Problem set – Benchmark model
Economics 2 (Macroeconomics)
Lecturer: Tamás Fazekas
1
Problem
Consider an economy which is represented by the following equations:
Y
=
AK 0.5 L0.5
A =
5
S
=
300
S
=
250
K
L
1. Calculate the the equilibrium level of output for this economy.
2. Write out the labor demand function.
3. Calculate the the equilibrium level of real wage for this economy.
4. Write out the capital demand function.
5. Calculate the the equilibrium level of real rental rate of capital for this economy.
6. Using the graph below label the equilibrium level of real wage and real rental rate of capital.
7. The technological parameter (the total factor productivity, T F P ) increases and it will be A0 = 6. Calculate
the new equilibrium value of output and real rental rate of capital for this economy. Show in the graph
the change.
8. The technological parameter (the total factor productivity, T F P ) decreases and it will be A0 = 3. Calculate the new equilibrium value of output and real wage for this economy. Show in the graph the change.
1
2
Problem
Consider an economy which is represented by the following equations:
Y
=
AK 0.3 L0.7
A =
KS =
4
4000
LS
1500
=
1. Calculate the the equilibrium level of output for this economy.
2. Write out the labor demand function.
3. Calculate the the equilibrium level of real wage for this economy.
4. Write out the capital demand function.
5. Calculate the the equilibrium level of real rental rate of capital for this economy.
6. Using the graph below label the equilibrium level of real wage and real rental rate of capital.
0
7. The capital level increases (new inventions) and it will be K S = 4800. Calculate the new equilibrium
value of output and real rental rate of capital for this economy. Show in the graph the change.
0
8. The supply of labour decreases (demographic change or migration) and it will be LS = 1200. Calculate
the new equilibrium value of output and real wage for this economy. Show in the graph the change.
3
Problem
We assume that the output is 2000, the autonomous consumption is 20, the marginal propensity to consume
is 0.8. We can that the the autonomous investment is 500 and the investment sensitivity to interest rate is 40.
The consumption- and investment function are linear.
1. Calculate the value of consumption.
2. Calculate the value of investment.
3. Calculate the equilibrium value of the real interest rate.
4. Calculate the values of point 1, 2 and 3, if the autonomous consumption rises to 30.
4
Problem
It is known about an economy, that its consumption function is linear. What is more, if the disposable income
is Y − T = 3000, then C = 2800 and if the disposable income is Y − T = 3500, then private saving is SP = 325.
1. Calculate the marginal propensity to consumption.
2. Calculate the marginal propensity to save.
2
3. Write out the equation of consumption function.
4. Write out the equation of saveing function.
5
Problem
Consider an economy which is represented by the following equations:
Y
=
A =
AK 0.5 L0.5
2
KS
=
500
S
=
720
C
=
125 + 0.75YDI
I
=
200 − 10r
L
G =
100
T
100
=
1. Calculate the equilibrium level of
(a)
(b)
(c)
(d)
(e)
(f)
output
consumption
investment
real wage
real rental rate
real interest rate
for this economy.
2. Calculate the new equilibrium level of above variables for this economy, if the consumer confidence is
stronger and the autonomous consumption will be 200.
6
Problem
Consider an economy which is represented by the following equations:
Y
= AK 0.5 L0.5
A
=
1
S
=
900
S
=
6400
C
=
350 + 0.6YDI
I
=
650 − 20r
K
L
G =
300
T
300
=
1. Calculate the equilibrium level of
(a)
(b)
(c)
(d)
(e)
(f)
output
consumption
investment
real wage
real rental rate
real interest rate
for this economy.
2. Calculate the new equilibrium level of above variables for this economy, if the the autonomous investment
will be 0.24.
3