Material is the book Mankiw chapter 7 and 8

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Material is the book Mankiw chapter 7 and 8
	
Document Preview: Econ 304 Summer 2012 Problem Set #4 Due by 11:59 PM MDT July 61. ( 4 points each part a and b)Suppose a country that is initially at a steady-state level of capital per-worker introduces a successful birth-control campaign that permanently reduces the growth rate of the populationa.Compare the initial steady state and the final steady state in terms of their:	i. levels of capital per worker and output per worker	ii. growth rates of capital per worker and output per workerb.What can you say about the growth rates of capital per worker and output per worker during the transition between the original and the final steady states?2. (10 points)In the Solow model, population growth leads to steady-state growth in total output, but not in output per worker. Do you think this would still be true if the production function exhibited increasing or decreasing returns to scale?3. (4 points each part)Suppose that the production function is Y=10(K)1/4(EL)3/4 and capital lasts and average of 10 years so that 10 percent of capital wears out every year. Assume that the rate of growth of population is 4 percent, the rate of technological growth is 2 percent, and the saving rate s = 0.128.a.Derive the equation for output per effective worker y=YEL=f(k), where k equals the amount of capital per effective workerb.Calculate the steady-state levels for each of the following: capital per effective worker, output per effective worker, consumption per effective worker, saving and investment per effective worker, and depreciation per effective workerc.Now, calculate the steady-state growth rates of capital per worker, output per worker, saving and investment per worker, and consumption per workerd.Finally, calculate the steady-state growth rates of capital, output, saving and investment, and consumption4. ( 4 points each part)The amount of education the typical person receives varies substantially among countries. Suppose you were to compare a country with a...

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Econ 304 Summer 2012  
Problem Set #4 Due by 11:59 PM MDT July 6
1. ( 4 points each part a and b) 
Suppose a country that is initially at a steady-state level of capital per-worker introduces a 
successful birth-control campaign that permanently reduces the growth rate of the population 
a. 
Compare the initial steady state and the final steady state in terms of their: 
i. levels of capital per worker and output per worker 
Answer: 
Consider the fundamental equation of the Solow economic growth model:
dk/dt = sf(k(t)) - (n + δ )k(t)    ………………………………………………………………… (1) 
Where ‘k (t)’ denotes capital per worker,  
‘dk/dt’ denotes change in per worker capital over time  
‘f (k(t))’ denotes per capita income (y) 
‘n' denotes population growth rate 
‘δ’ denote depreciation rate 
‘s’ denote saving rate 
At the steady state, we have dk/dt = 0 
Putting this in (1), we get steady state capital per worker as: 
k* = 
         
        
   …………………………………………………………………….. (2) 
We note that with decline in ‘n’ [population growth rate], steady state capital per worker i.e. k* 
increases. 
Since output per worker is direct function of capital per worker (from the production function), 
so when steady state capital per worker i.e. k* increases, the steady state output per worker 
would also increase. 
ii. growth rates of capital per worker and output per worker 
Answer: 
The growth rate of output per worker and capital per worker under Solow model is no way 
related to population growth rate in the economy. So decline in population growth rate would not 
cause any change in the growth rate of output per worker and capital per worker. 
b. 
What can you say about the growth rates of capital per worker and output per worker during the 
transition between the original and the final steady states? 
Answer: 
Both will have positive growth rate during the transition between the original and the final steady 
states. This positive growth rate between the transitional periods would cause both capital per 
worker and output per worker to increase to new steady state levels. At the steady state level, 
their growth rates would become zero.
2. (10 points) 
In the Solow model, population growth leads to steady-state growth in total output, but not in 
output per worker. Do you think this would still be true if the production function exhibited 
increasing or decreasing returns to scale?

Material is the book Mankiw chapter 7 and 8 Document Preview: Econ 304 Summer 2012 Problem Set #4 Due by 11:59 PM MDT July 6 1. ( 4 points each part a and b) Suppose a country that is initially at a...

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