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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 functions. Total revenue equals price, P, times quantity, Q, or TR = P×Q. Multiply the inverse ...
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.
Mathematically, a demand curve is represented by a demand function, giving the quantity demanded as a function of its price and as many other variables as desired to better explain quantity demanded. The two most common specifications are linear demand, e.g., the slanted line =
The Hicksian demand function isolates the substitution effect by supposing the consumer is compensated with exactly enough extra income after the price rise to purchase some bundle on the same indifference curve. [2] If the Hicksian demand function is steeper than the Marshallian demand, the good is a normal good; otherwise, the good is inferior.
The inverse demand function is the same as the average revenue function, since P = AR. [4] To compute the inverse demand function, simply solve for P from the demand function. For example, if the demand function has the form = then the inverse demand function would be =. [5]
The elasticity of demand refers to the sensitivity of a goods demand as compared to the fluctuation of other economic factors, such as price, income, etc. The law of demand explains that the relationship between Demand and Price is directly inverse. However, the demand for some goods are more receptive to a change in price than others.
where (,) is the Hicksian demand and (,) is the Marshallian demand, at the vector of price levels , wealth level (or, alternatively, income level) , and fixed utility level given by maximizing utility at the original price and income, formally given by the indirect utility function (,).