01.02.2023 Lecture Notes
Determinants of Aggregate Production:
Factors of Production (inputs):
Labour (L)
Capital (K)
Both factors are assumed to be exogenous and fixed over time.
K = K (autonomous)
L = L (autonomous)
Production Function
the aggregate production function - a description of how much output (Y) is
produced for any amount of factor inputs
Y = F(K, L)
where F is the function that translates K and L into Y
An efficient, developed economy generally produces more with the same
quantity of capital and labour than an inefficient, primitive economy.
The shares of labour and capital income in the US economy have remained
relatively constant over time at about 70% labour and 30% capital.
Cobb-Douglas Production Function
This function incorporates the two ideas:
Y = F(K, L) = AK^(0.3) L^(0.7)
where A describes productivity (total factor productivity)
01.02.2023 Lecture Notes 1
, From the perspective of workers, labour productivity is the amount of output
produced per unit of labour.
Unlike labour productivity, total factor productivity takes into account how
productive labour and capital are together.
A = Y / (K^0.3 L^0.7)
Example: Y = $10 trillion, K = $10 trillion, L = 100 million workers
A = 10 / ((10^0.3) (100^0.7)) = -0.20
Why are some countries rich and others poor?
Assuming every citizen works, so that per capita income is the same as average
income (output) per worker, Y/L.
Income per worker becomes:
where k is capital per worker.
The shortfall of per capita income in other countries relative to the US is due
more to lower productivity than it is to lower amounts of capital per person.
Two particularly attractive characteristics of the function:
1. constant returns to scale
2. diminishing marginal product
01.02.2023 Lecture Notes 2
Determinants of Aggregate Production:
Factors of Production (inputs):
Labour (L)
Capital (K)
Both factors are assumed to be exogenous and fixed over time.
K = K (autonomous)
L = L (autonomous)
Production Function
the aggregate production function - a description of how much output (Y) is
produced for any amount of factor inputs
Y = F(K, L)
where F is the function that translates K and L into Y
An efficient, developed economy generally produces more with the same
quantity of capital and labour than an inefficient, primitive economy.
The shares of labour and capital income in the US economy have remained
relatively constant over time at about 70% labour and 30% capital.
Cobb-Douglas Production Function
This function incorporates the two ideas:
Y = F(K, L) = AK^(0.3) L^(0.7)
where A describes productivity (total factor productivity)
01.02.2023 Lecture Notes 1
, From the perspective of workers, labour productivity is the amount of output
produced per unit of labour.
Unlike labour productivity, total factor productivity takes into account how
productive labour and capital are together.
A = Y / (K^0.3 L^0.7)
Example: Y = $10 trillion, K = $10 trillion, L = 100 million workers
A = 10 / ((10^0.3) (100^0.7)) = -0.20
Why are some countries rich and others poor?
Assuming every citizen works, so that per capita income is the same as average
income (output) per worker, Y/L.
Income per worker becomes:
where k is capital per worker.
The shortfall of per capita income in other countries relative to the US is due
more to lower productivity than it is to lower amounts of capital per person.
Two particularly attractive characteristics of the function:
1. constant returns to scale
2. diminishing marginal product
01.02.2023 Lecture Notes 2
