Lecture 10 - Economic Growth In Long-Run Equilibrium

Question 1

Production function in per worker terms, and what assumption do we have to make for it to work?

Answer 1

First assume CRS by adding z
zY= F(zK,zN)

Replace z with 1/n
Y/N = F (K/N , 1)

Question 2

MPK formula

Answer 2

f(k+1) - f(k)

Where f(k) = F(k/n , 1)

I.e the output gained from an additional unit of capital per worker (k/n)

Question 3

Thats the supply side: Now Household behaviour

What is the national income identity IN PER WORKER TERMS

Answer 3

y= C+I

Where in per worker terms…
y= Y/N
c=C/N
i=I/N

Question 4

What is the consumption (c) function?

Answer 4

c=(1-s)y

Where s IS MPS

Question 5

So what is the national identity function now?

Answer 5

Sub in consumption function (2) into (1)
y=(1-s)y+i

where i=sy through expanding brackets and rearranging

Question 6

Capital stock - key determinant of output

2 aspects that influences/changes capital stock

Answer 6

Investment and depreciation

Question 7

When will capital stock rise

Answer 7

If I>0

And remember from the national identity equation, i=I/N so also I/N>O

Question 8

How to link investment to output.

2. Learn graph pg 8. How can we find consumption per worker (c) or C/N?

Answer 8

1. We know i = sy

And y=f(k)
So i=sf(k)

f(k) = F(K/N, 1)

2. Consumption per worker (c=C/N) is gap in between y and i since what is not saved is saved.

Question 9

Change in capital stock k equation

2. what do we have to do to get the long run equilbrium in PER WORKER TERMS?

Answer 9

1. Δk = i - δk = sf(k) - δk

δ is assumed a constant fraction e.g 0.1

2. Set Δk=0 to get the long run equilbrium, which rearranges to get it IN PER WORKER TERMS
   i=δk

Question 10

Steady state in long run diagram. State Axis’ and concept

Answer 10

If inv>dep, K increases (k₁ to k)
If dep>inv K decreasing (k₂ tok)

Y axis investment/depreciation (i=δk)
X axis is K (capital per worker)

K* is steady state, natural dynamics always bring k back to k*

Question 11

What would an increase in savings do, and what would it look like on the steady state inv/dep graph?

Answer 11

Increase in investment, as I=sf(k) in per worker terms. (Remember s=MPS)

Higher savings means people can invest.

In graph, it will lead to a higher steady state point k*₂

Question 12

How to include government budget in Solow model.

Answer 12

Use national savings
Sn = S+T-G , replace S for sf(k)d which is disposable income per worker.

Where t=T/N and g=G/N (taxation per worker, gov spending per worker)

So we get:
Sn = Sn/N = sf(k)d + t -g
National savings = disposable income per worker + taxation revenue per worker - gov spending per worker

Which makes sense if we think about it.

Question 13

1. If the Government spends taxes on capital in the same proportion as households (i.e s times t) , what will happen?
2. If the government spends more on capital than households (s times t), what happens?

Answer 13

No effects on the equilibrium and we replace private capital with public capital.

2. capital per worker (k) will be higher.

Note: assume productivity of capital is the same across public and private ownership so that f(k) is unaffected.

Question 14

So far we have consider closed.

If we have open capital markets, what is the savings investment function in per worker terms

Answer 14

In open capital markets, remember
Sn = I+CF, or Sn - CF= I.

So in per worker terms
sn -cf =i

Where cf is CF/N. (Per worker terms)

Question 15

What happens if cf<0?

Answer 15

cf (capital flows per worker) is negative, so CI>CO

There would be an increase in investment domestically, so k increases.

E.g let cf = -10
Sn - -1 is adding 10, so so k is increasing faster from k₀ since investment at k₀ is now even more bigger than dep.

Question 16

Limitations of this steady state model

Answer 16

Cannot explained sustained growth.

Question 17

How can we show output and living standards still grow

Answer 17

Consider population growth and technical progress