Question

3. Suppose members of a 3 person community would each benefit from basic medical research that found a cure for a deadly disease. Assume that such research is collectively (i.e. non-rivally) consumed, and that "units of research" can be measured by the number of "full-time equivalent" scientists, R, engaged in medical research. Assume further that each person's marginal valuation or willingness to pay for medical research is given by the following demand functions, where P is the marginal valuation, or willingness to pay for research, and R is the amount of research.

Person 1: P = 270 - 25R;

Person 2: P = 150 - 10R;

Person 3: P = 120 - 10R.

Assume further that additional research can be obtained at a constant marginal resource cost of $360 per unit.

a. Plot each demand curve as well as the marginal cost curve. How much medical research would any single individual be willing to support, given the marginal cost of research? (5 points)?

b. What is the socially efficient amount of medical research? Show your answer graphically and explain it. (8 points).

c.

Discuss the reason for the difference in your answer to questions 1 and 2. (7 points).

d.   Suppose a local private university proposed to fund the desired medical research by setting up a non-profit foundation financed by contributions from each person. Drawing on the lectures, the text, and the readings on the syllabus, discuss how the following factors might affect the likelihood that the foundation would receive enough contributions to fund the socially efficient amount of research on a voluntary, cooperative basis: (a) free rider incentive, (b) group size, (c) norms of cooperation, (e) altruism. (10 Points).

Answer 1

Given
Person 1: P = 270 - 25R;
Person 2: P = 150 - 10R;
Person 3: P = 120 - 10R.
and MC = $360 per unit

Thus MR will be
MR for
Person 1 MR: P = 270 - 50R;
Person 2 MR: P = 150 - 20R;
Person 3 MR: P = 120 - 20R.
therefore,

a) Adding all three individuals demand curve, we have
Person 1: P = 270 - 25R;
Person 2: P = 150 - 10R;
Person 3: P = 120 - 10R.
Thus P = 540 - 45R and MR = 540 - 90R
Thus at MC = 360 we have
540 -90R = 360
90R = 180
R = 2

thus any single individual be willing to support 2 medical research, given the marginal cost of research.

b) The social efficeint amount will be when P = MC thus 360 = 540 - 45R
which gives R = 4

c) There is difference between the answer to problem 1 and problem 2 because answer to problem 1 is looking only at private gains from medical research while answer to problem 2 talks about societal gains from medical research.