For a monopolist allocating outputs in two different geographical markets Price 1/ P1=15-Q1, P2= 25-2Q2, TC=5+3(Q1+Q2). What are price, output, profits and MR, IF:a. The monopolist can price discriminate?
b.The monopolist prohibited to price discriminate?
answer
To find the price, output, profits, and marginal revenue (MR) for a monopolist with the given cost and demand functions, we can follow these steps:
a. If the monopolist can price discriminate:
Step 1: Calculate the individual demand functions for market 1 (D1) and market 2 (D2):
D1: P1 = 15 - Q1
D2: P2 = 25 - 2Q2
Step 2: Set marginal cost (MC) equal to marginal revenue (MR) for each market to find the optimal output levels:
MR1 = MC: 15 - 2Q1 = 3
MR2 = MC: 25 - 4Q2 = 3
Solving these equations will give us the optimal output levels for market 1 (Q1) and market 2 (Q2).
Step 3: Calculate price (P) by substituting the optimal output levels into the demand functions:
P1 = 15 - Q1
P2 = 25 - 2Q2
Step 4: Calculate profits (π) by subtracting total cost (TC) from total revenue (TR):
TR1 = P1 x Q1
TR2 = P2 x Q2
π = TR1 + TR2 - TC
b. If the monopolist is prohibited from price discrimination:
Step 1: Calculate the total market demand (D) by summing the individual demand functions:
D = D1 + D2
Step 2: Set MC equal to MR to find the optimal output level for the monopolist:
MR = MC: (15 - Q1) + (25 - 2Q2) = 3
Solving this equation will give us the optimal output level (Q).
Step 3: Calculate price (P) by substituting the optimal output level into the total market demand function:
P = 15 - Q1 - 2Q2
Step 4: Calculate profits (π) by subtracting total cost (TC) from total revenue (TR):
TR = P x Q
π = TR - TC
Remember to substitute the values of Q1 and Q2 (from step 2) into the price and profit formulas to get the actual values.