Part III: Calculate the Following Questions by Using the Necessary Steps
(4 pts each)
1) A monopolist is deciding how to allocate output between two markets that are separated geographically. Demands for the two markets are P1 = 15 –Q1 and P2 = 25 – 2Q2. The monopolist’s TC is C = 5 + 3(Q1+Q2). What are price, output, profits, and MR if:
a) The monopolist can price discriminate?
b) The law forbids (prohibits) charging different prices in the two regions?
To calculate the price, output, profits, and MR in each scenario, we need to follow these steps:
Step 1: Calculate Total Revenue (TR)
Total revenue is calculated by multiplying the price (P) by the quantity (Q). Recall that TR = P * Q.
a) Price Discrimination:
In this scenario, the monopolist can charge different prices in each market: P1 and P2.
To find P1, we substitute Q1 from demand equation P1 = 15 - Q1.
So, P1 = 15 - Q1.
Likewise, to find P2, we substitute Q2 from the demand equation P2 = 25 - 2Q2.
So, P2 = 25 - 2Q2.
The total revenue is calculated as TR = (P1 * Q1) + (P2 * Q2).
b) Same Price in Both Markets:
In this scenario, the monopolist is not allowed to charge different prices in the two regions. Hence, the price will be the same for both markets.
To find the common price, we set P1 = P2:
15 - Q1 = 25 - 2Q2.
Step 2: Calculate Marginal Revenue (MR)
Marginal revenue is the change in total revenue resulting from a one-unit change in output. It is calculated as the derivative of total revenue with respect to quantity.
In both scenarios, we calculate MR by taking the derivative of TR with respect to Q1 for the first market and with respect to Q2 for the second market.
Step 3: Find the Output Quantity
To find the output quantity, we equate the monopolist's total cost (TC) to the sum of Q1 and Q2.
Step 4: Calculate Profits
Profits are calculated by subtracting total cost (TC) from total revenue (TR).
Now, let's calculate these values for each scenario!