Firms and decision makers seek to maximize profits and benefits. To calculate profit maximization price and quantity, the supply function and demand function is needed. Upon having these calculated the equilibrium price needs to be determined. Graphically, it is the price where the supply curve and the demand curve intersects.
To calculate the equilibrium price the supply function and demand function needs to be set equal to each other.
If the demand function is Qd = 10-2P
and the supply function is Qs = -6 + 5p
set 15-2P= -6+5P
and solve for P
21 = 7P
Therefore the price is 3.
To solve the quantity, substitute 3 for P in either the demand function or the supply function.
15-2P = 15-2(3)= 15-6=9
Therefore the profit maximization quantity is 9.
To find the profit maximization levels, other approaches can be taken as well. Profit is simply the Total revenue minus the costs incurred. Therefore by simply doing a multiplication and subtraction approach, the quantity and price of different permutations can yield the profit maximization levels. Profit maximization = Total revenue (TR) – Costs (C).
How to Calculate Profit
Revenue is simply the quantity sold multiplied by the price each unit sold at. If good1 sold for $5 and 20 of them were sold, total revenue would be $100. If it cost $ 30 total for the goods, the profit maximization would make a profit of $70. One has to analyze the different permutations of this though. A firm could sell good1 for $4 and sell 30 of them with a cost of $40 and make a profit maximization profit of $80. Out of the approaches, this method, while the simplest to calculate, it is inefficient to work out each possible set.
Similar to the setting the demand function and the supply function equal to one another is setting marginal revenue equal to marginal cost to find the profit maximization levels. Profit maximization firms wish to have MR = MC. If MR > MC, then profit is increasing and marginal profit is positive. If MR < MC then profit is decreasing and marginal profit is negative. When MR = MC profit has increased to the highest level it can be and marginal profit is now 0. The only place it can go is negative and that is undesirable for a profit maximization.
The primary issue with profit maximizing firm trying to profit maximize is that they do not have access to their marginal revenue nor marginal cost information or are unwilling or incapable of calculating the data. In this case many profit maximization firms will use a simpler equation of : MR = ∆TR/∆Q =(P∆Q+Q∆P)/∆Q=P+Q∆P/∆Q and use the Mark Up approach.