Comparative statics in the steady-state: draw a new version of the graph from the previous question. Using this graph, explain what happens when the population growth rate increases from n1 to n2. In particular, do the following: (a) Draw the effect of this change on the functions in the graph. (b) What does an increase in n represent? (c) State the effect on steady-state capital per capita and steady-state output per capita - do these quantities increase or decrease
Question:
Comparative statics in the steady-state: draw a new version of the graph from the previous question. Using this graph, explain what happens when the population growth rate increases from n1 to n2. In particular, do the following:
(a) Draw the effect of this change on the functions in the graph.
(b) What does an increase in n represent?
(c) State the effect on steady-state capital per capita and steady-state output per capita - do these quantities increase or decrease
Previous question and answer :
Question:
Graphing the steady-state: reorganize the equilibrium law of motion into two functions, a linear function and a concave function, whose point of intersection defines the steady-state quantity of capital per capita. Name these two functions g1 (k) for the linear function and g2 (k) for the concave function. Circle the expression for these two functions. Graph the two functions of capital per capita derived in the previous step, with the function value on the y-axis and the argument of both functions (capital per capita) on the x-axis. Label the axes and label the functions: make it clear which line corresponds to which function (g1 (k) or g2 (k)).
Answer:
Given information
There are 2 function
1 function is liner function which is denoted by g1(k)
2nd function is concave function which is denoted by g2(k)
Intersection of both the curve is known as steady state growth rate
Y=f(K,L)
converting into per capita terms
y=f(k,1)
we know that
C+S=Y
S=I
I=sf(k)--- as f(k)=y
Change in capital=sf(k)-d(k)
For steady state growth golden rule
0=sf(k)-d(k)
sf(k)=d(k)--- steady state growth rate
sf(k)= =sy=g2(k)---- It is concave function as it production function.
It shows diminishing marginal productivity.
d(k)= g1(k)--- it is liner function as it shows the
Now we can plot both the functions on the diagram
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