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PROBLEMS FOR ECON 2450Preliminary, continuously updatedNippe Lagerl°fSeptember 12, 20111IntroductionTo be written.AThe IS-LM and Mundell-Fleming modelsProblem A.1Consider an IS-LM model where consumption,C, is given bythe following consumption function:C(Y°T) =a+b(Y°T).(1)wherea >0and0< b <1.(a) GraphC, as given by the function in (1), in a diagram withYon thehorizontal axis. Which is the lowest level of income (Y) that is consistentwith non-negative consumption?Now, let taxes be a function of income:T=°Y,(2)where0< ° <1.(b) How does your answer under (a) change when taxes are given by (2)?1
Recall that the IS curve is given by combinations ofrandYthat satisfyY=C(Y°T) +I(r) +G:(3)(c) Use (1), (2), and (3) to ±nd an expression for the slope of the IS curve(as drawn in a diagram withron the vertical axis andYon the horizontalaxis). That is, ±nd an expression fordrdYalong the IS curve.(d) We know thatI0(r)<0.What does your answer under (c) implyabout the slope of the IS curve? (Is it positive or negative?)Now let the investment function be given byI(r) =±r°°,(4)where± >0and² >0.(e) Say that we think that investment cannot be negative.Then whywould the investment function in (4) be more reasonable than a linear one?(f) Derive an expression for the IS curve when investment is given by (4).Your answer should be an equation withron the left-hand side, andYandexogenous parameters on the right-hand side.(g) Draw the graph of the IS curve derived under (f). You will ±nd thatpoints on the IS curve cannot fall below some level ofY. (Hint:rgoes toin±nity asYapproaches that level from above.)Derive an expression forthat minimum level, and explain intuitively whyYcannot fall below it.Problem A.2Consider the so-called Mundell-Fleming (or IS*-LM*)model, which describes a small open economy.The exchange rate, denotede, is the amount of foreign currency, say =Y(Japanese yen), that one must pay to buy one unit of the domestic currency,say $. A highethus means that the domestic currency is expensive: foreign-ers pay a lot for the domestic currency, and domestic agents pay little for theforeign currency.LetPfbe the price of foreign goods, andPdthe price of domestic goods.Also, let³be the spending share on domestic goods in the consumption2
basket of the typical consumer in the domestic country, and1°³the spendingshare on foreign goods, where0< ³ <1.(a) To the domestic consumer the price of a foreign good in terms of thedomestic currency isPf=e. Explain why.