Opening an economy that is closed
1. Consider an economy that is closed and is represented by the following equations.
Y = C + I + G
C = �0 + �1��
T = �0 + �1�
I = �0 + �1� − �2�
G = �0 + �1�
Also assume that:
r = �̅
�0,�0, �0, �0 > 0
0 < �1,�1, �1, �2,�1, �1 < 1
a. Solve for the equilibrium level of output as a function of the parameters. What is the
multiplier?
b. Suppose the economy starts with a balanced budget (G = T). Now suppose that G and
T increase by one unit each. Derive the change in Y.
c. Explain how the slope of the IS curve is related to the parameter �2.
d. Now suppose that real money demand is given by the function:
(
�
�)
�
= �� − ��, where �, � > 0
Solve for r as a function of Y, M and P.
Econ 304 Intermediate Macroeconomics Fall 2018
Colorado State University (Optional) Extra Credit Assignment Briggs
e. Use your answers from parts a. and d. to derive the IS curve as a function of the
exogenous variable ��, and the parameters. (Hint: r ≠ �̅, and the answer should not
contain r.)
2. Using the Wage setting equation:
� = ���(�, �)
and the price setting equation:
� = (1 + �)�
a. Derive the function for the natural rate of unemployment (note: show every step of
the derivation using the correct propositions and theorems for full credit)
b. Suppose expected inflation is given by the function:
�� = (1 − �)�̅ + ���−1.
Using your answer to part a., derive the augmented Phillips curve for � = 1.
c. What does this tell us about the impact of nominal wages on the change of inflation?
d. Draw the IS-LM-PC curve for �� > � and explain the response of the central bank if
� = 1.
e. Now suppose that the central bank has hit the “zero lower bound”. What will be the
impact to inflation, unemployment and output if the government does not use fiscal
policy to correct the problem?
3. Consider two countries, Wu-kanda and EPMDmia, whose production is described by the
Solow growth model. Each has the same Cobb-Douglas production function:
� = ��(�, �)
�(�, �) = ����1−�, � = 1
2
but the levels of capital and labor vary for each country.
Wu-kanda saves 22% of its income and has a population growth rate of 2% per year.
EPMDmia saves 13% of its income and has a population growth rate of 4% per year.
Both countries have a constant technological growth rate of 2% per year and a
depreciation rate of 5% per year.
Econ 304 Intermediate Macroeconomics Fall 2018
Colorado State University (Optional) Extra Credit Assignment Briggs
(NOTE: y = �
�, k = �
�)
a. What is the per worker production function? What is the marginal productivity of
capital?
b. Solve for the ratios of Wu-kanda’s steady state income per worker, capital per worker
and investment per worker.
c. Solve for the ratios of EPMDmia’s steady state income per worker, capital per worker
and investment per worker.
d. Draw the production function, investment function and depreciation.
e. Solve for consumption per worker at the steady state level of capital and output.
4. Now consider the same two countries whose production is described by the Solow
growth model with human capital. Each has the same Cobb-Douglas production function:
� = ��(�, �, �)
�(�, �, �) = ������1−�−�, where � + � < 1, � = 1
3 , � = 1
3
but the levels of capital and labor vary for each country.
Wu-kanda invests 18% of its income in physical capital and invests 7% of its income in
human capital. The depreciation rate pf physical capital is 5% and the depreciation rate of
human capital is 2%. The country has a population growth rate of 2% per year, and a
constant technological growth rate of 2% per year.
EPMDmia invests 15% of income in physical capital and 10% its income in human
capital. The depreciation rate pf physical capital is 5% and the depreciation rate of human
capital is 2%. The country has a population growth rate of 4% per year, and a constant
technological growth rate of 3% per year.
a. What is the per worker production function? What is the marginal productivity of
physical and human capital?
b. Solve for the ratios of Wu-kanda’s steady state income per worker, physical capital
and investment per worker and human capital and investment per worker
Econ 304 Intermediate Macroeconomics Fall 2018
Colorado State University (Optional) Extra Credit Assignment Briggs
c. Solve for the ratios of EPMDmia’s steady state income per worker, physical capital
and investment per worker and human capital and investment per worker
d. Draw the production function, investment function and depreciation.
e. Solve for consumption per worker at the steady state level of physical and human
capital and output.