Final answer:
The equation to determine units needed to achieve a target profit is the difference between total revenue and total cost equals desired profit. In a perfectly competitive market, this equation simplifies to (Price x Quantity) - (Average Cost x Quantity) = Target Profit.
Step-by-step explanation:
The equation to determine how many units must be sold to attain a target profit can be derived from understanding that firms, especially in a perfectly competitive market, earn profit by selling goods at a market price. This profit is calculated as the difference between total revenue and total cost.
To calculate the quantity of output needed for a target profit, one must find the point where total revenue minus total cost equals the desired profit level. Since a perfectly competitive firm must accept the price as given by the market, the formula simplifies to (Price)(×)Quantity produced - (Average cost)(×)Quantity produced = Target Profit. The firm needs to adjust the quantity produced until this equation is satisfied.
To illustrate this with an example, consider a small farmer producing raspberries at $4 per pack. If the average cost to produce one pack is $3, and the farmer aims for a target profit of $40, the equation would be ($4×Quantity) - ($3×Quantity) = $40, which simplifies to $1×Quantity = $40, hence the quantity required is 40 packs.