1.  The Keynesian Beauty  Contest:  Go to Canvas and complete the Cavas Quiz for assignment 3.

2.  The Paradox of Thrift:  Consider the simple model of the good markets: Y = C + I + G

C = C0 + C1(Y − T)

I = I0 − I1r

G =

T =

Saving in the simple model of the goods market is defined as S = Y − C − G.

(a) Using the goods market equilibrium and the definition of saving, find the predicted change in equilibrium aggregate savings if consumers decided to save more (C0 ⇓). Explain why the effect of an aggregate increase in savings is called a paradox using your answer.

Answer:   Let’s suppose that everyone decided to save more and represent this by decreasing C0 .  This change will have two competing effects.  At first it seems like S should rise.

S    =   (Y − C − G)

S    =   (Y − C0 − C1(Y − T) − G)

S ↑  ⇒  C0 ↓

But, C0  also affects Y .   So we need to determine how much a change in C0  affects Y .  To do this lets look at the equilibrium expression for output and let’s label the old level of autonomous consumption C0(old)  and the new level C0(new) .

Yold     =    [C0(old) − C1 + I0 − I1r + ]

−Ynew     =    [C0(new) − C1 + I0 − I1r + ] ∆Y   =    [∆C0]

Now, compare the change in Y to the change in C0 .

 > 1   ⇒   [∆C0] > ∆C0

The net change in savings is

S   =   (Yold − C0(old) − C1(Yold − T) − G)    −S   =   (Ynew − C0(new) − C1(Ynew − T) − G)

...

∆S   =   ∆Y (1 − C1) − ∆C0

∆S   =    [∆C0](1 − C1) − ∆C0

∆S   =   0

The  Paradox  of  Thrift:   If everyone increases saving at the same time, the equilibrium effect is no additional saving in the economy. One person spending is another’s income, so in this model income falls and results in no additional saving.  The paradox is thus that increasing saving leads to no additional aggregate savings in equilibrium.

3. Fine  Tuning the Economy:

Consider the following behavioral equations:

IS                                               LM

C = C0 + C1(Y − T) − C2r        =

I = I0 − I1r                                   = l0Y − l1i

G =                                         i = r + π e

T =

(a) The behavioral equation for consumption now includes the interest rate. Give an economic reason for why consumption may depend on the interest rate.

Answer:   Some portion of consumption is commonly debt financed. This in- cludes purchases of durable goods such as cars, houses, and major appliances.

A smaller portion of consumption is financed by credit card purchases. Or, consumer saving depends on the interest rate.

(b) Explain intuitively why C2r appears with a negative sign in front of it.

Answer:   The portion of consumption that is financed by debt will have a negative relationship with the interest rate.  When interest rates are low, it is relatively inexpensive to finance current consumption with debt.  When interest rates are high, the cost of financing consumption today with debt increases.

Or, consumers prefer to save more as interest rise and save less as interest fall.

(c) Solve for the IS-LM equilibrium algebraically.  How does the change in the

consumption function change the multiplier? Is it now larger or smaller?

Answer:

Y   =   C + I + G

Y   =   C0 + C1(Y − ) − C2r + I0 − I1r +

Y   =   C0 + C1(Y − ) − (C2 + I1)r + I0 +

Sub in r

Y   =   C0 + C1(Y − ) − (C2 + I1)( Y −   − πe) + I0 +                Y   =   C1Y − (C2 + I1) Y + (C2 + I1)(   + πe) + C0 − C1 + I0 +  Y   =    [(C2 + I1)(   + πe) + C0 − C1 + I0 + ]

Therefore, the multiplier is

1

1 − C1 + (C2 + I1)  .

The multiplier is smaller in this case because the denominator of the multiplier is larger with the addition of C2 .

4. Demand Pull Inflation:  Suppose that the central bank wants to increase output, but the economy is already at the natural rate.

(a) Show the short and long run effects of a monetary expansion (M ⇑) in this situation in the AD/AS model. You can omit the labor market and production function graphs and you should assume sticky prices for the SRAS.

Answer:   The short run effect is an increase in output and decrease in the real rate of interest.

The long run effect is increase in the price level and no change in output or real interest rates.

r

LM(,πe ) = LM(,πe )

LM(,πe )

0

1

P

YN    Y1

IS(G0,T0 )

Y

1

SRAS1

SRAS

AD(G0,T0 ,M1 ) AD(G0,T0 ,M0 )

Y

(b) As you can see from above (hint), in the long run output is unchanged but the price level is higher. What happens if the central banks tries this strategy over and over again?

Answer:   The price level will continue to rise.  It may start having an effect on inflation expectations.

(c) Now assume that these repeated increases in the money supply have caused expected inflation (πe ) to increase.  Furthermore, assume the central bank stops its repeated increases of the money supply at the same time (assume M is constant). What is the net effect of the increase inflation expectations on output and the price level in the short run?

Answer:   The net effect is an increase in output while the price level remains unchanged and a decrease in the real rate of interest. It basically mimics the effect the a monetary expansion. The policy becomes self-fulfilling.

r

LM( ,π0(e))

LM( ,π1(e))

0

1

IS(G0,T0 )

YN    Y1

P

SRAS

AD(G0,T0 ,M0 ,π1(e)) AD(G0,T0 ,M0 ,π0(e))

Y

5.  Combination Policy

(a) Graph an AD/AS model with sticky wages and show graphically and ex- plain with words how the Australian government with the help of the Reserve Bank could increase government spending while keeping the economy at full

employment without causing changes in the price level.

Answer:   See the graph below:

W P

W¯ P0

Y

YN

r

LS