To maximize profit, you need to sell your output at the highest price (analyze the validity of this statement)

Most certainly selling outputs of a company at the highest
price will not result in highest profit. As a matter of fact trying to sell product at
very high prices may result in the highest losses rather than highest
profits.

The profit of a company is the surplus of the
total revenue over the total cost. A high price will give a company a high revenue per
unit sold. But a high price is also most likely to reduce the demand and hence the total
number of unit sold. In this way maximum total revenue may increase with increase in
price, but after certain point level of price it begins to fall. The firm is likely to
make maximum profit at a point where the price is equal to or less than the price that
corresponds to the price that gives maximum revenue.

Even
the price that gives the maximum revenue will not give maximum profit if this price is
less than the marginal cost of the product. In such cases the company's saving in cost
by reducing total revenue is more than the amount of total revenue lost. This means that
surplus of total revenue over total cost, which represents the profit, will increase by
reducing total revenue.