Question 1

Consider a consumer whose preferences are defined over bundles of non-negative con- sumption 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 non-satiated. Denote the price of Widgets by pi, the consumption of Widgets by gi, the price of "All Other Goods" by pa, the consumption of "All Other Goods" by 42, and the consumer's income by y. Use the composite consumption commodity (that is, "All Other Goods" ) as the numeraire throughout this question. (In other words, assume that py = $1 throughout this question. Note that this assumption allows you to interpret the amount of "All Other Goods" consumption as expenditure on "All Other Goods", because q2 = 1q2 = paqz.) Suppose that this consumer's uncompensated demand function for Widgets is given by 41 (P1, y; p2 = 1) = (0.02) y - (2) p1. (Uncompensated demands are also known as Marshallian demands or Walrasian de- mands.) Initially, this consumer has an income of $6,500 and faces a Widget price of $50 per Widget. Following an economic shock, the Widget price rises to $60 per widget. This economic shock has no impact whatsoever on either this consumer's income or the "All Other Goods" price. 1. Illustrate the total impact of the economic shock on this consumer's optimal con- sumption decision using an "indifference curve / budget line" diagram. (Assume that the consumer's indifference curves have the conventional "downward sloping and bowed-in towards the origin" shape.) Make sure that you indicate the various numerical values of the intercepts of the budget lines with the axes, along with the numerical values of the pre-shock and post-shock optimal consumption bundles. (8 marks.) 2. Illustrate the revealed preference approximation of the Slutsky decomposition of the total effect of the economic shock on this consumer in an "indifference curve / budget line" diagram, using the "pre-shock consumption bundle, post-shock prices" approach to this decomposition. (Assume that the consumer's indifference curves have the conventional "downward sloping and bowed-in towards the origin" 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 effect in terms of widgets, and the size (including both magnitude and sign) of the income effect in terms of widgets. (10 marks.) 3. Does the revealed preference approximation to the substitution effect that you found in part 3 of this question overstate, exactly equal, or understate the true (or Hick- sian) substitution effect that it is approximationg? Does the revealed preference approximation to the income effect that you found in part 3 of this question over- state, exactly equal, or understate the true (or Hicksian) income effect that it is approximationg? Justify your answers. (7 marks.)