A new chemical has been discovered that can be produced at a constant marginal c
ID: 1190828 • Letter: A
Question
A new chemical has been discovered that can be produced at a constant marginal cost of $10 by its patent holder, Johnson inc. Two industries, A and B, find the chemical, Cloreen, to be useful in their production processes. Industry A has a demand for Cloreen of q1=100-p1. Industry B's demand is q2=60-p2.
a.) If Johnson can prevent resales between industries A and B, what prices will it charge to A and B? It can be assumed that the patent gives Johnson monopoly power. What quantities will be sold to the two industries, and what will be Johnson's profit?
b.)Assume now that it is illegal for Johnson to charge different prices to A and B. What price will Johnson now charge, and what will be its profit? What is Johnson's quantity sold?
c.) IS total economic surplus higher in part a or in part b? What is the difference in total surplus in the two cases?
d.) Assume now that the demand for Cloreen by industry B is less than before, and is q2 = 40 - p2. Aside from this change, the facts are as given previosuly. Answer parts a, b and c given the changed demand by industry B.
Explanation / Answer
a.
For firm A:
Given, Marginal cost (MC) = $10 and q1 = 100 – p1
Therefore, p1 = 100 – q1 and TR = (100 – q1) × q1
= 100q1 – (q1)^2
Derivative of TR = MR = 100 – 2q1
Equilibrium condition, MR = MC
100 – 2q1 = 10
2q1 = 90
And, q1 = 45
Answer: Equilibrium quantity is 45 and equilibrium price is (100 - 45 =) $55
For firm B:
Given, Marginal cost (MC) = $10 and q2 = 60 – p2
Therefore, p2 = 60 – q2 and TR = (60 – q2) × q2
= 100q2 – (q2)^2
Derivative of TR = MR = 60 – 2q2
Equilibrium condition, MR = MC
60 – 2q2 = 10
2q1 = 50
And, q2 = 25
Answer: Equilibrium quantity is 25 and equilibrium price is (60 - 25 =) $35
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