Question

A firm is planning to manufacture a new product. The sales department estimates that the quantity that can be sold depends on the selling price. As the selling price is increased, the quantity that can be sold decreases. Numerically they estimate:

P = $35.00 - 0.02Q
where P =selling price per unit
Q = quantity sold per year
On the other hand, the management estimates that the average cost of manufacturing and selling the product will decrease as the quantity sold increases.
They estimate
C = $4.00Q + $8000
where C = cost to produce and sell Q per year
The firm's management wishes to produce and sell the product at the rate that will maximize profit, that is, where income minus cost will be a maximum. What quantity should the decision makers plan to produce and sell each year?"

Answer 1

To maximize profit, the firm should produce at the quantity where marginal revenue equals marginal cost. Analyzing cost and revenue curves is critical. An example shows a profit at a quantity of 40 units with certain revenue and cost figures.

The firm's management seeks the optimal quantity of a new product to maximize profit, where profit is defined as total revenue minus total cost. To attain the highest profit, the firm should determine the output level where the difference between total revenue and total cost is greatest. Considering the selling price per unit (P) decreases with higher quantities sold (Q) and the average cost of manufacturing and selling (C) decreases with an increase in Q, the management must calculate the quantity at which marginal revenue equals marginal cost.

An example scenario indicates that with a quantity of 40 units at a price of $16, the firm makes an economic profit, as this price is above the average cost. The total revenue at this point is $640, and the total cost is $580, resulting in a profit of $60. It's essential to thoroughly analyze the cost and revenue curves to determine the exact quantity that maximizes profit.