Answer to Question #202895 in Microeconomics for Saman Ghazal

Question

     Pfizer own the copyright for “Pfizer COVID Vaccine (PCV)”. The total cost of producing Q units of PCV is: . The annual demand for PCV is. Q is the number of units of PCV. The annual interest rate facing all agents in the economy is 8.75%. 

a.      How many units of PCV should Pfizer produce? What price should Pfizer charge for one unit of PCV? Clearly explain your reasoning.

b.     What is TR from PCV to Pfizer? What are Pfizer’s annual profits from PCV?

c.      Suppose the Pfizer copyright of PCV was due to expire by 2021. Describe the new market structure that would occur if PCV entered the public domain, meaning anybody could use PCV. What would be the new price of one unit of PCV? How many units of PCV would be sold by the COVID vaccine industry?

Answer 1

Given

TC=100+50Q+0.5Q²

P=300-0.2Q

a.

PCV should Pfizer produce at maximum level, and it will be achieved where

MR = MC.

TC=100+50Q+0.5Q²

Now Differentiate TC with respect to Q to calculate MC

$MC =\frac{ ∂TC}{∂Q}$

MC = 50+Q

 

The demand function is given as P=300-0.2Q.

Now TR is calculated as Price* Quantity

TR = (300-0.2Q)Q

TR = 300Q - 0.2Q²

Now Differentiate TR with respect to Q to calculate MR

$MR = \frac{∂TR}{∂Q}$

MR = 300 - 0.4Q

The maximum level of production is achieved where MR = MC

300 - 0.4Q = 50+Q

250 = 1.4Q

$Q =\frac{250}{1.4}$

Q = 178.57

 Pfizer should produce 178.57

Price for Pfizer is calculated by putting Q = 178.57 in-demand Equation to calculate the price

P= 300-0.2Q

P= 300-0.2*(178.57)

P= 300-35.71

P = 264.28

b.

TR for Pfizer is given as 

TR = 300Q - 0.2Q²

$TR = 300\times(178.57) - 0.2\times(178.57)^2$

TR = 53,571 - 6,377.44

TR = 47,193.56

therefore TR = 47,193.56 is generated by Pfizer from PCV

Annual Profit is calculated as TR - TC

here TC is calculated as 

TC=100+50Q+0.5Q²

$TC=100+50\times(178.57)+0.5\times(178.57)^2$

TC = 100 + 8928.5 + 15,943.622

TC = 100 + 8928.5 + 15,943.622

TC = 24972.122

Now Profit = TR - TC

Profit = 47,193.56 - 24972.122

Profit = 22,221.438

c.

Suppose the Pfizer copyright of PCV was due to expire by 2021. now if PCV entered the public domain, meaning anybody could use PCV, this means it enters into the Perfect Competition Market structure.

Now Units of PVC produced in this market structure is calculated as

P = MC

300-0.2Q = 50+Q

250 = 1.2Q

Q = 208.33

Therefore new quantity should be produced = 208.33 units.

Now to Calculate the price put Q = 208.33 in-demand Equation, we get

P = 300-0.2Q

$P = 300-0.2\times(208.33)$

P = 300-41.6666

P = 258.33