demands for the two markets are p1 = 15 _ q1 & p2= 25-2 q2. the monopolist`s tc is c = 5+3(q1+ q2). what are price, output,profits,& mr if.
a.the monopolist can price discriminate?
b.the law forbids charging d/ f prices in the two regions?
mands for the two markets are p1 = 15 _ q1 & p2= 25-2 q2. the monopolist`s tc is c
To find the price, output, profits, and marginal revenue (MR) for a monopolist in two different scenarios, we can follow these steps:
a. Pricing Discrimination:
Step 1: Determine the monopolist's profit-maximizing output level for each market by equating marginal revenue (MR) to marginal cost (MC). MR is the change in total revenue resulting from selling one additional unit.
In each market, the demand functions are given as:
Market 1: p1 = 15 - q1
Market 2: p2 = 25 - 2q2
The monopolist's total revenue (TR) can be calculated by multiplying the price by the quantity sold:
TR1 = p1 * q1
TR2 = p2 * q2
The marginal revenue (MR) is the derivative of total revenue with respect to quantity sold:
MR1 = d(TR1) / d(q1)
MR2 = d(TR2) / d(q2)
Step 2: Find the monopolist's profit-maximizing output level for each market by setting MR equal to MC. The marginal cost (MC) is given as:
MC = 5 + 3(q1 + q2)
Equating MR1 to MC:
MR1 = MC
d(TR1) / d(q1) = MC
15 - 2q1 - 5 - 3q2 = 0
-2q1 - 3q2 + 10 = 0
-2q1 - 3q2 = -10 (Equation 1)
Equating MR2 to MC:
MR2 = MC
d(TR2) / d(q2) = MC
25 - 4q2 - 5 - 3q1 = 0
-3q1 - 4q2 + 20 = 0
-3q1 - 4q2 = -20 (Equation 2)
Step 3: Solve equations 1 and 2 simultaneously to find the output levels (q1 and q2) for each market.
Once the output levels are obtained, substitute the values of q1 and q2 into the respective demand equations to find the prices (p1 and p2).
The profits can be calculated by subtracting the total cost (TC) from the total revenue (TR) for each market:
Profit1 = TR1 - TC
Profit2 = TR2 - TC
To find MR, differentiate the total revenue equation for each market with respect to quantity sold:
MR1 = d(TR1) / d(q1)
MR2 = d(TR2) / d(q2)
b. Law Forbids Charging Different Prices:
If the law forbids charging different prices in the two regions, the monopolist would have to charge the same price in both markets. Therefore, the prices (p1 and p2) would be equal.
To find the common price, set p1 equal to p2 and solve for q1 and q2 simultaneously.
Once the common output levels (q1 and q2) are obtained, substitute the values of q1 and q2 into the respective demand equation to find the common price (p1 = p2).
The profits and MR can be calculated using the same steps as in part a, but taking into account the common price and output levels.
Note: To provide a more accurate answer, please provide the total quantity demanded (Q) for each market.