# Straight with slope 65 rajan has well behaved

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straight, with slope = -6/5 Rajan has well-behaved preferences, and his optimal bundle contains 10 scones. b) (4) Illustrate his optimal bundle in your diagram for (a); label it A. Why is this choice optimal? What conditions does it satisfy? Ans: Why optimal? Max's utility on his feasible set; Two conditions: i) MRS=(price of bananas)/(price of scones); ii) ii) all income is spent - bundle is on budget line. Picture: needs an IC tangent to BL at point corresponding to 10 scones. c) (2) How many kg of bananas does he buy? (Show how you derived this number.)

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Name___________________________________________________________ Student number _________________________________ Lab LF0__________ Economics 203 (F01), 2005; midterm 1 Page 3 of 5 Ans: derivation - uses budget constraint: 0.6 0.5 10 b s x x + = . Substituting in for the value of 10 s x = yields 1 50/6 25/3 8 3 b x = = = kg of bananas. d) (3) Suppose the price of bananas doubles. In your diagram for (a), identify the total effect of this price increase on Rajan's optimal choice. (Label his new optimal bundle G.) Ans: if price of bananas doubles, BL pivots about vertical axis; new horizontal intercept is 100/12=25/3. New optimal bundle is on new BL, where IC is tangent to BL. Notice: there is no need for the number of scones to be the same in bundles A and G; in fact, it would be unusual if the number did not change. e) (6) Briefly explain the meaning of the following terms: i) the substitution effect of the price change on both goods; Ans: the substitution effect measures the change in the quantity purchased in response to a change in relative prices. The doubling of the price of bananas, with a constant price of scones, means that bananas are now more expensive relative to scones. Because the individual is willing to make trade-offs between the two goods (the IC is negatively sloped), the increased relative price of bananas should lead Rajan to purchase more scones, and fewer bananas.
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