For a monopolist's product, the demand function is p equals 75 minus 0.05 q and the cost function is c equals 700 plus 25 q, where q is number of units, and both p and c are expressed in dollars per unit. At what level of output will profit be maximized? At what price does this occur, and what is the profit?

The correct answer is at 500 units offering at $50, the monopolist will have a profit equal to $11,800.

Step-by-step explanation:

For a monopolist's product, where q is number of units, and both p and c are expressed in dollars per unit,

Demand function is p = 75 - 0.05 × q

Revenue function is R = Demand function × Quantity = 75 × q - 0.05 ×

Cost function is c = 700 + 25 × q

Profit function is given by π = R - c = 75 × q - 0.05 × - 700 - 25 × q

⇒ π = -0.05 × + 50 × q - 700

Now for profit to be maximum ⇒ π = 0

⇒ -0.1 ×q + 50 = 0

⇒ 0.1 × q = 50

⇒ q = 500.

We can easily see that the second order derivative is negative hence telling us that the profit is maximum.

There at 500 units of the product the monopolist will have his maximum output.

Price at which the profit occurs = 75 - 0.05 × 500 = $50

Profit = -0.05 × 500 × 500 + 50 × 500 - 700 = -12500 + 25000 -700 = $11800

can you give me more detail on this! ?

step-by-step explanation:

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