A firm is a monopolist in the production of a fuel sensor system. It faces monthly market demand that varies according to the equatioin Q=310-0.25P, where P is the price per system in dollars. The firm earns Marginal revenue accordind to the equation MR=1240-8Q & incurs marginal costs according to the function MC=140+2Q, where Q is the quantity of these systems produced.
A. How many of these Systems will the firm produce per month to Maximize profit? What price will the firm charge per system?
Always always always. Maximize where MC=MR. You are given both equations. Use algebra and solve for Q. Plug this optimal Q into the demand equation to get P.
To find the quantity of systems the firm will produce per month to maximize profit, we need to determine the level of output where marginal revenue equals marginal cost.
First, let's calculate the marginal revenue (MR) function:
MR = 1240 - 8Q
Next, let's calculate the marginal cost (MC) function:
MC = 140 + 2Q
To maximize profit, we need to set MR equal to MC and solve for Q:
1240 - 8Q = 140 + 2Q
Combining like terms:
10Q = 1100
Dividing both sides by 10:
Q = 110
So, the firm will produce 110 fuel sensor systems per month to maximize profit.
Next, to find the price the firm will charge per system, we can substitute the value of Q into the demand function:
Q = 310 - 0.25P
110 = 310 - 0.25P
Rearranging the equation:
0.25P = 310 - 110
0.25P = 200
Dividing both sides by 0.25:
P = 800
Therefore, the firm will charge $800 per fuel sensor system to maximize profit.