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Mathematically, a supply curve is represented by a supply function, giving the quantity supplied as a function of its price and as many other variables as desired to better explain quantity supplied. The two most common specifications are: 1) linear supply function, e.g., the slanted line =, and
When a non-price determinant of demand changes, the curve shifts. These "other variables" are part of the demand function. They are "merely lumped into intercept term of a simple linear demand function." [14] Thus a change in a non-price determinant of demand is reflected in a change in the x-intercept causing the curve to shift along the x ...
In some cases, there is a unique utility-maximizing bundle for each price and income situation; then, (,) is a function and it is called the Marshallian demand function. If the consumer has strictly convex preferences and the prices of all goods are strictly positive, then there is a unique utility-maximizing bundle.
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 ...
The marginal revenue function is the first derivative of the total revenue function or MR = 120 - Q. 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 ...
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 (,).
Together with the law of supply, the law of demand provides to us the equilibrium price and quantity. Moreover, the law of demand and supply explains why goods are priced at the level that they are. They also help us identify opportunities to buy what are perceived to be underpriced (or sell overpriced) goods or assets. [7]
Supply is often plotted graphically as a supply curve, with the price per unit on the vertical axis and quantity supplied as a function of price on the horizontal axis. This reversal of the usual position of the dependent variable and the independent variable is an unfortunate but standard convention.