Posted: April 13th, 2023

3 Question Of MACROECONOMIC ANALYSIS( With Some Data)

ECON3353 Macroeconomic Analysis
Assignment 2

Instruction: Please read the following instruction before you start your homework.
For short-answer questions, you need to show the instructor your work. When working on a calculation, an equation or a formula, you should write down the process for your solution and then show each step on a separate line below. If you need more steps, write down each one on a separate line. If you just write bare answers (final answers), only partial credits will be given to them even they are correct. Your homework will be graded for content and neatness.

Question 1.
A country’s production function is specified as below.
• y = f(k) = 2k(1/2); here y is output per capita; k is capital stock per capita.
Use this production function to finish the following questions.

(1) If we assume capital depreciation ratio (δ) is 0.25 and saving rate (s) is 50 percent or 0.5. Then, what is steady-state capital stock per capita (k*) and steady state output per capita (y*)? Here we do not consider population growth rate and technological progress.
Tip: recall definition of a steady-state and how capital stock change at a steady state.

(2) Now consider population rate is 4 percent (n = 0.04) in this country and saving rate is 58 percent (s = 0.58). Then, how much will be steady state capital stock (k*) and steady state output per capita (y*)? How the two values (k* and y*) change compared with part (1) and why?
Tip: remember we need to consider the impact of population growth rate (n) to capital stock. So the outflow of capital stock will be faster than the previous scenario (no population growth rate). Also the saving rate is different in this case.

(3) Suppose, population growth rate in this country increases to 5 percent (n = 0.05) now. To maintain steady state capital stock (k*) and steady state output (y*) at the same level as above, the country is trying to increase saving rate (s). Then what is the new saving rate should be to keep k* and y* at the same level.
Tip: a higher population growth rate (n) would lead to a faster outflow of capital stock. To keep steady state capital stock (k*) and steady state output (y*) at the same level, we need a higher saving rate (a higher inflow of capital) to offset the impact of higher population growth rate.

(4) How much is steady-state consumption per capita (c) when saving rate is 0.58 as in part (2)? Then how much will be consumption per capita when saving rate increases to 0.6 in part (3)?
Tip: You need the parity between consumption, saving and national output at per capita levels. Also be careful, you have different values of stead-state output with different saving rates.

Question 2.
With the same production function in Question 1 above, try to find out stead-state graphically. The following table presents various values of capital stock (k). Note: the attached spreadsheet is the same as the table below. You can use either one to finish the following parts. Keep your answers 2 to 3 digit decimals.

Capital stock (k) Output
y = f(k) Depreciation = δ * k Saving1 = s*f(k)
s = 0.5 or 50% Saving2 = s*f(k)
s = 0.25 or 25%
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(1) Fill in the table for the values of output per capita f(k), depreciation and savings (investment) per capita with two different saving rates as given.

(2) To graph capital depreciate line and investment (saving) curves with two saving rate. You can use the spreadsheet attached to make graphs.

(3) Highlight the steady state k with different colors in the table for two saving rates.

Question 3.
Read the case study “The Miracle of Japanese and German Growth”. This article discusses what happens when part of the capital stock is destroyed in a war. Now suppose that a war does not
directly affect the capital stock, but that casualties reduce the labor force. Assume the economy was in a steady state before the war, the saving rate is unchanged, and the rate of population growth after the war is the same as it was before. What is the immediate impact of the war on total output? What happens subsequently to output per worker in the postwar economy?
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