Price Theory Analysis

The assignment content discusses price theory and market power, focusing on two firms (Firm 1 and Firm 2) with different demand functions. The equilibrium prices are determined by solving the response functions, resulting in P2 = $36 and P1 = $54. The equilibrium quantities are computed as Q1 = 64 and Q2 = 164, respectively. The equilibrium profits for Firm 1 and Firm 2 are $2,816 and $2,624, respectively. Market power is calculated using the formula (P-MC)/P, revealing that Firm 1 has a higher market power of 81.48% compared to Firm 2's 44.44%, indicating that Firm 1 has more control over prices due to its inelastic demand.

PRICE THEORY
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PRICE THEORY
Question 1
The demand function for Firm 1 is indicated below.
Q1 = 100 –P1 + P2/2
Differentiating the above with respect to P2, we get
(dQ1/dP2) = 1/2
On the basis of the above it is apparent that as P2 increases, Q1 also increases. This implies that
Q1 and Q2 are substitutes and not complements.
Question 2
The demand function for Firm 2 is indicated below.
Q2=200-4P2+2P1
Differentiating the above with respect to P2, we get
(dQ2/dP2) = -4
The above result implies that as the price P2 tends to increase by 1 unit, the corresponding
decrease in quantity Q2 would be 4 units. Hence, the law of demand is satisfied and adhered to.
Question 3
The function for Q1is given as
Q1 = 100 –P1 + P2/2
Also, Total revenue for firm 1(TR1) = P1Q1 = P1*(100 –P1 + P2/2) = 100P1-P12 + 0.5P1P2
Also, MR1 = (dTR1/dP1) = 100 -2P1 +0.5P2
Further, MC1 = $10

PRICE THEORY
For response function, MR1 = MC1
Hence, 100 -2P1 +0.5P2 = 10
Solving the above we get, 2P1 - 0.5P2 = 90
Question 4
The function for Q2is given as
Q2=200-4P2+2P1
Also, Total revenue for firm 1(TR2) = P2Q2 = P2*(200 –4P2 + 2P1) = 200P2-4P22 + 2P1P2
Also, MR2 = (dTR2/dP2) = 200 -8P2 + 2P1
Further, MC2 = $20
For response function, MR2 = MC2
Hence, 200 + 2P1 -8P2 = 20
Solving the above we get, P1 - 4P2 = -90
Question 5
The equilibrium prices can be determined by simultaneously solving the two response functions
as derived in Q 3 and Q4. Solving the same, we get P2 = $ 36 and P1 = $54
The equilibrium quantities can be computed as indicated below.
Q1 = 100 –P1 + P2/2 = 100 -54 +(36/2) = 64
Q2=200-4P2+2P1 = 200 -4*36 +2*54 = 164
Hence, the equilibrium quantities for firm 1 and firm 2 are 64 and 164 respectively.

PRICE THEORY
Question 6
The respective equilibrium profits can be computed in the manner shown below.
Profit (Firm1) = P1Q1 – MC1Q1 = (54*64) – (10*64) = $ 2,816
Profit (Firm2) = P2Q2 – MC2Q2 = (36*164) – (20*164) = $ 2,624
The equilibrium profits for Firm1 and Firm 2 are $2,816 and $ 2,624 respectively.
Question 7
The market power is given by the following formula.
Market Power = (P-MC)/P
Market Power (Firm1) = (54-10)/54 = 81.48%
Market Power (Firm 2) = (36-20)/36 = 44.44%
From the above computation, it is apparent that the higher market power is possessed by Firm 1
owing to demand of Firm 1 being inelastic in comparison with Firm2.