Question

Corinth's labor supply grew by 1.4% and land stock grew by 1% from 425 BCE to 424 BCE. Landowners received 50% of income. If total factor productivity grew by 0.3% find the growth rate of aggregate output.

Answer 1

1.51%

Step-by-step explanation:

Recall that:

Total Output =
`A* K^a * ^(1-a)`

here;

A = total productivity factor

K = capital input

L = labor input

SInce Landowners gets 50% of income; then a = 0.50

`= A* K^ {0.50} * ^(1-0.50)`

Output at 424BBC

`= 1.003A * (1.014K)^(0.5)(1.01L)^(0.5)`

`= 1.003 * (1.007)(1.005)AK^(0.5)L^(0.5)`

`=1.0151AK^(0.5)L^(0.5)`

Thus, the growth rate from 425 BCE to 424 BCE :

= 1.0151 - 1

= 0.0151

= 1.51%