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# PS 5 with Answers - METU Department of Economics Econ 202...

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1/8 METU Department of Economics Econ 202 Macroeconomic Theory Instructor: Şirin Saraçoğlu - Ebru Voyvoda 2010-2011 Spring Semester Problem Set 5 with Answers Question 1: Casinolandia (C) and Marcolandia (M) are two close countries that trade with each other but not with the rest of the world. We can extend our multiplier model to a two country model where variables with the subscript C refer to Casinolandia and variables with the subscript M to Marcolandia. Each country is characterized by the following equations, ± ² ³´ ± µµµµ¶µµµµ·¸ ± ² ¹ ± ´µµµµ¶µµµµ· ± ² · ± µµµµ¶µµµµº ± ² º ± µµµµ¶µµµµ» ± ² ¼ where IM are imports and m is the marginal propensity to import and the subscript i is either C or M depending on whether we refer to Casinolandia or Marcolandia. Also note that investment and government spending are exogenous and that taxes are zero in both countries. The usual equilibrium condition applies here, ´ ± ² ½ ± ² ± ¾ · ± ¾ º ± ¾ ¿ ± À ·¸ ± Note that in a two country model, by definition, ¿ Á ² ·¸ Â and µ¿ Â ² ·¸ Á . a) Derive the reduced form equation of the equilibrium level of output of Casinolandia, ´ Á . That is, derive the equation for ´ Á as a function of µ· Á , º Á and ´ Â (note that from C's perspective, ´ Â is exogenous) and parameters. Similarly, derive the equation for ´ Â as a function of µ Â , º Â , · Â and ´ Á and parameters. Ã Ä ² Å Ä ¾ Æ Ä ¾ Ç Ä ¾ È Ä À ÆÉ Ä ² Å Ä ¾ Æ Ä ¾ Ç Ä ¾ ÆÉ Ê À ÆÉ Ä ² Ë Ä Ã Ä ¾ Æ Ä ¾ Ç Ä ¾ Ê Ê Ã Ê À Ê Ä Ã Ä Ã Ä ² Ì Ì À Ë Ä ¾ Ê Ä Ä ¾ Ç Ä ¾ Ê Ê Ã Ê )µµµµµ¶µµµµµµÃ Ê ² Ì Ì À Ë Ê ¾ Ê Ê Ê ¾ Ç Ê ¾ Ê Ä Ã Ä ) b) Let µ· Á ² º Á ² Í¼µ¶µ· Â ² º Â ² Î¼µ¶µµ³ Á ² ³ Â ² ¼ÏÐµ¶µ¹ Á ² ¼ÏÑµ¶µ¹ Â ² ¼ÏÒ . What are the equilibrium levels of output in the two countries? (Note that when solving this you should get two (easy to solve) equations and two unknowns, ´ Á and ´ Â ) What are the two countries current accounts respectively? Ã Ä ² ÓÔÔ ¾ ÕÃ Ê µµµµµ¶µµµµµµÃ Ê ² ÌÕÔ ¾ ÔÏ ÕÃ Ä µµµ²ÖµµµµµÃ Ä ² Ì×ÔÔµµ¶µµÃ Ê ² ×ÔÔ Current accounts; ÅØ Ä ² È Ä À ÆÉ Ä ² ÆÉ Ê À ÆÉ Ä ² Ê Ê Ã Ê À Ê Ä Ã Ä ² ÕÔµµ ²Ö µµµÅØ Ê ² ÀÕÔ c) Show that, in equilibrium, investment equals savings in both countries. Ã ² Ù ² Å ¾ Æ ¾ Ç ¾ È À ÆÉµµµµµµµÚÛÜµµµµµµÃ ² Å ¾ Ý ÞßàáÚâã ¾ äµµ ²Ö Æ ² Ý ÞßàáÚâã ¾ (ä À Ç) À (È À ÆÉ) ² Ý ÞßàáÚâã ¾ Ý åæáãßÛÊãÛâ ¾ Ý çæßãàåÛ Note that the current account is equal to È À ÆÉ and due to the balance of payments

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2/8 methodology; the current account is equal to minus the capital account. Since capital account is
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PS 5 with Answers - METU Department of Economics Econ 202...

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