Fall 2017 Social Sciences 7418 University of Wisconsin-Madison Problem Set 1 Answers
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1 Eonomis 435 enzie D. Cinn Fall 7 Soial Sienes 748 Universiy of Wisonsin-adison rolem Se Answers Due in leure on Wednesday, Sepemer. Be sure o pu your name on your prolem se. u oxes around your answers o e algerai quesions.. Suppose e eonomy is desried y e following equaions (so we are looking a a losed eonomy: Real Seor ( Z Oupu equals aggregae demand, an equilirium ondiion ( Z C I G Definiion of aggregae demand (3 C o D Consumpion fn, is e marginal propensiy o onsume (4 D T Tr Definiion of disposale inome (5 T Tax funion; is marginal ax rae. (6 Tr TR Transfer paymens; TR is lump sum ransfers. (7 I i Invesmen funion (8 G GO Governmen spending on goods and servies, exogenous Asse Seor (9 d s Equilirium ondiion ( s Real money supply d ( i Real money demand. Solve for e L urve (i as a funion of. s d i Solving for e ineres rae, i, yields e L urve: i. Solve for e IS urve ( as a funion of i. = Z = C + I + G = + D i + GO = a + ( - T + Tr i + GO = a + ( - + TR i + GO susiue in for C, I, G susiue in for D susiue in for ax, ransfers funions ring e "" erms o lef and side.
2 - ( = (-(- = + TR + + GO i divide o sides y (- (- - and le Λ + TR + + GO ( i le ] ( [.3 Wa is e annel (or variale y wi faors in e moneary or asse seor affe e real goods seor in is model? oneary poliy influenes (in par ineres raes. Ineres raes in urn affe invesmen, and via e simple Keynesian muliplier ( affes e enire real seor..4 Solve for e equilirium value of. To solve for e equilirium value of inome, susiue e L ino e IS equaion from.: ( ove e erm in pareneses (. and e (/ erm o e LHS; faoring ou e 's on e LHS yields: ( ( Dividing o sides y e erm in e pareneses yields: ] [ were / (.5 Grap e IS and L urves on one diagram. Clearly indiae e inereps and e slopes. Lael e equilirium inome and ineres rae and i.
3 3. Assume G dereases y ΔGO, and is ompleely ond finaned (no porfolio effes ere. Calulae e governmen spending muliplier. Take e oal differenial of your answer o.4. A To find e governmen spending muliplier, se e anges in real money o zero and e money onsan, and divide o sides y ΔGO: GO GO / (. Suppose insead Tr dereases y ΔTR. Calulae e governmen ransfers muliplier. Take e oal differenial again: To find e governmen ransfers muliplier, se e anges in real money o zero and e money onsan, se e ange in ΔΛ o equal ΔTR, and divide o sides y ΔTR: TR TR / ( L,, IS Λ R Slope = / ( slope A / -(/( / i
4 .3 Redraw your answer o.5. Ten in e same grap, sow wa appens o e equilirium inome and ineres rae if governmen spending on goods and servies is dereased y ΔGO. Inlude in your grap e level of inome a would e aieved if someow e ineres rae sayed onsan (lael is poin A. Λ / GO L,, GO i i IS Λ IS Λ -(/( / A.4 A e new equilirium, do we know if invesmen is iger or lower an e level i sared ou wi? Do we know if i is iger or lower an a A? Reall e invesmen funion is given y: I i So e ange in invesmen is given y: I i Noie a a e new equilirium, inome is lower (, u e ineres rae is lower as well (i. Hene, ere are offseing effes on invesmen, and e end resuls ould e iger or lower, depending on e magniudes of e anges in inome and ineres raes and e parameer values (, -. Regarding e seond quesion, if one were a A, and ineres rae i, en invesmen would unamiguously e lower..5 Suppose e Fed arges e ineres rae a i (all is iarge. Reurning o.3, sow grapially wa appens if governmen is dereased. Wa appens o e level of invesmen? 4
5 Λ / L,, GO L,, i Targe L Effeive i IS Λ IS Λ -(/( / A Wen e Fed arges e ineres rae, and e arge ineres rae remains onsan, en e L is now e Effeive L. A drop in governmen spending, reduing auonomous spending, indues an unamiguous reduion in invesmen, sine inome is lower, u ineres raes are unanged. Noe a e answer is e same if we are in a liquidiy rap. E435psa_f7.do
Output equals aggregate demand, an equilibrium condition Definition of aggregate demand Consumption function, c
Eonoms 435 enze D. Cnn Fall Soal Senes 748 Unversy of Wsonsn-adson Te IS-L odel Ts se of noes oulnes e IS-L model of naonal nome and neres rae deermnaon. Ts nvolves exendng e real sde of e eonomy (desred
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