A firm with market power has an individual consumer demand of Q = 20 − 4P and costs of C = 4Q.What is the optimal amount of this product to package in a single block?
A) 2
B) 3
C) 4
D) 5

Question

Quizplus · Accepted Answer

To find the optimal amount of product to package in a single block, we need to maximize the firm's profit. The profit function is given by:
Profit = Total Revenue - Total Cost
Total revenue is equal to the price times the quantity sold. Since the firm has market power, it can set the price. The inverse demand function tells us that the price that consumers are willing to pay for each unit is equal to:
P = (20 - Q)/4
Therefore, the total revenue function is:
Total Revenue = P * Q = (20 - Q)/4 * Q = 5Q - 0.25Q^2
Total cost is given by the function C = 4Q.
Therefore, the profit function is:
Profit = 5Q - 0.25Q^2 - 4Q = Q - 0.25Q^2
To find the optimal amount of Q, we need to take the derivative of the profit function with respect to Q and set it equal to zero. This gives us:
d(Profit)/dQ = 1 - 0.5Q = 0
Solving for Q, we get:
Q = 2
Since the second derivative of the profit function is negative at Q = 2, we know that this is a maximum. Therefore, the optimal amount of product to package in a single block is 2.

A Firm with Market Power Has an Individual Consumer Demand