uppose the demand for these jets is given by the equation:
P = 3000 - Q,
where Q denotes the quantity of jets, and P denotes its price.
So that the marginal revenue facing the firm is:
MR = 3000 - 2Q.
The marginal cost of Lockheed Martin is given by the equation:
MC(Q) = 2Q
while the average variable cost is:
AVC(Q) = Q
Further it is known that Lockheed Martin has fixed costs of 500.
Suppose Lockheed sets one price for all its customers, what is the profit maximizing quantity in this case?
I found
Q*=750
P*=2250
WHAT IS FIRM'S PROFIT???????????
To find the firm's profit, we need to calculate the total revenue and total cost.
Total Revenue (TR) is equal to the price per unit (P) multiplied by the quantity (Q). In this case, the price is given by the equation P = 3000 - Q. Therefore, TR = P * Q.
Total Cost (TC) consists of fixed costs (FC) and variable costs (VC). The fixed costs for Lockheed Martin are given as 500. The variable costs can be calculated using the average variable cost (AVC) equation, which is AVC(Q) = Q. Variable costs (VC) are equal to AVC multiplied by the quantity (Q), so VC = Q * AVC.
Profit (π) is equal to total revenue (TR) minus total cost (TC). Therefore, π = TR - TC.
Now, let's calculate the profit.
Total Revenue:
TR = P * Q
TR = (3000 - Q) * Q
TR = 3000Q - Q^2
Total Cost:
TC = FC + VC
TC = 500 + (Q * AVC)
TC = 500 + (Q * Q)
Profit:
π = TR - TC
π = (3000Q - Q^2) - (500 + Q^2)
π = 3000Q - Q^2 - 500 - Q^2
π = 3000Q - 2Q^2 - 500
Now, we need to find the quantity (Q) that maximizes the profit. To find this, we take the derivative of the profit function with respect to Q and set it equal to zero:
dπ/dQ = 3000 - 4Q = 0
Solving for Q gives us Q* = 750.
Now that we have the quantity, we can substitute it back into the profit function to find the maximum profit:
π = 3000Q - 2Q^2 - 500
π = 3000(750) - 2(750^2) - 500
π = 2,250,000 - 1,125,000 - 500
π = 1,124,500
Therefore, the firm's profit is $1,124,500.