Solow

Question 1

How do you get investment as a function of capital and the savings rate?

Answer 1

1. Know output per capital is y=f(k)
2. Assume a simple model in which output is only used either for consumption or investment, so

y= c + i

3. Assume that consumption is defined as the proportion of output that is not saved, so

c= (1 - s)y

4. Subbing that into 2. and cancelling, we get

i = sy = sf(k)

Question 2

What’s the fundamental equation of the Solow model?

Answer 2

€ k = investment - depreciation

   = sf(k) - dk

Question 3

What does the real interest rate have anything to do with marginal products?

Answer 3

The real interest rate is the cost of borrowing, or the price of investment/saving (opportunity cost of using existing funds for investment), which is the price of capital, which is the marginal product of capital (through solving profit maximisation problem)

Question 4

DEF: Marginal product of capital/labour

Answer 4

Note: the assumption that it is diminishing is essential in LR analysis in both solow and production model

The amount of extra output produced when the capital/labour input increases by one unit

Question 5

To solve for steady state…

Answer 5

Start with the face that savings rate equals depreciation rate, solve for k* and sub into original production function

Question 6

Understanding steady state: why do we reach it, what do we learn (for CD)?
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Answer 6

Diminishing returns, so rate at which investment (from production) rises falls as the capital stock increases

k* depends on - depreciation rate, workforce size, savings rate, and productivity (derive CD cap stock and see for yourself)

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Question 7

What happens to capital per person when we have population growth? So change in k…

Implications for living standards
Aggregate level of output

Answer 7

Using approximations for derivatives we find that

Change in k= actual i - break-even i

nk needed to equip new workers with capital
Countries with higher population growth rates will therefore have lower levels of capital and income per worker in the LR (SOL worse)

BUT aggregate GDP level will rise, growing at same rate as n

g = g + g = 0 + n

Question 8

What is the Golden Rule? How do we find it?

Answer 8

It is the level of capital/worker (steady state level k*) for which consumptions is maximised.

To calculate it, have to find consumptions as a function of capital:
c= y - i = f(k) - (d + n)k

So is optimised when MPK = d + n

Question 9

What happens if our initial steady state capital per worker k is

a) above the GRSS?
b) below?

Answer 9

a) if k* > k* [dynamically inefficient economy]

We want to reduce the level of capital in the economy. By doing so we want to reduce investment, so for that we reduce savings. As a result, consumption is higher at all points in time, income per capita falls, and investment falls.

b) k* < k* [dynamically efficient]

We want to increase the level of capital in the economy. For that we gotta increase the savings rate, in order to increase investment. Whilst doing that, in the SR consumers are worse off as they consumer fewer goods, but we know that f(k) rises, investment rises, and as consumption is a proportion of f(k) we see consumption rise in the long-run too!

Question 10

Pros of solow model?

Cons?

Answer 10

Pros:
1. Explains how we reach steady state, how rich a country is in the LR
2. The principle of transition dynamics:
Explains why a country further from SS will grow faster, allows for understanding for growth rate differences across countries.

Cons:

1. Focuses on investment in capital, but doesn’t explain why we got the A we do.
2. Doesn’t explain why we have differences in A and investment rates across countries (perhaps a better model would endogenise the investment rate)
3. Doesn’t provide theory of SUSTAINED LR ECONOMIC GROWTH

Question 11

What can we do to encourage technical progress?

Answer 11

Grants
Industrial policy 
Patent laws
Institutions 
Tax breaks