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Microeconomics Assignement help - Choice & CARP, Comparative statics & Engel Curves !
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Economics - Microeconomics - Choice

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  1. Comparative statics:
    Let's hold prices fixed and allow income to vary; the resulting locus of utility-maximizing bundles is known as the income expansion path. From the income expansion path, we can derive a function that relates income to the demand for each commodity (at constant prices). These functions are called Engel curves.

  2. Comparative statics using the first-order conditions:
    The Slutsky equation can also be derived by differentiating the first-order conditions. Since the calculations are a bit tedious, we will limit ourselves to the case of two goods and just sketch the broad outlines of the argument.
    1. The income expansion path (and thus each Engel curve) is a straight line through the origin. In this case the consumer is said to have demand curves with unit income elasticity. Such a consumer will consume the same proportion of each commodity at each level of income.

    2. The income expansion path bends towards one good or the other-i.e., as the consumer gets more income, he consumes more of both goods but proportionally more of one good (the luxury good) than of the other (the necessary good).

    3. The income expansion path could bend backwards-in this case an increase in income means the consumer actually wants to consume less of one of the goods. For example, one might argue that as income increases I would want to consume fewer potatoes. Such goods are called inferior goods; goods for which more income means more demand are called normal goods.(See Figure)


  3. Comparative statics using revealed preference: Since CARP is a necessary and sufficient condition for utility maximization; it must imply conditions analogous to comparative statics results derived earlier. These include the Slutsky decomposition of a price change into the income and the substitution effects and the fact that the own substitution effect is negative.

  4. The discrete version of the Slushy equation: We can derive the Slutsky equation by differentiating an identity involving Hicksian and Marshallian demands.
 
 

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