ECON 320 SDSU Intermediate Macroeconomic Theory Problem Set Worksheet 1 The Natural Rate of Unemployment Suppose that the markup of goods prices over margi

ECON 320 SDSU Intermediate Macroeconomic Theory Problem Set Worksheet 1 The Natural Rate of Unemployment
Suppose that the markup of goods prices over marginal cost is 5%, and that the wage-setting
equation is
W = P(1 − u)
where u is the unemployment rate.
1. What is the real wage, as determined by the price-setting equation?
2. What is the natural rate of unemployment?
3. Suppose that the markup of prices over costs increases to 10%. What happens to the natural
rate of unemployment? Explain the logic behind your answer. 2 The AD Curve
Consider the following IS-LM model:
C = 1 + .3YD
I = .3Y − 10i
G = 7
T = 10
Md
P
= Y − 100i
M = 80
1. Solve for the IS relationship.
2. Solve for the LM relationship allowing P to vary (i.e. your expression will have Y , i, and P
variables in it).
3. Using your answers above, derive the AD curve. 3 AS-AD Model
Consider the following extension to the problem above. All the information in the previous problem
will hold here so that the AD curve will be your answer from Question 2.3. However, the following
information relevant to aggregate supply is given below:
Production function:
Y = N
Wage Setting relationship:
w = P
e
z
u
z =
1
16
Price setting relationship:
P = (1 + m)w
m = 0.6
Unemployment rate:
u =
U
L
Unemployment level:
U = L − N
L = 20
where Y is real output, N is the number of employed workers, w is the nominal wage, P
e
is
the expected price level, P is the price level, u is the unemployment rate, U is the number of
unemployed workers, L is the size of the labor force, and z is our catch-all variable for other labor
market conditions.
1. Solve for the natural rate of unemployment and the natural level of output.
2. Derive the AS curve; this should be an equation with P, Y , and P
e
in it.
3. Suppose P
e = 72, what are P and Y ? Is this a medium run equilibrium?
4. Given your answers above, do you expect P
e
to rise or fall? Explain.
5. Suppose P
e = 12, what are P and Y ? Is this a medium run equilibrium?
6. Given your answers above, do you expect P
e
to rise or fall? Explain.
7. Solve price level P that corresponds to the medium-run AS-AD equilibrium.
8. Provide an AS-AD graph showing the above changes in P
e
.