|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| In [[microeconomics]], a consumer's '''Marshallian demand function''' (named after [[Alfred Marshall]]) specifies what the consumer would buy in each price and wealth situation, assuming it perfectly solves the [[utility maximization problem]]. Marshallian demand is sometimes called '''Walrasian demand''' (named after [[Léon Walras]]) or '''uncompensated demand function''' instead, because the original Marshallian analysis ignored [[wealth effect]]s.
| | Let me initial start by introducing myself. My name is Boyd Butts although it is not the title on my beginning certification. To do aerobics is a factor that I'm completely addicted to. My day job is a meter reader. Puerto Rico is exactly where he's always been living but she needs to transfer simply because of her family.<br><br>Feel free to surf to my weblog - [http://www.ninfeta.tv/blog/66912 at home std testing] |
| | |
| According to the utility maximization problem, there are ''L'' commodities with prices ''p''. The consumer has wealth ''w'', and hence a set of affordable packages
| |
| | |
| :<math>B(p, w) = \{x : \langle p, x \rangle \leq w\},</math>
| |
| | |
| where <math> \langle p, x \rangle </math> is the [[inner product]] of the prices and quantity of goods. The consumer has a [[utility function]]
| |
| | |
| :<math>u : \textbf R^L_+ \rightarrow \textbf R.</math>
| |
| | |
| The consumer's '''Marshallian demand correspondence''' is defined to be
| |
| | |
| :<math>x^*(p, w) = \operatorname{argmax}_{x \in B(p, w)} u(x).</math>
| |
| | |
| If there is a unique utility maximizing package for each
| |
| price and wealth situation, then it is called the '''Marshallian demand function'''. See the [[utility maximization problem]] entry for a discussion of this definition.
| |
| | |
| ==Example==
| |
| If there are two commodities, and the consumer has the utility function <math>U(x_1,x_2) = x_1^{0.5}x_2^{0.5}</math> (Cobb-Douglas), he chooses to spend half of its income on each commodity, and its Marshallian demand function is the following:
| |
| | |
| :<math>x(p_1,p_2,w) = \left(\frac{w}{2p_1}, \frac{w}{2p_2}\right).</math> | |
| | |
| In general, an agent with Cobb-Douglas preferences, given by <math>U(x_1,x_2) = x_1^{a}x_2^{1-a}</math>, will use a constant share of his income in order to buy each of the two commodities, as follows:
| |
| | |
| :<math>x(p_1,p_2,w) = \left(\frac{aw}{p_1}, \frac{(1-a)w}{p_2}\right).</math>
| |
| | |
| If we are in a more general case, i.e. <math>U(x_1,x_2) = x_1^{a}x_2^{b}</math>, we have:
| |
| | |
| :<math>x(p_1,p_2,w) = \left(\frac{aw}{(a+b)p_1}, \frac{bw}{(a+b)p_2}\right).</math>
| |
| | |
| ==See also==
| |
| * [[Hicksian demand function]]
| |
| * [[Utility maximization problem]]
| |
| | |
| ==References==
| |
| *{{cite book |authorlink=Andreu Mas-Colell |last=Mas-Colell |first=Andreu |last2=Whinston |first2=Michael |lastauthoramp=yes |last3=Green |first3=Jerry |year=1995 |title=Microeconomic Theory |location=Oxford |publisher=Oxford University Press |isbn=0-19-507340-1 }}
| |
|
| |
| [[Category:Demand]]
| |
| [[Category:Consumer theory]]
| |
Let me initial start by introducing myself. My name is Boyd Butts although it is not the title on my beginning certification. To do aerobics is a factor that I'm completely addicted to. My day job is a meter reader. Puerto Rico is exactly where he's always been living but she needs to transfer simply because of her family.
Feel free to surf to my weblog - at home std testing