# Finding profit maximizing price and quantity relationship

### Profit maximizing monopolist setting single price Profit Maximization – Short Run pp. 0. Cost,. Revenue,. Profit. (\$s per year ) ATC and AVC to determine profits . Competitive firms determine quantity to. This arises because a competitive firm is too small in relation to its market in . Find the profit-maximizing quantity and price as well as the total profit of this. Marginal Analysis of Revenue and Costs Total Revenue = Price x Quantity Sold To maximize its profit in the short run a perfectly competitive firm (facing a . We use the constraint to substitute forgiving profit as a function of alone: To find the value of that maximizes this function, we differentiate with respect to using the product differentiation rule,: The first-order condition for optimization iswhich may be rearranged as follows: The profit-maximizing quantity,satisfies this equation.

If we knew the specific form of the functions andwe could try to solve the equation to find explicitly. The profit-maximizing price could then be calculated as. But without knowing the functions, we can still interpret the first-order condition. We know that the optimal value of is on the demand curve, soand that is marginal cost MC.

• The Economy
• 7.5.1 The profit-maximizing price

So the first-order condition can be written: The left-hand side of this equation is the slope of the demand curve. We showed in Leibniz 7. Thus the first-order condition tells us precisely that the profit-maximizing choice lies at a point of tangency between the demand and isoprofit curves.

For Beautiful Cars, this is point E in Figure 7.

### The Economy: Leibniz: The profit-maximizing price

The profit-maximizing choice of price and quantity for Beautiful Cars. Expressing the data in terms of dollars The next step in the mental process is to convert the units of output into dollar amounts by multiplying the amount of output times the market price of the output. Axes on the graph are now dollar amount and quantity of variable input. Marginal value product can be described several ways: In Stage II, the value of the output produced by using one more unit of variable input will be decreasing because the quantity of additional output MPP is declining in Stage II -- according to the law of diminishing marginal productivity.

Perfect Competition and Profit Maximization

Marginal input cost MIC is the cost of using an additional unit of variable input; restated, it is the change in total cost due to using additional units of variable input. The MIC will remain constant regardless of how much of the variable input is used. This is based on the assumption that no one business is large enough to influence the market price for the input regardless of how much of the input the business wants to use. What level of output maximizes profit? As more variable input is used, the value of the product resulting from the additional input is declining MVP. When the quantity of variable input reaches the level that the cost of the additional variable MIC exceeds the value of its additional output MVPthe manager should decide to use no more of the variable input during this production period.