Pieal aational incotne (GDP) is a doend econceny (withoat trade) be wiven by Y=C+1+G where Y is real GDP, C is consumption, I is (prinate) irvotment, and G is gowrennent expenditure. We assume that consumers will spend on eonsumption goods in propertion consume (b), such that C=Cn+c+P+ their only alternative in to kave, wo the margetial propernify fo stre in o =1 b. Firms' invertments are negatively related to the real imerest rate ( M ), such that t=f2iR where l is exogenoes investment, and t>0 reflecting that bigher interest tates caved out firmn' ievertments. Goverament expenditures afe determinnd eockrosody, and afe equal to G=G In the muecy marlot, the supply abd dranand foe moary mest be oqual. The sipply of mobey is determined exosenotsely, and is net at M=M2 The demand for money (or liquinity, 2 ) is determined both by the demabel foe mabey for transactional purposs and the demand for mober as a sake haven, which is inversely proportioal to the demand for boble (sisce buads yield a rate or setarn, while motsy boliliags do not). We can therefoee write the drmand foir mosry as L=1Y+(H2hF) with H>0,k>0 and h>0. (b) Uing, equations (7) and (8), detive an exjresing for the liarear t.M4 earve. (c) Using the lierear exptesoinas for the LM curve, find as aloritabe (symbilc) solution fot the real national income (Y) in terma of R, the farameterk and the exnermotis values. Sulstifute this expirencios in for Y is the 15 to drrive an algetiraic (symbulic) coppecosion for the equilibrium real interest rate (2) in terne of enly the parametern and exogenous valurs. (d) Now, axsume the following values for the paranactes and raograsias valuos in this model: C=128;e=0.6;I=200;i=100;G=250;3=500t+46; H=126; and h=700. Ving the alpebraic expestion derived in 2(c) abone, find rgaantitative solutions fot the equilibrium real intered rate (R) and the mal national Y=C+I+G where Y is real GDP, C is consumption, I is (private) investment, and G is government expenditures. We assume that consumers will spend on consumption goods in proportion to their income, with that proportion determined by consumers' maryinal propensity to constme (b), such that C=Cn+oY where C>0 is an exogenously determined minimal level of eonstmption expenditures, and 00 reflecting that higher interest rates crowd out firms' invertments. Government expenditures are determined ecogenously, and are equal to G=G In the mobes nuricet, the supply and demand for money mast be equal. The aupply of monny in determined exogenously, and is set at M=M The demand fot money for liquality, b ) is deturmined both by the slemand for naoney for trunactional purposen and the demand for money a a safe haven, which is inversely holdings do not). We can thisefore write the demand for maney as L=fY+(HHhR) with H=0,k>0 and h>0. (a) Using equations (3), (4), (5), and (6), derive an expression for the linear IS curve. (b) Using equations (7) and (8), derive an expression for the linear LM curve. (c) Using the linear expressions for the LM curve, find an algebraic (symbolic) solution for the real national income (Y) in terms of R, the parameters, and the exogenous values, Substitute this expression in for Y in the IS to derive an algebraic (symbolic) expression for the equilibrium real interest rate (R) in terms of only the parameters and exogenous values. (d) Now, assume the following values for the parameters and exogenous values in this model: C=128;c=0.6;I=200;i=100;G=250;M=500;t=0.6; H=126; and h=700. Using the algebraic expressions derived in 2(c) above, find quantitative solutions for the equilibrium real interest rate (R) and the real national income (Y). Pieal aational incotne (GDP) is a doend econceny (withoat trade) be wiven by Y=C+1+G where Y is real GDP, C is consumption, I is (prinate) irvotment, and G is gowrennent expenditure. We assume that consumers will spend on eonsumption goods in propertion consume (b), such that C=Cn+c+P+ their only alternative in to kave, wo the margetial propernify fo stre in o =1 b. Firms' invertments are negatively related to the real imerest rate ( M ), such that t=f2iR where l is exogenoes investment, and t>0 reflecting that bigher interest tates caved out firmn' ievertments. Goverament expenditures afe determinnd eockrosody, and afe equal to G=G In the muecy marlot, the supply abd dranand foe moary mest be oqual. The sipply of mobey is determined exosenotsely, and is net at M=M2 The demand for money (or liquinity, 2 ) is determined both by the demabel foe mabey for transactional purposs and the demand for mober as a sake haven, which is inversely proportioal to the demand for boble (sisce buads yield a rate or setarn, while motsy boliliags do not). We can therefoee write the drmand foir mosry as L=1Y+(H2hF) with H>0,k>0 and h>0. (b) Uing, equations (7) and (8), detive an exjresing for the liarear t.M4 earve. (c) Using the lierear exptesoinas for the LM curve, find as aloritabe (symbilc) solution fot the real national income (Y) in terma of R, the farameterk and the exnermotis values. Sulstifute this expirencios in for Y is the 15 to drrive an algetiraic (symbulic) coppecosion for the equilibrium real interest rate (2) in terne of enly the parametern and exogenous valurs. (d) Now, axsume the following values for the paranactes and raograsias valuos in this model: C=128;e=0.6;I=200;i=100;G=250;3=500t+46; H=126; and h=700. Ving the alpebraic expestion derived in 2(c) abone, find rgaantitative solutions fot the equilibrium real intered rate (R) and the mal national Y=C+I+G where Y is real GDP, C is consumption, I is (private) investment, and G is government expenditures. We assume that consumers will spend on consumption goods in proportion to their income, with that proportion determined by consumers' maryinal propensity to constme (b), such that C=Cn+oY where C>0 is an exogenously determined minimal level of eonstmption expenditures, and 00 reflecting that higher interest rates crowd out firms' invertments. Government expenditures are determined ecogenously, and are equal to G=G In the mobes nuricet, the supply and demand for money mast be equal. The aupply of monny in determined exogenously, and is set at M=M The demand fot money for liquality, b ) is deturmined both by the slemand for naoney for trunactional purposen and the demand for money a a safe haven, which is inversely holdings do not). We can thisefore write the demand for maney as L=fY+(HHhR) with H=0,k>0 and h>0. (a) Using equations (3), (4), (5), and (6), derive an expression for the linear IS curve. (b) Using equations (7) and (8), derive an expression for the linear LM curve. (c) Using the linear expressions for the LM curve, find an algebraic (symbolic) solution for the real national income (Y) in terms of R, the parameters, and the exogenous values, Substitute this expression in for Y in the IS to derive an algebraic (symbolic) expression for the equilibrium real interest rate (R) in terms of only the parameters and exogenous values. (d) Now, assume the following values for the parameters and exogenous values in this model: C=128;c=0.6;I=200;i=100;G=250;M=500;t=0.6; H=126; and h=700. Using the algebraic expressions derived in 2(c) above, find quantitative solutions for the equilibrium real interest rate (R) and the real national income (Y)