lista de problemas 4 - uabpareto.uab.es/lgambetti/hw4_sol.pdf · lista de problemas 4 i. preguntas...

Universitat Autònoma de BarcelonaCurs 2013-2014Macroeconomia I

Lista de Problemas 4

I. Preguntas multirespuesta

1. a 6. a 11. a 16. b2. d 7. d 12. a 17. a3. b 8. c 13 d 18. a4. d 9. d 14 b 19. a5. a 10. c 15. b 20. b

II. Ejercicios

1. Respuestas:

a) En la aspa Keynesiana la función de gasto planificado es E = C (Y − T ) + I +G.La condición de equilibrio señala que el gasto efectivo debe ser igual al gasto realY = E, tal como muestra la Figura 10–6.

PPrroobblleemmss aanndd AApppplliiccaattiioonnss1. a. The Keynesian cross graphs an economy’s planned expenditure function, E =

C(Y – T) + I + G, and the equilibrium condition that actual expenditure equalsplanned expenditure, Y = E, as shown in Figure 10–6.

An increase in government purchases from G1 to G2 shifts the planned expendi-ture function upward. The new equilibrium is at point B. The change in Y equalsthe product of the government-purchases multiplier and the change in govern-ment spending: !Y = [1/(1 – MPC)]!G. Because we know that the marginalpropensity to consume MPC is less than one, this expression tells us that a one-dollar increase in G leads to an increase in Y that is greater than one dollar.

b. An increase in taxes !T reduces disposable income Y – T by !T and, therefore,reduces consumption by MPC " !T. For any given level of income Y, plannedexpenditure falls. In the Keynesian cross, the tax increase shifts the planned-expenditure function down by MPC " !T, as in Figure 10–7.

86 Answers to Textbook Questions and Problems

Y

A

B

G!

45˚

Income, output

E

Plan

ned

expe

ditu

re

Y1Y2

E2 = C(Y – T) + I + G2

E1 = C(Y – T) + I + G1

Y = E

Plan

ned

expe

nditu

re

FFiigguurree 1100––66

Y = E

MPC T" !

Y

– MPC1 – MPC !T

Income, output

45˚

B

A

E

Plan

ned

expe

nditu

re

E = C(Y – T ) + I + G

Y2 Y1

Income, output


Un incremento en el gasto público de G1 a G2 desplaza la función de gasto plani-ficado hacia arriba. El nuevo equilibrio se encuentra en el punto B. El cambio enY se obtiene multiplicando el cambio en el gasto público por el multiplicador del

1

gasto público: �Y = [1/ (1−MPC)]�G. Dado que sabemos que la propensiónmarginal al consumo (MPC) es menor que uno, esta expresión nos dice que unincremento de un euro en G conlleva un aumento de Y mayor que un euro.

b) Un incremento de los impuestos �T reduce la renta disponible Y −T en �T , porlo tanto, el consumo se reduce en MPC ×�T . Para cualquier nivel de renta Y ,el gasto planificado cae. En la aspa keynesiana, un incremento de los impuestosdesplaza la función de gasto planificado en MPC × �T hacia abajo, tal comoindica la Figura 10–7.

PPrroobblleemmss aanndd AApppplliiccaattiioonnss1. a. The Keynesian cross graphs an economy’s planned expenditure function, E =

C(Y – T) + I + G, and the equilibrium condition that actual expenditure equalsplanned expenditure, Y = E, as shown in Figure 10–6.

An increase in government purchases from G1 to G2 shifts the planned expendi-ture function upward. The new equilibrium is at point B. The change in Y equalsthe product of the government-purchases multiplier and the change in govern-ment spending: !Y = [1/(1 – MPC)]!G. Because we know that the marginalpropensity to consume MPC is less than one, this expression tells us that a one-dollar increase in G leads to an increase in Y that is greater than one dollar.

b. An increase in taxes !T reduces disposable income Y – T by !T and, therefore,reduces consumption by MPC " !T. For any given level of income Y, plannedexpenditure falls. In the Keynesian cross, the tax increase shifts the planned-expenditure function down by MPC " !T, as in Figure 10–7.


Y

A

B

G!

45˚

Income, output

E

Plan

ned

expe

ditu

re

Y1Y2

E2 = C(Y – T) + I + G2

E1 = C(Y – T) + I + G1

Y = E

Plan

ned

expe

nditu

re


Y = E

MPC T" !

Y

– MPC1 – MPC !T

Income, output

45˚

B

A

E

Plan

ned

expe

nditu

re

E = C(Y – T ) + I + G

Y2 Y1

Income, output


La cuantía del decremento de Y viene dada por el producto entre el multiplicadorde los impuestos y el cambio en los impuestos: �Y = [−MPC/ (1−MPC)]�T .

c) Podemos calcular el efecto de la misma subida en impuestos y gasto público su-mando los dos efectos multiplicadores que hemos calculado en el apartado (a) y(b):

�Y = [(1/ (1−MPC))�G] − [(MPC/ (1−MPC))�T ]

Multiplicador Gasto Multiplicador Impuestos

Público

Dado que los impuestos y el gasto público aumentan en la misma cuantía, sabemosque �G = �T . Entonces, podemos volver a escribir la ecuación anterior como:

�Y = [(1/ (1−MPC))− (MPC/ (1−MPC))]�G = �G

2

Esta expresión nos dice que un aumento del gasto público y los impuestos de lamisma cuantía generará un aumento de Y de la misma magnitud que el incrementoen G. Es decir, este multiplicador “sin déficit público” es exactamente uno.

2. Respuestas:

a) El gasto total planificado es E = C (Y − T ) + I +G. Si sustituimos la función deconsumo y los valores para la inversión I, el gasto público G, y los impuestos T ,obtenemos que el gasto planificado es E = 200 + 0,75 (Y − 100) + 100 + 100 =

0,75Y + 325. Esta ecuación es la dibujada en la Figura 10–8.

The amount by which Y falls is given by the product of the tax multiplier and theincrease in taxes:

!Y = [ – MPC/(1 – MPC)]!T.c. We can calculate the effect of an equal increase in government expenditure and

taxes by adding the two multiplier effects that we used in parts (a) and (b):

!Y = [(1/(1 – MPC))!G] – [(MPC/(1 – MPC))!T].Government TaxSpending MultiplierMultiplier

Because government purchases and taxes increase by the same amount, we knowthat !G = !T. Therefore, we can rewrite the above equation as:

!Y = [(1/(1 – MPC)) – (MPC/(1 – MPC))]!G= !G.

This expression tells us that an equal increase in government purchases and taxesincreases Y by the amount that G increases. That is, the balanced-budget multi-plier is exactly 1.

2. a. Total planned expenditure is

E = C(Y – T) + I + G.Plugging in the consumption function and the values for investment I, govern-ment purchases G, and taxes T given in the question, total planned expenditure Eis

E = 200 + 0.75(Y – 100) + 100 + 100= 0.75Y + 325.

This equation is graphed in Figure 10–8.

b. To find the equilibrium level of income, combine the planned-expenditure equa-tion derived in part (a) with the equilibrium condition Y = E:

Y = 0.75Y + 325Y = 1,300.

The equilibrium level of income is 1,300, as indicated in Figure 10–8.c. If government purchases increase to 125, then planned expenditure changes to

E = 0.75Y + 350. Equilibrium income increases to Y = 1,400. Therefore, an

Chapter 10 Aggregate Demand I 87

Y = E

E = 0.75 Y + 325

YY * = 1,300Income, output

45

325

E

Plan

ned

expe

nditu

re


b) Para encontrar la renta de equilibrio, basta con combinar la expresión para el gastoplanificado que hemos encontrado en (a) con la condición de equilibrio Y = E:Y = 0,75Y + 325 = 1300. El nivel de renta de equilibrio es 1.300, tal como indicala Figura 10–8.

c) Si el gasto público aumenta hasta 125, el gasto planificado cambia a E = 0,75+350.La renta de equilibrio aumentará hasta Y = 1400. Por lo tanto, un aumento delgasto público de 25 (i.e., 125 – 100 = 25), generar un incremento de la renta de100. Este no debería ser un resultado sorprendente, dado que el multiplicador delgasto público es 1/ (1−MPC) y dado que el MPC es 0,75, el multiplicador delgasto público es 4.

d) Un nivel de renta de 1.600 representa un incremento de 300 respecto al nivelinicial. El multiplicador del gasto público es 1/ (1−MPC). En este ejemplo, elMPC es 0,75, es decir, el multiplicador del gasto público es 4. Esto significa que el

3

gasto público debe aumentar en 75 unidades (a un nivel de 175) para que la rentaaumente en 300.

3. Respuestas:

a) Cuando los impuestos no dependen de la renta, un incremento de la renta deun euro se traduce en un incremento de la renta disponible de también un euro.Incremento del consumo viene dado por la propensión marginal a consumir (MPC).Cuando los impuestos sí dependen de la renta, un incremento de la renta de uneuro se traduce en un incremento de la renta disponible de tan sólo (1− t) euros.El aumento del consumo viene dado por el producto entre el MPC y el aumentoen la renta disponible, es decir, (1− t)MPC. Esta cantidad es menor que MPC.La idea clave es que la renta disponible cambia en menor proporción que la rentatotal, lo que conlleva un efecto menor en el consumo.

b) Cuando los impuesto son fijos, sabemos que �Y/�G = 1/ (1−MPC). Paraencontrar esta expresión uno debe considerar un incremento en el gasto público de�G. El efecto inicial de esta cambio es aumentar la renta en �G. Este aumento,a su vez, incrementa el consumo en un cantidad igual a la propensión marginal aconsumir multiplicada por el cambio en la renta, MPC ×�G. Este aumento delconsumo incrementa el gasto planificado y la renta aún más. El proceso continuade manera indefinida, hasta que derivamos el multiplicador. Cuando los impuestosdependen de la renta, sabemos que un incremento de �G aumenta la renta totalen �G. Sin embargo, la renta disponible aumenta solo en (1− t)�G. Por tanto,el consumo aumenta en (1− t)MPC × �G. El gasto planificado aumenta enesta cantidad, lo que genera un incremento aún mayor del consumo. El procesocontinua, de forma que podemos escribir el cambio en la renta como:

�Y =�G�1 + (1− t)MPC + [(1− t)MPC]2 + [(1− t)MPC]3 + . . .

�

=�G [1/ (1− (1− t)MPC)]

Por lo tanto, podemos escribir el multiplicador del gasto público como 1/ (1− (1− t)MPC),en lugar de 1/ (1−MPC). Esto significa que el multiplicador es mucho menor. Porejemplo, si la propensión marginal al consumo (MPC) es 3/4 y t es 1/3, entoncesel multiplicador será 1/ (1− (1− 1/3) (3/4)), es decir 2, en lugar de 1/ (1− 3/4)

o 4.

c) Para determinar como este sistema impositivo altera la curva IS, podemos derivarla curva IS para el caso en que los impuestos dependen de la renta. Empezamos

4

considerando la identidad de la contabilidad nacional sobre la renta: Y = C+I+G.La función de consumo es C = a + b (Y − T − tY ). Note que en esta funciónde consumo los impuestos son una función de la renta. La función de inversiónI = c − dr. Sustituyendo la función de consumo e inversión el la identidad de larenta obtenemos: Y = [a+ b (Y − T − tY )] + c− dr +G. Resolviendo por Y :

Y =1

1− b (1− t)

�a+ c+G− bT -dr

�

Sabemos que t es menor que 1, por lo tanto, concluimos que la curva IS tiene unapendiente más pronunciada que cuando los impuestos no dependen de la renta.

4. Respuestas:

a) Si la sociedad se convierte en más austera, es decir, para cualquier nivel de rentala gente ahorra más y consume menos, entonces la función de gasto planificado sedesplaza hacia abajo, como en la Figura 10–9 (fijase que C2 < C1). La renta deequilibrio cae de Y1 a Y 2.


This IS equation is analogous to the one derived in the text except that each termis divided by 1 – b(1 – t) rather than by (1 – b). We know that t is a tax rate, whichis less than 1. Therefore, we conclude that this IS curve is steeper than the one inwhich taxes are a fixed amount.

4. a. If society becomes more thrifty—meaning that for any given level of income peoplesave more and consume less—then the planned-expenditure function shifts down-ward, as in Figure 10–9 (note that C2 < C1). Equilibrium income falls from Y1 to Y2.

b. Equilibrium saving remains unchanged. The national accounts identity tells usthat saving equals investment, or S = I. In the Keynesian-cross model, weassumed that desired investment is fixed. This assumption implies that invest-ment is the same in the new equilibrium as it was in the old. We can conclude thatsaving is exactly the same in both equilibria.

c. The paradox of thrift is that even though thriftiness increases, saving is unaffect-ed. Increased thriftiness leads only to a fall in income. For an individual, we usu-ally consider thriftiness a virtue. From the perspective of the Keynesian cross,however, thriftiness is a vice.

d. In the classical model of Chapter 3, the paradox of thrift does not arise. In thatmodel, output is fixed by the factors of production and the production technology,and the interest rate adjusts to equilibrate saving and investment, where invest-ment depends on the interest rate. An increase in thriftiness decreases consump-tion and increases saving for any level of output; since output is fixed, the savingschedule shifts to the right, as in Figure 10–10. At the new equilibrium, the inter-est rate is lower, and investment and saving are higher.

Thus, in the classical model, the paradox of thrift does not exist.

Y = EE

Plan

ned

expe

nditu

re

A

B

Y

Income, output

E 1 = C1 + c (Y – T ) + I + G

E 2 = C2 + c (Y – T ) + I + G

Y1Y2


A

B

I, SInvestment, Saving

r

Rea

l int

eres

t rat

e

I(r)

r1

r2

S2S1


b) El ahorro de equilibrio no cambia. La identidad de la contabilidad nacional nosdice que la inversión es igual al ahorro S = I. En el modelo de la aspa Keynesiana,asumimos que la inversión deseada es fija. Este supuesto implica que la inversión esla misma en el nuevo equilibrio que en el anterior. Por lo tanto, podemos concluirque el ahorro también será el mismo.

c) La paradoja de la austeridad es que aún que haya más austeridad, el ahorro no seve afectado. El aumento de la austeridad solo conlleva un descenso de la renta. Anivel individual solemos considerar la austeridad una virtud. Sin embargo, desde elpunto de vista de la aspa Keynesiana, la austeridad conlleva efectos no deseados.

5

d) En el modelo clásico, la paradoja de la austeridad no se produce. En ese modelo, eloutput está determinado por los factores de producción y la tecnología, y el tipo deinterés se ajusta para equilibrar ahorro e inversión, ya que la inversión depende deltipo de interés. Un aumento de la austeridad reduciría el consumo e incrementaríael ahorro para cualquier nivel de renta. Ya que el output se mantendría fijo, elahorro se desplazaría hacia la derecha, como en la Figura 10–10. En el nuevoequilibrio, el tipo de interés es menor, y la inversión y el ahorro mayores.


This IS equation is analogous to the one derived in the text except that each termis divided by 1 – b(1 – t) rather than by (1 – b). We know that t is a tax rate, whichis less than 1. Therefore, we conclude that this IS curve is steeper than the one inwhich taxes are a fixed amount.

4. a. If society becomes more thrifty—meaning that for any given level of income peoplesave more and consume less—then the planned-expenditure function shifts down-ward, as in Figure 10–9 (note that C2 < C1). Equilibrium income falls from Y1 to Y2.

b. Equilibrium saving remains unchanged. The national accounts identity tells usthat saving equals investment, or S = I. In the Keynesian-cross model, weassumed that desired investment is fixed. This assumption implies that invest-ment is the same in the new equilibrium as it was in the old. We can conclude thatsaving is exactly the same in both equilibria.

c. The paradox of thrift is that even though thriftiness increases, saving is unaffect-ed. Increased thriftiness leads only to a fall in income. For an individual, we usu-ally consider thriftiness a virtue. From the perspective of the Keynesian cross,however, thriftiness is a vice.

d. In the classical model of Chapter 3, the paradox of thrift does not arise. In thatmodel, output is fixed by the factors of production and the production technology,and the interest rate adjusts to equilibrate saving and investment, where invest-ment depends on the interest rate. An increase in thriftiness decreases consump-tion and increases saving for any level of output; since output is fixed, the savingschedule shifts to the right, as in Figure 10–10. At the new equilibrium, the inter-est rate is lower, and investment and saving are higher.

Thus, in the classical model, the paradox of thrift does not exist.

Y = EE

Plan

ned

expe

nditu

re

A

B

Y

Income, output

E 1 = C1 + c (Y – T ) + I + G

E 2 = C2 + c (Y – T ) + I + G

Y1Y2


A

B

I, SInvestment, Saving

r

Rea

l int

eres

t rat

e

I(r)

r1

r2

S2S1


En conclusión, en el modelo clásico la paradoja de la austeridad no existe.

5. Respuestas:

a) Si el banco central incrementa la oferta monetaria, la curva LM se desplaza haciaabajo, como muestra la Figura 11–4. La renta aumenta y el tipo de interés baja.El aumento en la renta disponible genera un incremento del consumo, mientras eldescenso del tipo de interés conlleva un aumento de la inversión.

4. Falling prices can either increase or decrease equilibrium income. There are two waysin which falling prices can increase income. First, an increase in real money balancesshifts the LM curve downward, thereby increasing income. Second, the IS curve shiftsto the right because of the Pigou effect: real money balances are part of householdwealth, so an increase in real money balances makes consumers feel wealthier and buymore. This shifts the IS curve to the right, also increasing income.

There are two ways in which falling prices can reduce income. The first is thedebt-deflation theory. An unexpected decrease in the price level redistributes wealthfrom debtors to creditors. If debtors have a higher propensity to consume than credi-tors, then this redistribution causes debtors to decrease their spending by more thancreditors increase theirs. As a result, aggregate consumption falls, shifting the IS curveto the left and reducing income. The second way in which falling prices can reduceincome is through the effects of expected deflation. Recall that the real interest rate requals the nominal interest rate i minus the expected inflation rate !e: r = i – !e. Ifeveryone expects the price level to fall in the future (i.e., !e is negative), then for anygiven nominal interest rate, the real interest rate is higher. A higher real interest ratedepresses investment and shifts the IS curve to the left, reducing income.

PPrroobblleemmss aanndd AApppplliiccaattiioonnss1. a. If the central bank increases the money supply, then the LM curve shifts down-

ward, as shown in Figure 11–4. Income increases and the interest rate falls. Theincrease in disposable income causes consumption to rise; the fall in the interestrate causes investment to rise as well.

Chapter 11 Aggregate Demand II 93

A

B

IS

Y

Income, output

Inte

rest

rate

rLM1

LM2

r1

r2

Y1Y2


6

b) Si el gasto público aumenta, el multiplicador del gasto público nos dice que la curvaIS se desplazará a la derecha en una cantidad igual a [1/ (1−MPC)]�G, comopuede verse en la Figura 11–5. Tanto la renta como el tipo de interés aumentan. Elincremento en la renta disponible lleva el consumo a crecer, mientras el aumentodel tipo de interés reduce la inversión.

b. If government purchases increase, then the government-purchases multiplier tellsus that the IS curve shifts to the right by an amount equal to [1/(1 – MPC)]!G.This is shown in Figure 11–5. Income and the interest rate both increase. Theincrease in disposable income causes consumption to rise, while the increase inthe interest rate causes investment to fall.

c. If the government increases taxes, then the tax multiplier tells us that the IScurve shifts to the left by an amount equal to [ – MPC/(1 – MPC)]!T. This isshown in Figure 11–6. Income and the interest rate both fall. Disposable incomefalls because income is lower and taxes are higher; this causes consumption to fall.The fall in the interest rate causes investment to rise.


LM

A

B

Inte

rest

rate

Y

Income, outputY2

r2

r1

IS2IS1

! G1 – MPC

r

Y1


LM

A

B

Inte

rest

rate

Y

Income, output

r

Y1

IS2

IS1

r2

r1

Y2

– MPC1 – MPC ! T


c) Si aumenta los impuestos, el multiplicado de los impuestos nos dice que la curvaIS se desplazará a la izquierda en una cantidad igual a [−MPC/ (1−MPC)]�T ,como muestra la Figura 11–6. Tanto la renta como el tipo de interés bajarán. Larenta disponible se reduce debido a la bajada de la renta y el incremento de losimpuestos, lo que genera un descenso del consumo. La reducción del tipo de interésconlleva un incremento de la inversión.

b. If government purchases increase, then the government-purchases multiplier tellsus that the IS curve shifts to the right by an amount equal to [1/(1 – MPC)]!G.This is shown in Figure 11–5. Income and the interest rate both increase. Theincrease in disposable income causes consumption to rise, while the increase inthe interest rate causes investment to fall.

c. If the government increases taxes, then the tax multiplier tells us that the IScurve shifts to the left by an amount equal to [ – MPC/(1 – MPC)]!T. This isshown in Figure 11–6. Income and the interest rate both fall. Disposable incomefalls because income is lower and taxes are higher; this causes consumption to fall.The fall in the interest rate causes investment to rise.


LM

A

B

Inte

rest

rate

Y

Income, outputY2

r2

r1

IS2IS1

! G1 – MPC

r

Y1


LM

A

B

Inte

rest

rate

Y

Income, output

r

Y1

IS2

IS1

r2

r1

Y2

– MPC1 – MPC ! T


d) Podemos establecer en cuánto la curva IS va a moverse en respuesta a un incre-

7

mento equivalente del gasto público y los impuestos sumando el efecto de los dosmultiplicadores usados en los apartados (b) y (c): �Y = [(1/ (1−MPC))�G]−[(MPC/ (1−MPC))�T ]. Dado que tanto el gasto público como los impuestosincrementan en la misma cantidad, sabemos que �G = �T . Entonces podemosvolver a escribir la ecuación anterior como:

�Y = [(1/ (1−MPC))− (MPC/ (1−MPC))]�G

�Y =�G

Esta expresión nos dice como cambia la renta, manteniendo el tipo de interés cons-tante. Dice que un incremento equivalente en gasto público y impuestos desplazala curva IS a la derecha en la misma magnitud en que aumenta G, tal como mues-tra la Figura 11–7. La renta aumenta, pero en menor medida que el aumento enG y T , lo que lleva a una caída de la renta disponible Y − T y una bajada delconsumo. El tipo de interés aumenta, causando una reducción de la inversión.

d. We can figure out how much the IS curve shifts in response to an equal increasein government purchases and taxes by adding together the two multiplier effectsthat we used in parts (b) and (c):

!Y = [(1/(1 – MPC))]!G] – [(MPC/(1 – MPC))!T] Because government purchases and taxes increase by the same amount, we knowthat !G = !T. Therefore, we can rewrite the above equation as:

!Y = [(1/(1 – MPC)) – (MPC/(1 – MPC))]!G!Y = !G.

This expression tells us how output changes, holding the interest rate constant. Itsays that an equal increase in government purchases and taxes shifts the IS curveto the right by the amount that G increases.

This shift is shown in Figure 11–7. Output increases, but by less than theamount that G and T increase; this means that disposable income Y – T falls. As aresult, consumption also falls. The interest rate rises, causing investment to fall.


LM

B

A

Inte

rest

rate

Y

Income, output

r

! G

Y2

IS1

r2

r1

Y1

IS2


6. Respuestas:

a) La invención de un chip de alta velocidad incrementa la demanda de inversión,lo que desplaza la curva IS hacia afuera. Es decir, para cada nivel de tipo deinterés, las empresas quieren invertir más. El aumento de la demanda de bienesde inversión desplaza la curva IS hacia afuera, aumentando la renta y el empleo,como muestra la Figura 11–8.

8

2. a. The invention of the new high-speed chip increases investment demand, whichshifts the IS curve out. That is, at every interest rate, firms want to invest more.The increase in the demand for investment goods shifts the IS curve out, raisingincome and employment. Figure 11–8 shows the effect graphically.

The increase in income from the higher investment demand also raises interestrates. This happens because the higher income raises demand for money; since thesupply of money does not change, the interest rate must rise in order to restoreequilibrium in the money market. The rise in interest rates partially offsets theincrease in investment demand, so that output does not rise by the full amount ofthe rightward shift in the IS curve.

Overall, income, interest rates, consumption, and investment all rise.b. The increased demand for cash shifts the LM curve up. This happens because at

any given level of income and money supply, the interest rate necessary to equili-brate the money market is higher. Figure 11–9 shows the effect of this LM shiftgraphically.


B

Inte

rest

rat

e

LM

Income, output

r

YY1 Y2

IS2

IS1

r1

r2

A


B

Inte

rest

rat

e

Income, output

r

YY2 Y1

IS

r2

r1

A

LM2

LM1


El aumento de la renta por la mayor demanda de inversión también incrementael tipo de interés. Esto ocurre porque una renta mayor aumenta la demanda dedinero, ya que la oferta de dinero no cambia, el tipo de interés debe aumentar paramantener el equilibrio en el mercado de dinero. El aumento del tipo de interéscontrarresta parcialmente el incremento en la demanda de inversión, es decir, larenta no aumenta en la misma cantidad en que la curva IS se desplaza haciala derecha. En conjunto, la renta, el tipo de interés, el consumo y la inversiónaumentan.

b) El incremento en la demanda de efectivo desplaza la curva LM hacia arriba. Estoocurre porque para cualquier nivel de renta y oferta de dinero, el tipo de interésnecesario para equilibrar el mercado de dinero es mayor, como muestra la Figura11–9.

9

2. a. The invention of the new high-speed chip increases investment demand, whichshifts the IS curve out. That is, at every interest rate, firms want to invest more.The increase in the demand for investment goods shifts the IS curve out, raisingincome and employment. Figure 11–8 shows the effect graphically.

The increase in income from the higher investment demand also raises interestrates. This happens because the higher income raises demand for money; since thesupply of money does not change, the interest rate must rise in order to restoreequilibrium in the money market. The rise in interest rates partially offsets theincrease in investment demand, so that output does not rise by the full amount ofthe rightward shift in the IS curve.

Overall, income, interest rates, consumption, and investment all rise.b. The increased demand for cash shifts the LM curve up. This happens because at

any given level of income and money supply, the interest rate necessary to equili-brate the money market is higher. Figure 11–9 shows the effect of this LM shiftgraphically.


B

Inte

rest

rat

e

LM

Income, output

r

YY1 Y2

IS2

IS1

r1

r2

A


BIn

tere

st r

ate

Income, output

r

YY2 Y1

IS

r2

r1

A

LM2

LM1


El desplazamiento hacia arriba de la curva LM disminuye la renta e incrementael tipo de interés. El consumo baja debido a la caída de la renta, y la inversión sereduce por el incremento en el tipo de interés.

c) Para cualquier nivel de renta, ahora los consumidores quieren ahorrar más y con-sumir menor. Debido a este desplazamiento haca abajo de la función de consumo,la curva IS se desplaza hacia adentro, como muestra la Figura 11–10.

The upward shift in the LM curve lowers income and raises the interest rate.Consumption falls because income falls, and investment falls because the interestrate rises.

c. At any given level of income, consumers now wish to save more and consume less.Because of this downward shift in the consumption function, the IS curve shiftsinward. Figure 11–10 shows the effect of this IS shift graphically.

Income, interest rates, and consumption all fall, while investment rises. Incomefalls because at every level of the interest rate, planned expenditure falls. Theinterest rate falls because the fall in income reduces demand for money; since thesupply of money is unchanged, the interest rate must fall to restore money-marketequilibrium. Consumption falls both because of the shift in the consumption func-tion and because income falls. Investment rises because of the lower interest ratesand partially offsets the effect on output of the fall in consumption.


B

Inte

rest

rate

LM

Income, output

r

YY1 Y2

IS2

IS1

r1

r2

A


La renta, el tipo de interés y el consumo caen, mientras la inversión aumenta. Larenta cae porque para cualquier nivel de tipo de interés, el gasto planificado esmenor. El tipo de interés se reduce porque la caída en la renta reduce la demanda

10

de dinero, dado que la oferta de dinero no se altera, el tipo de interés debe caerpara equilibrar el mercado de dinero. El consumo decrece tanto por la reducciónde la renta como por el desplazamiento de la función de consumo. La inversiónaumenta debido al menor tipo de interés y contrarresta parcialmente el efecto dela caída del consumo sobre la renta de equilibrio.

7. Respuestas:

a) La curva IS viene dada por:

Y = C (Y − T ) + I (r) +G

Podemos sustituir las funciones de consumo e inversión y los valores de G y T

dados en la pregunta y volver a escribir la expresión para la curva IS en estaeconomía:

Y =200 + 0,75 (Y − 100) + 200− 25r + 100

(1− 0,75)Y =425− 25r

Y =1700− 100r

Esta es la curva IS en la Figura 11–11 para r desde 0 hasta 8.

3. a. The IS curve is given by:

Y = C(Y – T) + I(r) + G.We can plug in the consumption and investment functions and values for G and Tas given in the question and then rearrange to solve for the IS curve for this econ-omy:

Y = 200 + 0.75(Y – 100) + 200 – 25r + 100Y – 0.75Y = 425 – 25r

(1 – 0.75)Y = 425 – 25rY = (1/0.25) (425 – 25r)Y = 1,700 – 100r.

This IS equation is graphed in Figure 11–11 for r ranging from 0 to 8.

b. The LM curve is determined by equating the demand for and supply of real moneybalances. The supply of real balances is 1,000/2 = 500. Setting this equal to moneydemand, we find:

500 = Y – 100r.Y = 500 + 100r.

This LM curve is graphed in Figure 11–11 for r ranging from 0 to 8.c. If we take the price level as given, then the IS and the LM equations give us two

equations in two unknowns, Y and r. We found the following equations in parts (a)and (b):

IS: Y = 1,700 – 100r.LM: Y = 500 + 100r.

Equating these, we can solve for r:

1,700 – 100r = 500 + 100r1,200 = 200r

r = 6.Now that we know r, we can solve for Y by substituting it into either the IS or theLM equation. We find

Y = 1,100.Therefore, the equilibrium interest rate is 6 percent and the equilibrium level ofoutput is 1,100, as depicted in Figure 11–11.


LMIS

Y1,7001,1005000

6

8

r

Inte

rest

rate

Income, output


b) La curva LM se determina igualando la oferta y la demanda real de dinero. Laoferta real de dinero es 1000/2 = 500. Igualando esta ecuación con la demandareal de dinero, obtenemos: Y = 500+100r. Esta curva LM es la que se representaen la Figura 11–11 para r desde 0 hasta 8.

11

c) Si tomamos el nivel de precios como dado, entonces la curva IS y LM se conviertenen un sistema de dos ecuaciones con dos incógnitas, Y y r. Hemos hallado estasecuaciones en los apartados (a) y (b):

IS: Y =1700− 100r

LM: Y =500 + 100r

Igualando estas dos ecuaciones podemos encontrar r:

1700− 100r =500 + 100r

r =6

Ahora que conocemos r, podemos encontrar Y sustituyendo en la curva IS o LM.Obtenemos que Y = 1100. Por lo tanto, el tipo de interés de equilibrio es 6 % y elnivel de renta de equilibrio es 1.100, como se muestra en la Figura 11–11.

d) Si el gasto público aumenta de 100 a 150, entonces la ecuación IS se convierteen: Y = 200 + 0,75 (Y − 100) + 200 − 25r + 150. Simplificando, obtenemos: Y =

1900− 100r. Esta curva IS está dibujada en la Figura 11–12 como IS2. Podemosver que la curva IS se ha desplazado a la derecha en 200.

d. If government purchases increase from 100 to 150, then the IS equation becomes:

Y = 200 + 0.75(Y – 100) + 200 – 25r + 150.Simplifying, we find:

Y = 1,900 – 100r.This IS curve is graphed as IS2 in Figure 11–12. We see that the IS curve shifts tothe right by 200.

By equating the new IS curve with the LM curve derived in part (b), we cansolve for the new equilibrium interest rate:

1,900 – 100r = 500 + 100r1,400 = 200r

7 = r.We can now substitute r into either the IS or the LM equation to find the newlevel of output. We find

Y = 1,200.Therefore, the increase in government purchases causes the equilibrium interestrate to rise from 6 percent to 7 percent, while output increases from 1,100 to1,200. This is depicted in Figure 11–12.


1,200500 1,100

LM

200

Y1,9001,7000

6

7

r

Inte

rest

rate

Income, output

IS2IS1

8


. Igualando la nueva curva IS con la curva LM que hemos encontrado en el apartado(b), podemos encontrar el nuevo tipo de interés:

1900− 100r =500 + 100r

r =7

12

Ahora podemos usar r para encontrar el nivel de renta. Obtenemos Y = 1200. Porlo tanto, el incremento del gasto público conlleva un aumento del tipo de interésdel 6 % al 7 %, mientras la renta crece de 1.100 a 1.200, tal como muestra la Figura11–12.

e) Si la oferta de dinero aumenta de 1.000 a 1.2000, la curva LM se convierte en:Y = 600 + 100r. Esta es la curva LM dibujada en la Figura 11–13 como LM2.Vemos que la curva LM se desplaza hacia la derecha en 100 debido al aumento enla cantidad real de dinero.

e. If the money supply increases from 1,000 to 1,200, then the LM equation becomes:

(1,200/2) = Y – 100r,or

Y = 600 + 100r.This LM curve is graphed as LM2 in Figure 11–13. We see that the LM curveshifts to the right by 100 because of the increase in real money balances.

To determine the new equilibrium interest rate and level of output, equatethe IS curve from part (a) with the new LM curve derived above:

1,700 – 100r = 600 + 100r1,100 = 200r

5.5 = r.Substituting this into either the IS or the LM equation, we find

Y = 1,150.Therefore, the increase in the money supply causes the interest rate to fall from 6percent to 5.5 percent, while output increases from 1,100 to 1,150. This is depictedin Figure 11–13.

f. If the price level rises from 2 to 4, then real money balances fall from 500 to1,000/4 = 250. The LM equation becomes:

Y = 250 + 100r.


IS

Y1,7001,1501,1006005000

r

6.05.5

Inte

rest

rate

Income, output

100

LM1 LM2


Para determinar el nuevo tipo de interés y nivel de renta, igualamos la nueva curvaLM con la curva IS que hemos encontrado en el apartado (a):

1700− 100r =600 + 100r

r =5,5

Con el tipo de interés, encontramos que la nueva renta de equilibrio es Y = 1150.El aumento en la oferta de dinero genera una caída de tipo de interés del 6 % al5,5&, mientras la renta aumenta de 1.100 a 1.150, como muestra la Figura 11–13.

f ) Si el nivel de precios aumenta de 2 a 4, la cantidad real de dinero cae de 500 a250. La ecuación LM se convierte en: Y = 250 + 100r. Como muestra la Figura11–14, la curva LM se desplaza a la izquierda en 250 ya que el aumento de losprecios reduce la cantidad real de dinero.

13

As shown in Figure 11–14, the LM curve shifts to the left by 250 because theincrease in the price level reduces real money balances.

To determine the new equilibrium interest rate, equate the IS curve frompart (a) with the new LM curve from above:

1,700 – 100r = 250 + 100r1,450 = 200r7.25 = r.

Substituting this interest rate into either the IS or the LM equation, we find

Y = 975.Therefore, the new equilibrium interest rate is 7.25, and the new equilibrium levelof output is 975, as depicted in Figure 11–14.

g. The aggregate demand curve is a relationship between the price level and thelevel of income. To derive the aggregate demand curve, we want to solve the ISand the LM equations for Y as a function of P. That is, we want to substitute outfor the interest rate. We can do this by solving the IS and the LM equations forthe interest rate:

IS: Y = 1,700 – 100r100r = 1,700 – Y.

LM: (M/P) = Y – 100r100r = Y – (M/P).

Combining these two equations, we find

1,700 – Y = Y – (M/P)2Y = 1,700 + M/PY = 850 + M/2P.

Since the nominal money supply M equals 1,000, this becomes

Y = 850 + 500/P.


250

ISr

7.25

6.0

Inte

rest

rate

0975 1,200 1,700 Y600

250

Income, output

LM2 LM1

1,100


Para determinar el nuevo equilibrio igualamos la curva IS encontrada en (a) conla nueva LM:

1700− 100r =250 + 100r

r =7,25

El nuevo nivel de renta es Y = 975. El nuevo tipo de interés es 7,25 % y el nivelde renta es 975, como indica la Figura 11–14.

g) La curva de demanda agregada expresa la relación entre el nivel de precios y elnivel de renta. Para obtener la curva de demanda agregada, vamos a expresar lasecuaciones LM y IS como función de P :

IS: 100r =1700− Y

LM: 100r =Y − (M/P )

Combinando estas dos ecuaciones:

1700− Y =Y − (M/P )

Y =850 +M/2P

Dado que la oferta nominal de dinero M es igual a 1,000, Y = 850 + 500/P . Estaes la curva de demanda agregada de la Figura 11–15.

14

This aggregate demand equation is graphed in Figure 11–15.

How does the increase in fiscal policy of part (d) affect the aggregate demandcurve? We can see this by deriving the aggregate demand curve using the IS equa-tion from part (d) and the LM curve from part (b):

IS: Y = 1,900 – 100r100r = 1,900 – Y.

LM: (1,000/P) = Y – 100r100r = Y – (1,000/P).

Combining and solving for Y:

1,900 – Y = Y – (1,000/P),or

Y = 950 + 500/P.By comparing this new aggregate demand equation to the one previously derived,we can see that the increase in government purchases by 50 shifts the aggregatedemand curve to the right by 100.

How does the increase in the money supply of part (e) affect the aggregatedemand curve? Because the AD curve is Y = 850 + M/2P, the increase in themoney supply from 1,000 to 1,200 causes it to become

Y = 850 + 600/P.By comparing this new aggregate demand curve to the one originally derived, wesee that the increase in the money supply shifts the aggregate demand curve tothe right.

4. a. The IS curve represents the relationship between the interest rate and the level ofincome that arises from equilibrium in the market for goods and services. That is,it describes the combinations of income and the interest rate that satisfy the equa-tion

Y = C(Y – T) + I(r) + G.


P

4.0

2.0

1.0

0.5

0975 1,100 1,350 1,850 Y

Pric

e le

vel

Income, output


¿Cómo afecta el cambio de política fiscal descrito en (d) a la demanda agregada?Podemos responder derivando la demanda agregada a partir de la IS de (d) y laLM de (b):

IS: 100r =1900− Y

LM: 100r =Y − (1000/P )

Resolviendo para Y : Y = 950+500/P . Comparando esta nueva demanda agregadacon la anterior, podemos ver que el incremento del gasto público en 50 unidadesdesplaza la demanda agregada hacia la derecha en 100. ¿Cómo afecta el incrementode oferta monetaria de (e) la demanda agregada? Dado que la AD es Y = 850 +

M/2P , el aumento de la oferta monetaria de 1.000 a 1.200, lleva a Y = 850+600/P .La curva de demanda agregada se desplaza hacia la derecha.

8. Para aumentar la inversión manteniendo la renta constante, el gobierno debe adoptaruna política monetaria expansionaría y una política fiscal contractiva, como muestra laFigura 11–20. En el nuevo equilibrio en el punto B, el tipo de interés es menor, lo quegenera una inversión mayor. La política fiscal contractiva, reduciendo gasto público porejemplo, contrarresta el efecto del aumento de la inversión sobre la renta.

15

An example may make this clearer. Consider a linear version of the LMequation:

M/P = eY – fr.Note that as f gets larger, money demand becomes increasingly sensitive to theinterest rate. Rearranging this equation to solve for r, we find

r = (e/f)Y – (1/f)(M/P).We want to focus on how changes in each of the variables are related to changes inthe other variables. Hence, it is convenient to write this equation in terms ofchanges:

! r = (e/f)!Y – (1/f)!(M/P).The slope of the LM equation tells us how much r changes when Y changes, hold-ing M fixed. If !(M/P) = 0, then the slope is !r/!Y = (e/f). As f gets very large, thisslope gets closer and closer to zero.

If money demand is very sensitive to the interest rate, then fiscal policy isvery effective: with a horizontal LM curve, output increases by the full amountthat the IS curve shifts. Monetary policy is now completely ineffective: an increasein the money supply does not shift the LM curve at all. We see this in our exampleby considering what happens if M increases. For any given Y (so that we set !Y =0), !r/!(M/P) = ( – 1/f); this tells us how much the LM curve shifts down. As f getslarger, this shift gets smaller and approaches zero. (This is in contrast to the hori-zontal LM curve in part (c), which does shift down.)

5. To raise investment while keeping output constant, the government should adopta loose monetary policy and a tight fiscal policy, as shown in Figure 11–20. In thenew equilibrium at point B, the interest rate is lower, so that investment is high-er. The tight fiscal policy—reducing government purchases, for example—offsetsthe effect of this increase in investment on output.


A

B

Y

r

Inte

rest

rate

IS1

Income, output

r1

r2

Y1

LM2

LM1

IS2


La combinación de políticas en los inicios de los ochenta hizo exactamente lo contrario.La política fiscal era expansionaría, mientras la política monetaria era constrictiva. Estacombinación desplaza la curva IS a la derecha y la LM a la izquierda, como muestra laFigura 11–21. El tipo de interés aumenta y la inversión se reduce.

The policy mix in the early 1980s did exactly the opposite. Fiscal policy wasexpansionary, while monetary policy was contractionary. Such a policy mix shiftsthe IS curve to the right and the LM curve to the left, as in Figure 11–21. The realinterest rate rises and investment falls.

6. a. An increase in the money supply shifts the LM curve to the right in the short run.This moves the economy from point A to point B in Figure 11–22: the interest ratefalls from r1 to r2, and output rises from Y to Y2. The increase in output occursbecause the lower interest rate stimulates investment, which increases output.

Since the level of output is now above its long-run level, prices begin to rise.A rising price level lowers real balances, which raises the interest rate. As indicat-ed in Figure 11–22, the LM curve shifts back to the left. Prices continue to riseuntil the economy returns to its original position at point A. The interest ratereturns to r1, and investment returns to its original level. Thus, in the long run,there is no impact on real variables from an increase in the money supply. (This iswhat we called monetary neutrality in Chapter 4.)


Income, output

Y1

r2

r1

IS2IS1

LM2LM1

A

B

Y

r

Inte

rest

rate


Figure 10-19

A

B

IS

Y

r

Inte

rest

rate

r1

LM2

Y= Y

Income, output

LM1

Y Y2

r2


9. Respuestas:

a) Un aumento en la oferta de dinero desplaza la curva LM hacia la derecha en elcorto plazo. Esto mueve la economía del punto A al punto B en la Figura 11–22.El tipo de interés baja de r1 a r2 y la renta crece de Y a Y 2. El aumento de larenta ocurre porque el menor tipo de interés estimula la inversión.

16

The policy mix in the early 1980s did exactly the opposite. Fiscal policy wasexpansionary, while monetary policy was contractionary. Such a policy mix shiftsthe IS curve to the right and the LM curve to the left, as in Figure 11–21. The realinterest rate rises and investment falls.

6. a. An increase in the money supply shifts the LM curve to the right in the short run.This moves the economy from point A to point B in Figure 11–22: the interest ratefalls from r1 to r2, and output rises from Y to Y2. The increase in output occursbecause the lower interest rate stimulates investment, which increases output.

Since the level of output is now above its long-run level, prices begin to rise.A rising price level lowers real balances, which raises the interest rate. As indicat-ed in Figure 11–22, the LM curve shifts back to the left. Prices continue to riseuntil the economy returns to its original position at point A. The interest ratereturns to r1, and investment returns to its original level. Thus, in the long run,there is no impact on real variables from an increase in the money supply. (This iswhat we called monetary neutrality in Chapter 4.)


Income, output

Y1

r2

r1

IS2IS1

LM2LM1

A

B

Y

r

Inte

rest

rate


Figure 10-19

A

B

IS

Y

r

Inte

rest

rate

r1

LM2

Y= Y

Income, output

LM1

Y Y2

r2


Dado que ahora el nivel de renta esta por encima de su nivel en el lagro plazo, losprecios empiezan a crecer. El incremento de los precios reduce la cantidad real dedinero, lo que aumenta el tipo de interés. Como indica la Figura 11–22, la curvaLM vuelve a la izquierda. Los precios siguen creciendo hasta que la economíavuelve a su punto inicial en A. El tipo de interés vuelve a r1, y la inversión vuelvea su nivel original. En conclusión, en el largo plazo, el aumento en la oferta dedinero no afecta las variables reales.

b) El aumento del gasto público desplaza la curva IS hacia la derecha, y la economíase mueve del punto A al B en la Figura 11–23. En el corto plazo, la renta crece deY a Y 2, y el tipo de interés aumenta de r1 a r2.

b. An increase in government purchases shifts the IS curve to the right, and theeconomy moves from point A to point B, as shown in Figure 11–23. In the shortrun, output increases from Y to Y2, and the interest rate increases from r1 to r2.

The increase in the interest rate reduces investment and “crowds out” part of theexpansionary effect of the increase in government purchases. Initially, the LMcurve is not affected because government spending does not enter the LM equa-tion. After the increase, output is above its long-run equilibrium level, so pricesbegin to rise. The rise in prices reduces real balances, which shifts the LM curveto the left. The interest rate rises even more than in the short run. This processcontinues until the long-run level of output is again reached. At the new equilibri-um, point C, interest rates have risen to r3, and the price level is permanentlyhigher. Note that, like monetary policy, fiscal policy cannot change the long-runlevel of output. Unlike monetary policy, however, it can change the compositionof output. For example, the level of investment at point C is lower than it is atpoint A.

c. An increase in taxes reduces disposable income for consumers, shifting the IScurve to the left, as shown in Figure 11–24. In the short run, output and the inter-est rate decline to Y2 to r2 as the economy moves from point A to point B.


C

B

A

Y

r

Inte

rest

rate r3

r2r1

IS1

IS2

LM2

LM1

Income, output

Y= Y

Y Y2


AB

C

Y

r

Inte

rest

rate

Y= Y

LM2

LM1

IS1

IS2

Income, output

YY2

r2

r3

r1


El aumento en el tipo de interés contrarresta parte del efecto expansivo del incre-mento del gasto público. Inicialmente, la curva LM no se ve afectada porque elgasto público no está en la ecuación LM. Después del aumento, la renta está por

17

encima de su nivel en el largo plazo y los precios empiezan a subir. El incrementode los precios reduce la cantidad real de dinero, lo que mueve la LM a la izquierda.El tipo de interés aumenta aún más hasta que la renta de equilibrio se alcanzaotra vez. En el nuevo equilibrio, en el punto C, el tipo de interés ha subido hastar3 y el nivel de precios será más alto de forma permanente. Como en el caso dela política monetaria, la política fiscal no puede modificar el nivel de renta en ellargo plazo. Sin embargo, si puede cambiar la composición de la renta agregada.En el punto C, la inversión es menor que en el punto A.

c) Un aumento de los impuestos reduce la renta disponible de los consumidores des-plazando la curva IS a la izquierda, como muestra la Figura 11–24. En el cortoplazo, la renta y el tipo de interés caen a Y2 y r2 mientras la economía se muevedel punto A al B.

b. An increase in government purchases shifts the IS curve to the right, and theeconomy moves from point A to point B, as shown in Figure 11–23. In the shortrun, output increases from Y to Y2, and the interest rate increases from r1 to r2.

The increase in the interest rate reduces investment and “crowds out” part of theexpansionary effect of the increase in government purchases. Initially, the LMcurve is not affected because government spending does not enter the LM equa-tion. After the increase, output is above its long-run equilibrium level, so pricesbegin to rise. The rise in prices reduces real balances, which shifts the LM curveto the left. The interest rate rises even more than in the short run. This processcontinues until the long-run level of output is again reached. At the new equilibri-um, point C, interest rates have risen to r3, and the price level is permanentlyhigher. Note that, like monetary policy, fiscal policy cannot change the long-runlevel of output. Unlike monetary policy, however, it can change the compositionof output. For example, the level of investment at point C is lower than it is atpoint A.

c. An increase in taxes reduces disposable income for consumers, shifting the IScurve to the left, as shown in Figure 11–24. In the short run, output and the inter-est rate decline to Y2 to r2 as the economy moves from point A to point B.


C

B

A

Y

r

Inte

rest

rate r3

r2r1

IS1

IS2

LM2

LM1

Income, output

Y= Y

Y Y2


AB

C

Y

r

Inte

rest

rate

Y= Y

LM2

LM1

IS1

IS2

Income, output

YY2

r2

r3

r1


Inicialmente, la curva LM no está afectada. En el largo plazo, los precios empiezana bajar porque la renta está por debajo de su nivel de equilibrio y la curva LMse desplaza hacia la derecha por el aumento de la cantidad real de dinero. Eltipo de interés baja aún más hasta r3, se estimula la inversión y crece la rentaagregada. En el largo plazo, la economía llega al punto C. La renta vuelve a Y , elnivel de precios y el tipo de interés son menores, y la bajada del consumo ha sidocompensada por un aumento en la inversión.

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