Then P=R−C where R is the revenue, and R=xp, the price function multiplied by x. We need to figure out what the function for profit is, find the value of x that maximizes it, and then plug that value of x into our price function. This will give us the price that maximizes the profit.

To obtain the profit maximizing output quantity, we start by recognizing that profit is equal to total revenue (TR) minus total cost (TC). Given a table of costs and revenues at each quantity, we can either compute equations or plot the data directly on a graph.

We know that to maximize profit, marginal revenue must equal marginal cost. This means we need to find C'(x) (marginal cost) and we need the Revenue function and its derivative, R'(x) (marginal revenue). To maximize profit, we need to set marginal revenue equal to the marginal cost, and solve for x.

To obtain the cost function, add fixed cost and variable cost together. 3) The profit a business makes is equal to the revenue it takes in minus what it spends as costs. To obtain the profit function, subtract costs from revenue.

the derivative of Q

The profit-maximizing choice for a perfectly competitive firm will occur at the level of output where marginal revenue is equal to marginal cost—that is, where MR = MC. This occurs at Q = 80 in the figure.

The monopolist’s profit maximizing level of output is found by equating its marginal revenue with its marginal cost, which is the same profit maximizing condition that a perfectly competitive firm uses to determine its equilibrium level of output.

Total profit is maximized where marginal revenue equals marginal cost. In this example, maximum profit occurs at 4 units of output. A perfectly competitive firm will also find its profit-maximizing level of output where MR = MC.

A manager maximizes profit when the value of the last unit of product (marginal revenue) equals the cost of producing the last unit of production (marginal cost). Maximum profit is the level of output where MC equals MR.