1. The U.S. government wants to encourage the development of a pharmaceutical dr
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1. The U.S. government wants to encourage the development of a pharmaceutical drug to cure HIV/AIDS. If developed, the demand per year for the medicine would be Q = 100,000,000-400,000P. The cost of R&D; is $200,000,000 and the marginal cost of production is $100. R&D; occurs at time 0 and the discovery lasts forever. The probability of discovery depends on the number of firms doing R&D;: p(n)-1-e". The interest rate is 10%. Calculate social surplus per period under perfect competition (given that the medicine to cure HIV has been discovered) Calculate social surplus per period if there is a single firm in the market (given that the medicine to cure HIV has been discovered) How many firms would a social planner (the government) select to do R&D; assuming that once developed the all your work) Suppose first that the government offers a prize X to the first firm that develops such a medicine. Once discovered, the good (the knowledge) is made available to any firm. That is, once discovered there is perfect competition in the market. What is the size of the prize that the government should offer? (show all your work) a. b. c. is perfect cormpetition in the market for this medicine? (show d. e. Instead of a prize, suppose the government offers the first firm to discover such a medicine a permanent patent. How many firms will do R&D;? Is this more or less than what the government would prefer? What length should the patent be to have the same number of firms that you found in part c? f.Explanation / Answer
Social surplus it is sum of consumer surplus and prodcuer surplus in an economy. Consumer satisfaction with respect to utility is measured with social surplus.
a. It is given to us that the demand function for the drug is Q = 100,000,000 - 400,000P. It is also given to us that the marginal cost is $100 and and the R & D cost is $200,000,000.
Now, we know that equilibrium occurs at a point where P = MC. From the demand function we can calculate P as follows :
Q = 100,000,000 - 400,000P
Q - 100,000,000 = 400,000P
P = (100,000,000 - Q)/400,000
When we equate this with the marginal cost MC, we get:
(100,000,000 - Q)/400,000 = 100
100,000,000 - Q = 100 x 400,000
Q = 100,000,000 - 40,000,000
Q = 60,000,000
When we substitute the value of Q in the demand functon we get P = $100
Now, to find out the consumer surplus we need to find P. To do this we assume that the initial quantityt supplied is 0. So, P in that case is
P = (100,000,000 - Q)/400,000
P = (100,000,000 - 0)/400,000
P = 100,000,000/400,000
P = $250
So, now the formula for consumer surplus is :
CS = 1/2 x P x Q
= 1/2 x 250 x 60,000,000
= 7,500,000,000
The cost for R & D is given as $200,000,000. So, the total surplus is :
Social Surplus = 7,500,000,000 - 200,000,000
= 7,300,000,000
We do not take into account the producer surplus as there is no supply function given for the drug.
So, the social surplus under perfect competition is $7,300,000,000.
b. The social surplus in a monopoly will be higher than that in perfect competition as there are no external costs in a perfect competition. Whereas in a monopoly, the firm will always withold the good/service to get a higher price for the commodity. Since there are no external cost in a perfect competition, the overall surplus for the entire economy in perfect competition is smaller.
c. It is given to us that the probability of the drug being discovered is P(n) = 1 - e-n. Here n represents the number of firms in the economy. So, if we assume that there is only one firm in the market, then the probability of the drug being discovered is :
P = 1 - e-1 = 1 - 0.367 = 0.633
However, this will not be accpetable by the social planner as they would the drug to be discovered for certainty. (A probability of 1 indicates that the drug will be discovered for certain.)
Now, if we assume there are three firms in the market, the probability of the drug being discovered is :
P = 1 - e-3 = 1 - 0.049 = 0.951. Though this is much better than when there is one firm in the economy, this is still not a certainty.
If we continue to plug in numbers for n and calculate, we realise that the probability of the drug being discovered is certain when there are 10 firms (we only calculate till four digits after the decimal point for convenience.
So, the government will select 10 firms to do the R & D.
d. Now, let's assume that the government offers a price X for the first firm. We know that the cost of R & D is $200,000,000. So, the government will have to offer an amount higher than this to give an incentive to the firms to develop the drug as quickly as possible.
We know from part a. of the question that the consumer surplus is $7,300,000,000.
The total cost for the drugs is TC = P x Q
= 60,000,000 x 100 (we will take the price calculated from the demand function in part a. instead of when Q = 0)
= 6,000,000,000
So, the incentive the government will have to offer is :
X = 7,300,000,000 - 6,000,000,000
X = 1,300,000,000
The government will have to offer incentive of $1,300,000,000 to the firms so that they discover the drug faster.
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