Revenue Function Inverse Demand

This is the cournot nash assumption suppose q 2 40.

Revenue function inverse demand. Why it is important. Such a demand function treats price as a function of quantity i e what p 1 would have to be at each level of demand of x 1 in order for the consumer to choose that level of the commodity. In the case of gasoline demand above we can write the inverse function as follows. P q 300 q 4 3.

The demand function inverse and the marginal cost function of a manufacturing supply firm are as follows. The higher the price the lower the demand for gasoline. However if the price is 70 dollars the demand is 5000. P 200 q firms outputs q 1 q 2.

This way we know what price we get from a certain amount of quantity sold. P 4 7q 240 mc 2 6q a write the total revenue function from the inverse demand. Find the revenue function. We know that total revenue is price time quantity so.

The two demand functions are not intrinsically different from. After some research a company found out that if the price of a product is 50 dollars the demand is 6000. Therefore to calculate it we can simply reverse p of the demand function. If we rule out perverse demand price quantity relationship as is shown by the giffen example we can speak of the inverse demand function.

Firm 1 sees itself facing residual demand curve p 200 40 q 1 residual marg. To compute the inverse demand equation simply solve for p from the demand equation. Tr p q q 300 q 4 3 q. In this video we maximize the revenue from a linear demand function by.

To compute theinverse demand function simply solve for p from thedemand function. In this video we maximize the revenue from a linear demand function by finding the vertex of a quadratic function. Revenue curve rmr 1 160 2 q 1 setting this equal. The inverse demand function is useful in deriving the total and marginal revenue functions.

First it should be said that the demand function in this case is price as a function of quantity so let s denote the inverse demand function as. 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. Note that in this linear example the mr function has the same y intercept as the inverse demand function the x intercept of the mr function is one half the value of the demand function and the slope of the mr function is twice that of the. Mc 1 100 mc 2 120 each chooses its output taking the other s output as given.

The marginal revenue function is the first derivative of the total revenue function or mr 120 q. P qd 12 0 5 2qd 24. The inverse demand function is the same as the average revenue function since p ar.