Total Revenue Function From Demand Function

Letting tr be the total revenue function.

Total revenue function from demand function. In this video we maximize the revenue from a linear demand function by. π r c 1 2 q. Note we are measuring economic cost not accounting cost. Marginal cost marginal revenue and marginal profit all involve how much a function goes up or down as you go over 1 to the right this is very similar to the way linear approximation works.

If x is the number of units produced and sold and p is its unit price then the total revenue function r x is defined as r x px where x and p are positive. Revenue is the amount realised on a commodity when it is produced and sold. Because marginal revenue is the derivative of total revenue we can construct the marginal revenue curve by calculating total revenue as a function of quantity and then taking the derivative. If r x px be the revenue function then.

Then you will need to use the formula for the revenue r x p x is the number of items sold and p is the price of one item. However if the price is 70 dollars the demand is 5000. Where q is the quantity of output sold and p q is the inverse demand function the demand function solved out for price in terms of quantity demanded. Since profit is the difference between revenue and cost the profit functions the revenue function minus the cost function.

Demand revenue cost profit demand function d q p d q in this function the input is q and output p q independent variable p dependent variable recall y f x p d q the price at which q units of the good can be sold unit price p most demand functions quadratic project 1 demand curve which is the graph of d q is generally downward sloping why. The equation for the cost function is. To calculate total revenue we start by solving the demand curve for price rather than quantity this formulation is referred to as the inverse demand. In this video we maximize the revenue from a linear demand function by finding the vertex of a quadratic function.

Find the revenue function. In symbols π r c p q f v q.