Question 3Assume an open economy characterised by the following equations describing the behaviourof aggregate demand:Consumption function:Ct =Co+C1(Yt-T)Investment function:It bo-birtGovernment spending:Gt=GImports:Mt=mYtExports:Xt=Xwhere co is autonomous consumption,bo is autonomous investment,cis the marginalpropensity to consume,bis the interest sensitivity of investment,m is the propensity toimport.T,G and X are assumed to be exogenously fixed.a)Derive an expression for aggregate demand.b)Represent the equilibrium in the goods market on a diagram with output on the horizontalaxis and aggregate demand on the vertical axis.Clearly label the diagram.c)Solve for equilibrium in the goods market and show that the multiplier is equal to.1-C1+m1Assume that c1=0.5andm1=0.1.The government increases government spending by￡1billion,so that G increases by￡1 billion.Everything else remains the same.d)By how much does output increase?Represent your answer on the diagram in b)andexplain carefully the intuition for the multiplier effect.e)If the central bank had a mandate to stabilise inflation,would you expect output to increaseby this amount following a rise in government spending by￡1 billion?Justify your answer.(15 marks)

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