Duopoly Competition and Equilibrium Analysis

This economics assignment explores a duopoly market where two firms produce horizontally differentiated products. It analyzes the demand functions for each firm, their marginal cost structures, and derives the best response functions. The assignment then solves for the equilibrium prices, quantities, and profits for both firms, demonstrating how market power is distributed between them. Concepts like substitutes, law of demand, total revenue, and marginal revenue are applied to understand the competitive dynamics in this duopoly scenario.

Running head: ECONOMICS ASSIGNMENT
Economics Assignment
Name of the Student
Name of the University
Author Note

1ECONMICS ASSIGNMENT
Table of Contents
Introduction:....................................................................................................................................2
Answer 1:.........................................................................................................................................2
Answer 2:.........................................................................................................................................2
Answer 3:.........................................................................................................................................3
Answer 4:.........................................................................................................................................4
Answer 5:.........................................................................................................................................5
Answer 6:.........................................................................................................................................5
Answer 7:.........................................................................................................................................6

2ECONMICS ASSIGNMENT
Introduction:
In the given problem, the firm 1 and the firm 2 produce horizontally differentiated products.
Demand function of firm 1:
Q1 = 100 – P1 + (P2/2)
Demand function of firm 2:
Q2 = 200 – 4P2 + 2P1
MC1 = 10 and MC2 = 20
Answer 1:
If the demand function of firm 1 is differentiated with respect to P2, it can be seen that:
dQ1/dP2 = ½
This implies that if P2 increases by one unit, the demand for Q1 increases by ½ unit, which
implies that Q1 and P2 are positively related. This in turn indicates that the product of firm 2 is a
substitute of the product of firm 1.
Answer 2:
Differentiating the demand function of firm 2 with respect to P2, we can see that:

3ECONMICS ASSIGNMENT
dQ2/dP2 = -4
This implies that with the increase in the price of the product of firm 2 the demand for the same
decreases as the two variables are negatively related. This in its turn implies that the product of
firm 2 satisfies the law of demand which states that with increase in the price of a commodity the
demand for the commodity decreases.
Answer 3:
The demand function of firm 1:
Q1 = 100 – P1 + (P2/2)
Or, P1 = 100 + (P2/2) – Q1
Total revenue of firm 1:
TR1 = P1Q1 = 100Q1 + (P2Q1/2) – Q12
Therefore, MR1 = 100 + (P2/2) -2Q1
At the equilibrium condition, MR1 = MC1:
So, 100 + (P2/2) – 2Q1 = 10
2.Q1 = 90 + (P2/2)
Q1 = 45 + (P2/4) ---- (a)
Putting the value of Q1 in the function of P1:

4ECONMICS ASSIGNMENT
P1 = 100 + (P2/2) – [45 + (P2/4)]
P1 = 55 + (P2/4) ---- (A)
Equation – A is the best response function for the firm 1.
Answer 4:
The demand function for firm 2 is:
Q2 = 200 – 4P2 + 2P1
Therefore, P2 = 50 + (P1/2) – (Q2/4)
TR2 = P2Q2 = 50Q2 + (P1Q2/2) – (Q22/4)
MR2 = 50 + (P1/2) – (Q2/2)
At the equilibrium situation, MR2 = MC2:
50 + (P1/2) – (Q2/2) = 20
Q2 = 60 + P1 ---- (b)
Putting the value of Q2 in the function of P2:
P2 = 50 + (P1/2) – [(60 + P1)/4]
P2 = 50 -15 + (P1/2) – (P1/4)
P2 = 35 + P1/4 ---- (B)

5ECONMICS ASSIGNMENT
Equation B is the best response function for firm 2.
Answer 5:
Solving A and B:
P1 = 55 + (P2/4)
P1 = 55 + [(35 +P1/4)/4]
4P1 = 220 + 35 + (P1/4)
15P1 = 255*4 = 1020
P1 = 68 which is the equilibrium price of firm 1.
P2 = 35 + (68/4)
P2 = 35 + 17
P2 = 52 which is the equilibrium price for firm 2.
Answer 6:
From equations (a) and (b):
Q1 = 45 + (P2/4)
Q1 = 45 + (52/4) = 45 + 13
Q1= 58

6ECONMICS ASSIGNMENT
Therefore, equilibrium profit of firm 1 is:
Profit = TR1 – TC1
Profit = 68*58 – 10*58 = 3944 – 580 = 3364
Profit of firm 1 is 3364.
Q2 = 60 + P1 = 60 + 68 = 128
Q2 = 128
Therefore, equilibrium profit of firm 2 is:
Profit = TR2 – TC2
Profit = 128*52 – 20*128 = 6656 – 2560 = 4096
Profit of firm 2 is 4096.
Answer 7:
It is evident from the above result that between the two firms, firm 2 enjoys a greater share of
output (128>58) as well as a greater share of the equilibrium profit (4096>3364), than that of
firm 1. It is also able to keep its price lower than that of firm 1 (52<68) and thereby occupies a
greater share of the clientele. Thus, it can be concluded that between the two firms, firm 2 enjoys
a greater market power.