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Consider a consumer Whose preferences are dened over bundles of non negative consumption quantities for each of two commodities: Widgets and a composite consumption commodity
Consider a consumer Whose preferences are dened over bundles of non negative consumption quantities for each of two commodities: Widgets and a composite consumption commodity known as \"All Other Goods\". This consumer's preferences are both rational and locally nonsatiated. Denote the price of Widgets by p1, the consumption of Widgets by Q1, the price of \"All Other Goods\" by p2, the consumption of \"All Other Goods\" by qg, and the consumer's income by 3/. Use the composite consumption commodity (that is, \"All Other Goods\") as the numeraire throughout this question. (In other words, assume that p2 : $1 throughout this question. Note that this assumption allows you to interpret the amount of \"All Other Goods\" con sumption as expenditure on \"All Other Goods\\"All Other Goods77 price. 1. Illustrate the total impact of the economic shock on this consumer's optimal consumption decision using an \"indierence curve / budget line'7 diagram. (Assume that the consumer's indifference curves have the conventional \"downward sloping and bowed-in towards the ori- gin\" shape.) Make sure that you indicate the various numerical values of the intercepts of the budget lines with the axes, along with the nu merical values of the preshock and postshock optimal consumption bundles. 2. Illustrate the revealed preference approximation of the Slutsky de composition of the total effect of the economic shock on this con sumer in an \"indifference curve / budget line\" diagram, using the \"preshock consumption bundle, postshock prices'7 approach to this decomposition. (Assume that the consumer's indifference curves have the conventional \"downward sloping and bowedin towards the origin77 shape.) Be sure to identify the numerical values of each commodity in all of the relevant consumption bundles for this decomposition, the movement between bundles that constitutes the substitution effect, the movement between bundles that constitutes the income effect, the size (including both magnitude and sign) of the substitution eect in terms of Widgets, and the size (including both magnitude and sign) of the income effect in terms of Widgets. 3. Does the revealed preference approximation to the substitution eect that you found in part 3 of this question overstate, exactly equal, or understate the true (or Hicksian) substitution effect that it is approx imating? Does the revealed preference approximation to the income effect that you found in part 3 of this question overstate, exactly equal, or understate the true (or Hicksian) income effect that it is approximating? Justify your answers
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