CompStrat Corporation’s total cost function (where TC is total cost in dollars, and Q is quantity) is TC = 200 + 10Q + 2Q2
If the firm is a price taker and if the price of its product is $20, what is its optimal output?
2.5
How to calculate profit maximize ,loss
Not understand
To find the optimal output for CompStrat Corporation, we need to maximize its profit. Profit is calculated as the difference between revenue and total cost.
The revenue can be calculated by multiplying the price of the product ($20) by the quantity sold (Q):
Revenue = Price * Quantity
R = 20Q
Total cost (TC) is given by the function TC = 200 + 10Q + 2Q^2.
Profit (π) is calculated as:
Profit = Revenue - Total Cost
π = R - TC
Substituting the revenue and total cost functions, we have:
π = 20Q - (200 + 10Q + 2Q^2)
We need to find the value of Q that maximizes profit. This can be done by taking the derivative of the profit function with respect to Q, setting it equal to zero, and solving for Q.
dπ/dQ = 20 - 10 - 4Q
Setting the derivative equal to zero:
20 - 10 - 4Q = 0
Simplifying, we get:
-4Q + 10 = 0
-4Q = -10
Q = -10 / -4
Q = 2.5
Since the quantity cannot be negative for a physical product, the optimal output for CompStrat Corporation is Q = 2.5 units.