Savings, Capital Formation and long run growth

Growth rate Y formula (assuming A is contanst i.e. no growth)

gY = gK*α + gL*(1-α) + gA

Animal spirits

Describe the emotions, instincts, and confidence that influence economic decision-making.

e.g. autonomous consumption

Adjustment dynamics depends on time horizon

Short-run prices fixed, quantities flexible

• keynesian cross

• productions meet demand

Medium-run some price and quantity flexibility

• AD-AS model

Long-run prices flexible, quantity fixed

• Solo-swan

• Natural rate hypothesis; focused on supply side

Savings = 

Current income less spending on current needs

Savings rate

Saving divided by income

Motives for saving

Life-cycle saving, pre cautionary saving, bequests

Private savings (disposable income less consumption)

S = (Y-T) - C = I + G-T

National savings (S + Public savings)

NS = S + (T-G)

In a closed economy National savings and investment are equal?

True; because

• every dollar saved in the economy is used to finance investment spending (spending on capital)

• no foreign capital inflows/outflows, so investment must be funded by domestic savings only

Flow variables

Measured per unit of time

E.g. wage per unit, household savings per fortnight, GDP, consumption, investment per year, change overtime in a stock

Stock variables

Measured at a point in time

E.g. value of your assets, liabilities, Net wealth, physical capital stock

Net capital accumulation formula

Kt+1 = (1-δkt) + It

Simple mofel of saving and investment

Saving (s) —> Supply of loanable funds

Investment (i) —> Demand for loanable funds

Real interest (r ) —> Price that brings S and I into balance

Supply curve S(r)

Increasing in the real interest rate r

• save more when return to saving r is higher, investment decreases as borrowing costs more

Demand curve I(r)

Decreasing in the real interest rate r, saving decreases investment increases

• investment projects are more profitable when r decreases as borrowing costs are less and get less interest from savings

Long run growth

Growth in potential output Yt* —> Yt

Potential output Yt*

Maximum sustainable level of realGDP the economy can produce when

• labour and capital fully employed

• prices and wages are fully adjusted

Long run growth in potential output —> growth in living standards

Focus on on output per persons or output per worker

Limitations of focussing on output per person

• omits all non-market activity, including leisure

• does not capture changes in income inequality

• does not capture natural resources, environmental damage

Output per person

Is the product of output per worker and the employment/population ratio

Output per person formula

Output/population = output/employment * employment/population

Long run growth in output per person is driven by

growth in output per worker, also known as labour productivity

Output per worker

Means how much output realGDP the average worker produces (measure of labour productivity)

• the higher output per worker, the higher economy’s living standards

Output per worker formula

Y/L

• Y = total real output (realGDP)

• L = number of workers

What determines output per worker?

technology, human capital, physical capital, organisation capital, political and legal institutions, property rights, land, natural resources

Factors of production

Resources used to produce goods/services in an economy

Function of inputs/Factors of production

K physical capital

L Labour

A total factor productivity (everything else)

• production function and inputs represent the long run supply side fundamentals of the economy

Aggregate Production Function

Y = A*F(K,L)

Y = aggregate output i.e. realGDP

K = value of physical capital

L = labour force

A = total factor productivity

Cobb-Douglas production function

Shows how the output changes when you change the amount of labour and capital used

Cobb-Douglas production function formula

Y = A * K^αL^1-α, 0<α<1

α

how sensitive output is to changes in capital

Factor shares

• share of income going to capital is α

• share going to labour is 1-α

3 important properties of Cobb-Douglas production

1. Positive marginal products

2. Diminishing returns to each input

3. Constant returns to scale

Marginal products

Marginal product of an input is the amount of extra output from adding a small amount of that input holding all other inputs fixed.

—> Marginal product of capital (MPK) is positive

MPK formula (take the partial derivative of Y from K)

α(Y/K) > 0, holding L fixed

MPL formula (take the partial derivative of Y from L)

(1- α)Y/L > 0, holding K fixed

Diminishing Returns to Each input (holding 1 input constant)

Diminishing (marginal) returns to an input if using more of it decreases marginal product, again holding all other inputs fixed

• the more capital you have the less returns you will have from it/productivity doesn’t increase as much

Diminishing marginal returns to capital formula (double derivative of Y to K)

-α(1-α)AK^α-2L^1-α<0, holding L fixed

Diminishing marginal returns to labour formula (double derivative of Y to L)

-α(1-α)AK^αL^-α-1<0, holding K fixed

Constant returns to scale (CRS)

Scaling all inputs by the same amount —> output scaled by the same amount