$104	7%
5%	$72	$92	7%
7%	$52	$82	7%
9%	$42	$72	7%
11%	$32	$64	7%

Answer 1

In the given question, we draw the private demand curve and the social demand curve separately since these are two different scenarios where DPrivate depicts investment made by the firm only for receiving benefits of investing in R&D while DSocial depicts investment made by the firm for receiving additional social benefits as well.

Since borrowing costs need to be shown as a horizontal line, rate of return should be on the y-axis of the graph while financial capital required should be on the x-axis. Please refer the attached images for looking at the demand curve for Investment Demand versus the rate of return.

Now, for calculating the financial investment that the firm would be looking for, we take into account the diminishing rate of return and thus, the financial investment that the firm would make is as long as returns the firm gets are higher than the borrowing costs.

Thus, for private benefits (DPrivate), the maximum investment that the firm would make is $52 million, while considering the social benefits (DSocial), the maximum investment that the firm would make is $82 million.