14.02 Quiz 2 Solutions Fall 2004 Multiple-Choice Questions

Long Question I (40/100 points)Open Economy IS-LMAssume that the economy is described by the following model:• C = c 0 + c 1 (Y–T), where C is consumption; Y is income; T represents taxes; andc 0 and c 1 are positive constants• I = b 1 Y– b 2 i, where I is investment; i is the interest rate; and b 1 and b 2 are positiveconstants____• G = G , where G is a positive constant• IM = im 1 Y, where IM is imports; and im 1 is a positive constant• X = x 1 Y* , where X is exports; Y* is foreign income (exogenous); and x 1 is a•positive constant 1The LM equation in this economy is i =m 2(m 1 Y – M s ), where M s is moneysupply (M s >1); and m 1 and m 2 are positive constants• Let P*=P=1Assume that the Marshall-Lerner condition is satisfied (that is, following a depreciationof the exchange rate, the trade balance improves).Note, given that IM = im 1 Y and X = x 1 Y* the Marshall-Lerner condition actually doesnot hold. NX are actually equation to x 1 Y* -- ε(im 1 Y), and therefore only the only effect ofa depreciation is a price effect. As the currency depreciates, ε increases and NXdecrease (not increase!). Whether you used the supposition that the Marshall-Lernercondition holds here or if you used the expressions given to you, we gave you full credit.Part I. Fixed Exchange Rate.Assume for now that the real exchange rate is fixed at one (ε = 1). Assume that theinterest rate parity condition holds, and the interest rate in the foreign country is i*.1. Find the expression for equilibrium income. (2 points)Y = C + I + G + X - εIM = c 0 + c 1 (Y–T) + b 1 Y – b 2 i* + G + x 1 Y* – (1)( im 1 Y)1Y =(c 0 – c 1 T – b 2 i* + G+ x 1 Y*)1 − c 1− b 1+ im 1__2. Calculate the change in output (Y), net exports (NX), the domestic interest rate (i),and the real exchange rate if taxes increase by ∆T. Also draw a diagram. (5 points)If there is an increase in taxes, the resulting change in income would be