331as5-q4-key - ECON 331 Assignment 5: Answer Key to...

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Unformatted text preview: ECON 331 Assignment 5: Answer Key to Question 4 4. A simple form of the IS LM model is M0 ) P Y = C(Y; + I(r) + G0 M0 =P = L(Y; r) Note that the term, M appears in the consumption function. This what is sometimes P referred to as the Real Balances E¤ect. (a) Make a sensible assumption about the sign of @C=@( M )? Justifying your assumpP tion (only your …rst sentence will be read). (b) Setup and sign the Jacobian of this system. (c) Determine the comparitive static results about how changes in M0 a¤ect Y and r. Use the normal economic assumptions about the derivatives of, I(r) and L(Y; r). (d) Redo (c) except this time let P be the exogenous variable that in‡ uences Y and r (remember to use the chain rule). Answers: (a) (1 0 Cy )dY I 0 dr = dG0 C M M2 dP + C M P P P 1 0 LY dY + Lr dr = p dM0 M2 dP P Matrix form (1 I0 Lr Cy ) LY dY dr = " dG0 (+) dM M0 P2 CM 1 P dP + C M P P 1 0 dM0 M2 dP p P The Jacobian is jJj = (1 1 P dM # (+) ( ) ( ) Cy )Lr + LY I 0 < 0 (b) C M > 0 the real balance e¤ect is usually assumed to be positive. P @r @Y (c) Find @M and @M " # 1 CM P (1 Cy ) I0 dY =dM P = 1 LY Lr dr=dM p 1 P CM P @Y = @M 1 p @r = @M = 1 P Cy C M P LY jJj 1 p (+) (+) ( ) 1 Lr P P CM jJj and 1 I0 Lr ( )(+) 1 p + I0 jJj (+) (1 (+) 1 p CY ) = jJj 1 = ( ) >0 ( ) (+) (+) (+) 1 LY P P CM = (?) ?0 ( ) Find @Y @P and @r @P (1 Cy ) LY M P2 CM P @Y = @P @r = @P dY =dP dr=dP I0 Lr M p2 Cy LY jJj CM M P2 CM P ( ) M p2 P = jJj and 1 I0 Lr = " P (+) ( ) M Lr P2 M p2 ( )(+) 1 I0 p jJj (+) (1 CY ) = ( ) M p2 (+) + CM jJj 2 # M P2 CM P = (+) <0 ( ) (+) (+) M LY P2 = (?) ?0 ( ) ...
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331as5-q4-key - ECON 331 Assignment 5: Answer Key to...

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