Study Guide # 2 (Keys)
Keynesian: Money, Interest, Income
1- Draw two schemes: one that explains where interest rates intervene in the Neoclassical model, and
one that explains where interest rates intervene in the Keynes’s theory.
Neoclassical
Keynes
Y
Y
MPC
i
C
S
C
S
Financial wealth
i
Illiquid assets
Liquid assets
2- Which school of thought as a flow-theory of interest rate? Which one has a stock-theory of interest
rate?
Neoclassical: flow theory (equality of saving and investment, which are both flows)
Keynes: Stock theory (equality of demand and supply of money, which are stocks)
3- What are the different motive of money demand? How are those different from the Classical
approach?
Transaction (money held because of time delay between income receipt and expenditures), Precaution
(money held to face unexpected cost or opportunities), Speculation (money held to speculate in financial
markets)
The Neoclassical model only has the transaction motive
4- Knowing that Md = c0 + c1Y – c2i, what does c0 represent? c1? c2?
c0: Autonomous money demand
c1: Sensitivity of money demand to income
c2: Sensitivity of money to interest rate
5- Using the preceding demand function, draw the graph of the money market: include all the
relevant information (the graph should have the following variables on it: i*, M*, i, M, Y , Md, Ms)
i
Ms
i*
Md( Y , i)
M*
M
6- How is the liquidity preference theory different from the loanable funds theory?
Monetary factors have a direct role to play in the determination of interest rate
An increase in investment (with affect Y) will not necessarily lead to an increase in interest rate: it
depends on what happens to money supply and the different c’s
IS-LM model
1- What explanations does the IS-LM combine?
Income determination via aggregate demand (Y = E), interest rate determination by monetary factors (M d
= Ms), investment determination (mek = i)
2- Write down the structural system of equations of the IS-LM model and explain each equation.
What are the endogenous variables? What are the exogenous variables?
Y  C  I  G 


YD  Y  T 
C  a  bYD 

  IS curve
 I  e  di

G  G



T  T


M d  c0  c1Y  c2i 


M s  M
  LM curve
M  M

d

 s
3- What does the IS curve represent? What does the LM curve represent?
IS: equilibria in the commodity market
LM: equilibria in the money market
4- From the structural model, put in brackets the equations you need to combines to get IS and to get
LM.
See above
5- Draw the graph of the IS-LM model?
i
LM
i*
IS
Y*
Y
6- What causality is involved in the IS curve? What about the LM curve? Draw the causality on the
previous graph.
LM: i = f1(Y)
IS: Y = f2(i)
7- Knowing the causality implied by each curve, what does Δi/ΔY represent? what about ΔY/Δi?
(use plain English to answer this question)
Δi/ΔY is the slope of the LM curve: how a given change in Y affects i.
ΔY/Δi is the slope of the IS curve: how a given change in i affects Y.
8- Draw a flat LM curve and complete the following sentence: “A given change in ___ leads to ____
change in ___.” Express this sentence algebraically.
A given change in Y leads to no change in i. Δi/ΔY = 0
9- Draw a horizontal IS curve and complete the following sentence: “A given change in ___ leads to
____ change in ___.” Express this sentence algebraically.
A given change in i leads to an extremely large change in Y. ΔY/Δi → ∞
10- What are the factors that affect the slope of the IS curve? The slope of the LM?
See notes and book
11- What are the factors that affect intercept of the IS curve? The intercept of the LM curve?
See notes and book
12- On the following graphs and draw the effect of
a. A higher sensitivity of money demand to income
i
LM
IS
Y
b. An increase in the money supply
i
LM
IS
Y
c. A higher autonomous demand for money
i
LM
IS
Y
d. A lower sensitivity of money demand to interest rate
i
LM
IS
Y
e. Higher taxes
i
LM
IS
Y
f. A lower autonomous investment
i
LM
IS
Y
g. A higher sensitivity of investment to interest rate
i
LM
IS
Y
13- Given the following system of equations:
Y  C  I  G
Y  Y  T
 D
C  100  0.5YD

 I  50  5i

G  50
T  40

M d  150  20Y  2i

M s  1000
M s  M d
a. Finding the IS curve and the LM curve
IS curve: Y = C + I + G  Y = 100 + 0.5(Y – 40) + 50 – 5i + 50  Y = 360 – 10i
LM curve: Ms = Md  1000 = 150 + 20Y – 2i  i = -425 + 10Y
b. Finding the equilibrium value of income and interest rate
Method 1 (substitute i into IS): Y* = 360 – 10(-425 + 10Y*)  Y* = 46  (by substituting in LM) i* =
31.4
Method 2 (substitute Y into LM): i* = -425 + 10(360 – 10i*)  i* = 31.4  (by substituting in IS) Y* = 46
c. Say that the government increases spending by +200. What would be the effect of this on
Y* and i*.
This implies that the IS curve is now Y = 760 – 10 i. Substituting into the unchanged LM curve we have:
Y* = 50 and i* = 71.04
14- Going back to the initial conditions. Say that in the previous system, money demand becomes
completely insensitive to interest rate. Solve the model.
Then we have Md = 150 + 20Y  LM curve is: Y = 42.5, which is also the equilibrium level of income
The IS curve is the same and so i* = 31.75
15- Say that income earners save all their income. Solve the previous model.
Then we have: C = 100  IS curve is: Y = 200 – 5i
LM is unchanged and the equilibrium values are: Y* = 45.5 and i* = 30.88
16- Characterize the situation at each point in the following graph.
i
LM
b
i*
a
IS
c
Y*
Y
Point a: reach back LM by increasing i  excess demand in money market; reach back IS by decreasing
Y  excess supply in commodity market
Point b: reach back LM by decreasing i  excess supply in money market; already on IS  equilibrium
in commodity market
Point c: reach back LM by increasing i  excess demand in money market; reach by IS by increasing Y
 excess demand in the commodity market
AS-AD model
1- What is the purpose of this model? i.e. what does it criticize?
The model provides an alternative way, relative to the Neoclassical model, to explain how aggregate
supply and aggregate demand are determined: aggregate supply is not fixed and aggregate demand
depends on other variables than money and price.
2- How is it different from the IS-LM model?
The AS-AD model provides an explanation of how price and output are determined: It splits Y into two
components, Y = PQ.
3- Would flexibility in wage lead the system back to full employment?
No: it is actual demand that matters for the determination of full employment
4- Say we have the following system of equations:
 PQ  C  I  G

YD  PQ  T
C  150  0.9YD

 I  40  i
G  100

T  60

M d  110  2 PQ  4i
M  1500
 s
M s  M d

 P  w / MPL
Q  N 3 / 4 K

K  1
w  0.75

a. Find the IS and LM curve in real terms
IS curve: PQ = C + I + G  PQ = 150 + 0.9(PQ – 60) + 40 – i + 100  Q = 2360/P – 10r, with r = i/P
LM curve: Ms = Md  1500 = 110 + 2PQ – 4i  r = -347.5/P + 0.5Q
b. Find the aggregate demand function
By putting the value of r given by LM into IS we have: Qd = 972.5/P
c. Knowing that MPL = 0.75K/N1/4 and that N1/4 = x  N = x4. Find the aggregate supply
curve
We know that P = w/MPL  P = w/(0.75K/N1/4) (with K = 1 and w = 0.75) P = N1/4  N = P4
We also know that Q = N3/4K = N3/4. By substituting the value of N we have: Q = (P4)3/4  Qs = P3
d. Determine the equilibrium value of Q, P, i, and Y.
At equilibrium Qs = Qd  P3 = 972.5/P  P4 = 972.5  P* = 5.58
Q* is obtained by substituting P* into Qs or Qd  Q* = 174.15
i* is obtained by using the LM curve in real terms: i/5.58 = -347.5/5.58 + 0.5*174.15  i* = 138.37
Y* = 5.58*174.15  Y* = 971.76