Download ECON 222 Assignment 2: Macroeconomic Models and Applications and more Assignments Economics in PDF only on Docsity!
ECON 222 Assignment 2
Ammar Lakdawala, 20214226
*All Graphs created using Python programming language
- Question 1:
a. Total factor productivity rises today and remains persistently high in the future.
Impact on Investment would be an increase in equilibrium investment due to larger
expected return on capital. This happens because when TFP rises, firms can
produce more output with less cost. This causes firms to anticipate this return on
capital and invest more to maximize future output.
Impact on Interest Rate would be an increase in equilibrium interest rate due to an
increase in demand for investment with the same savings. This happens because
the increase in demand for investments puts an upward pressure on the interest
rate as firms need funds to finance these investments and increase borrowing.
b. An increase in government consumption financed by a higher effective tax rate on
capital income.
Impact on Investment would be a decrease in equilibrium investment since
investors are less likely to invest in capital if there are less returns. By increasing
government consumption funded by higher tax rates, this would reduce after-tax
returns on capital for investors. With lower returns, this would have a lower
incentive to invest in capital.
Impact on Interest Rate would be a decrease in interest rate due to a lower demand
for investment funds. The reduced investment demand decreases the demand for
funds and exerts a downward pressure on interest rate. With less firms and investors
looking to borrow, a decrease in interest rate would encourage consumptions.
- Question 2:
a. To find global equilibrium world interest rate ๐
๐ค
๐
๐น
๐
๐
๐น
๐
๐ค
Equilibrium values:
Domestic:
๐
๐
Foreign:
๐น
๐
๐น
๐
Current account balances:
๐
๐
๐น
๐น
๐
๐น
๐
b. New Savings function:
๐
= 65 + 200r
New equilibrium condition:
๐ค
Equilibrium values:
Domestic:
๐
๐
Foreign:
๐น
๐
๐น
๐
Current account balances:
๐
๐
๐น
๐น
๐
๐น
๐
c. New Investment function:
๐
= 75 โ 200r
New equilibrium condition:
๐ค
Equilibrium values:
Domestic:
๐
๐
Foreign:
๐น
๐
๐น
๐
Current account balances:
๐
๐
๐น
๐น
๐
๐น
๐
The steady state for capital effective worker is:
๐
๐
โ
๐
โ
We know that ๐(๐
๐
๐
- 5
, so we substitute n, s, g, and d :
๐
โ
- 5
๐
โ
๐
โ
- 5
๐
โ
๐
โ
- 5
๐
โ
๐
โ
Using the production function, we can find the steady state output per effective
worker:
๐
โ
๐
โ
- 5
๐
โ
- 5
๐
โ
e. In the steady state, the output per worker grows at the rate of productivity growth g =
0.15 or 15% because in steady state terms, output per effective worker stays
constant which makes any growth in output per worker due to A.
Because A is growing at rate g , output per worker is also growing at the same rate of
15% in the steady state.
- The production function is: ๐ = ๐ด๐พ
๐ผ
๐ฝ
1 โ๐ผโ๐ฝ
a. To get output per worker, we do:
๐ผ
๐ฝ
1 โ๐ผโ๐ฝ
๐พ
๐
capital per worker, and โ =
๐ป
๐
human capital per worker, Simplify:
๐ผ
๐ฝ
b. In the steady state, โ๐ = 0 and โโ = 0
๐
โ
๐
โ
Using the formula from a), we can substitute A = 1 :
๐ผ
๐ฝ
Substitute this into the steady state equations and isolate for k and h :
๐
๐ผ
๐ฝ
๐
1
๐ผโ 1
โ
โ๐ฝ
๐ผโ 1
โ
๐ผ
๐ฝ
โ
1
๐ผ โ
1 โ๐ฝ
๐ผ
c. In the diagram below, the two curves are representing the physical capital per
worker (k) in blue, and human capital per worker (h) in the red dotted line.
The curves were drawn this way because each curve shows a different relationship
between the two outputs depending on the different investment shares for k and h.
The intersection represents the steady state levels of k and h where both physical
and human capital per worker is at 0. โ๐ = 0 and โโ = 0. This intersection is at an
equilibrium at the (2,4) point.
d. We can see from the diagram that there is an intersection at only one point between
the two curves in the positive quadrant which shows the positive steady state
solution. This is due to the different parameters of both functions and the alpha and
beta values which are different for both. The shape of these curves is also
determined by the diminishing returns in capital which can be seen in the exponents
of the two equations of the curves. This is why there can only be 1 pair of positive
values for the steady state that could satisfy both equations.
e. Using the equations from before:
๐
๐ผ
๐ฝ
โ
๐ผ
๐ฝ
need to increase the nominal money supply M for the higher demand for
money.
e. Increase M :
i. An increase in price level would reduce the real value of the current nominal
supply and in order to maintain the purchasing power, people would have an
increased demand for money. This would cause an increase in the nominal
demand for money. To maintain a constant interest rate, the central bank
would need to increase the nominal money supply M for the higher demand
for money.
