A monopolist is deciding how to allocate output between two markets thata separated geographically. Demands for two market are P1=15-Q1 and P2=25-2Q2. The monopolist's TC is C=5+3(Q1+Q2).What are*price
*output
*profit
*MR
Ifa)the monopolis can price discriminate?
b)the law prohabits charging different price in two regions?
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To find the price, output, profit, and MR for a monopolist, we will use the given demand functions, cost function, and the formula for marginal revenue. Let's break it down step by step:
1. Price:
To find the price, we need to equate the quantity demanded (Q) in each market to the given demand functions. The demand functions are P1 = 15 - Q1 and P2 = 25 - 2Q2.
a) For Market 1 (P1):
Set P1 = 15 - Q1
b) For Market 2 (P2):
Set P2 = 25 - 2Q2
2. Output:
The monopolist's output is the sum of the quantities demanded in both markets. Thus, we need to find Q1 (quantity demanded in Market 1) and Q2 (quantity demanded in Market 2).
3. Profit:
The monopolist's profit is the difference between total revenue (TR) and total cost (TC). Total revenue is calculated by multiplying the price (P) by the output (Q).
Profit = TR - TC
4. Marginal Revenue (MR):
Marginal revenue is the change in total revenue when the output is increased by one unit. It can be calculated using the formula:
MR = dTR/dQ
Now, let's solve each part according to the given information:
a) If the monopolist can price discriminate:
Price Discrimination occurs when a monopolist charges different prices to different customers based on their willingness to pay. To determine if price discrimination is possible, we need to check if the monopolist can separate the markets and charge different prices in each market while preventing arbitrage.
b) If the law prohibits charging different prices in two regions:
In this case, the monopolist will need to set the same price for both markets.
Please note that I will need additional information about the quantity the monopolist is producing or any other specific instructions in order to calculate the outputs, profits, and MR.