After spending 10 years and $1.5 billion, you have finally gotten the Food and D
ID: 1252683 • Letter: A
Question
After spending 10 years and $1.5 billion, you have finally gotten the Food and Drug Administrationís approval to sell your patended wonder drug which reduces he aches and pains associated with aging. Market research indicates that the elasticity of demand for your drug is -1.25 and you estimate the marginal cost of manufacturing and selling on additional dose to be $1.a. What is the profit maximizing price per dose of your drug?
b. Would you expect the elasticity of demand you face to rise or fall when your patent
expires?
Explanation / Answer
a. The formula for price elasticity is: E = Q' * (P/Q) where P' is dQ/dP In this case: -1.25 = Q' * (P/Q) (1) -1.25*Q = P*Q' Take the derivative with respect to Q of both sides -1.25 = P*Q" Q" = -1.25/P (2) The formula for profit is: V = (P - MC)*Q In this case: V = (P - 1)*Q (3) (1) implies: -1.25 = Q' * (P/Q) P = -1.25*Q/Q' (1) and (3) imply: V = (P - 1)*Q V = (-1.25*Q/Q' - 1)*Q V = -1.25*Q^2/Q' - Q Set the derivative equal to zero -1.25*(2Q*Q' - Q"*Q^2)/(Q')^2 -1 = 0 (2Q*Q' - Q"*Q^2)/(Q')^2 = -1/1.25 (2Q*Q' - Q"*Q^2)/(Q')^2 = -4/5 Solve for Q" Q" = ((4/5)*(Q')^2 + 2Q*Q')/Q^2 Substitute (2) Q" = -1.25/P ((4/5)*(Q')^2 + 2Q*Q')/Q^2 = -1.25/P P = -1.25*(Q^2)/((4/5)*(Q')^2 + 2Q*Q') P = -(Q^2)/((Q')^2 + 2Q*Q') If you had an inverse demand curve, you could substitute in the values for Q and Q' to solve for a number value of P. b. The elasticity of demand will fall. That is, it will become more negative and more elastic when the patent runs out because substitutes can be introduced, which give consumers additional options.