Merck pharmaceuticals has a monopoly over the sale of a new drug proven effectiv
ID: 1187432 • Letter: M
Question
Merck pharmaceuticals has a monopoly over the sale of a new drug proven effective in numerous laboratory tests. They estimated the demand funciton for this drug to be: QD= 60- (2/3)P
Total cost funciton given by: TC=Q^2+50
1) If the company profit maximizes, determine the price, output and elasticity of demand at the profit max level of output. Please show all steps!!
2) Suppose Merck is forced to behave as if it was a perfectly competitive firm. Assuming no change in costs, determine the profit max level of output, price and elasticity of demand. Please show all steps!!
3) By clever market manipulation, Merck is now able to act as a perfect price discriminator. What will be the change in consumer surplus as a result of the move?
4) In a diagram, label the information gathered in #'s 1,2 and 3.
Explanation / Answer
1)P = 90-3/2Q^2
profit =Q*P -TC =-3Q^2/2 +90Q-Q^2 -50 =-5Q^2/2 +90Q -50
for profit max dPROFIT /dQ =0
hence -5Q+90 =0
Q =18
P =63
elasticity =PdQ/QdP =P*(-2/3)(Q ) =-7/3
..........
2) for perfect competition
MC =2Q =P=90-3/2Q
hence 7Q/2 =90
Q=180/7 =25.7
P =51.4
.......
3) for perfect price desriminator same as 1..
ie
P = 90-3/2Q^2
profit =Q*P -TC =-3Q^2/2 +90Q-Q^2 -50 =-5Q^2/2 +90Q -50
for profit max dPROFIT /dQ =0
hence -5Q+90 =0
Q =18
P =63
elasticity =PdQ/QdP =P*(-2/3)(Q ) =-7/3