Why shouldn I rely on derived equations for finding maximum profit?
A common error is to apply previously derived equations whenever asked to find the demand that maximizes profit or revenue. It is easy to forget that the equations are derived from specific models. When asked to find the demand that maximizes profit or revenue, the following, more general approach should be used: i. Write the equation for the revenue, TR = REVENUE = price X Demand = pD = D f(D) The relationship between price and demand should be given p=f(D), which is price expressed as a function of demand or volume. ii. To maximize profit, continue by writing the equation for total cost. Total Cost = Fixed Cost + Variable Cost TC = CF + CV, where CV=g(D), usually = # items made X cost per item = D x cV iii. Finally use the equations you have to make the profit equation. By defintion, Profit is All Revenues minus All Costs so, P = TR – TC = D f(D) – [CF +g(D)] iv. To find D that maximizes profit, use calculus again. Take the first derivative of the profit equation to find the values o
