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deriving demand functions

# deriving demand functions - 1 Deriving demand functions and...

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Unformatted text preview: 1 Deriving demand functions and indirect util- ity functions This note reviews brie&amp;amp;y how we can derive demand functions directly from consumer preferences and how we can express consumer preferences directly in terms of prices and income (indirect utility). To illustrate the logic, we will consider a consumer whose preferences are given by a utility function U ( X;Y ) = X 1 = 2 Y 1 = 2 : The prices are given by p x and p y and the income level of the consumer is I: 1.1 Deriving demand functions Remember that the choice of optimal consumption bundle by the consumer is characterized by two conditions. First, we have that (for interior solutions) MU x MU y = p x p y : That is, the relative valuation of the two products by the consumer has to equal the relative cost of the two products. Second, we have that p x X + p y Y = I: That is, all income gets spent. We have two equations and two unknowns, where the unknowns are the amount of X and Y purchased in equilibrium. You are used to solving such problems for given prices and income, where you just plug in the prices and income and get the solution. A demand function does the same, but we simply derive the solution for any prices and income. If you are confused as to where you want to go, simply remember the denition of a demand function: An expression for the amount of X demanded as a function of prices and income. Thus, we want expressions such as X = F ( p x ;p y ;I ) and Y = F ( p y ;p x I ) : Step 1: solve MU x MU y : The only step in solving demand functions that is problem-specic is the relative valuation of the two goods by the consumer, as captured by the consumers mar-...
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deriving demand functions - 1 Deriving demand functions and...

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