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The marginal revenue function has twice the slope of the inverse demand function. [9] The marginal revenue function is below the inverse demand function at every positive quantity. [10] The inverse demand function can be used to derive the total and marginal revenue functions. Total revenue equals price, P, times quantity, Q, or TR = P×Q.
P(Q) = inverse demand function, and thereby the price at which Q can be sold given the existing demand C(Q) = total cost of producing Q. = economic profit. Profit maximization means that the derivative of with respect to Q is set equal to 0: ′ + ′ = where
To compute the inverse demand equation, simply solve for P from the demand equation. [12] For example, if the demand equation is Q = 240 - 2P then the inverse demand equation would be P = 120 - .5Q, the right side of which is the inverse demand function. [13] The inverse demand function is useful in deriving the total and marginal revenue ...
A demand curve is a graph depicting the inverse demand function, [1] a relationship between the price of a certain commodity (the y-axis) and the quantity of that commodity that is demanded at that price (the x-axis).
A synonymous term is uncompensated demand function, because when the price rises the consumer is not compensated with higher nominal income for the fall in their real income, unlike in the Hicksian demand function. Thus the change in quantity demanded is a combination of a substitution effect and a wealth effect.
This can also be represented as a derivative when the change in quantity sold becomes arbitrarily small. Define the revenue function to be [13] = (), where Q is output and P(Q) is the inverse demand function of customers. By the product rule, marginal revenue is then given by
The consumer demand for mineral water at price is denoted by (); the inverse of is written and the market-clearing price is given by = (), where = + and is the amount supplied by proprietor . Each proprietor is assumed to know the amount being supplied by his or her rival, and to adjust his or her own supply in the light of it to maximize his ...
() = inverse demand function; the price at which can be sold given the existing demand = total cost of producing . = economic profit; This is done by equating the derivative of with respect to to 0. The profit of a firm is given by total revenue (price times quantity sold) minus total cost: