Question

An economy on the balanced growth path experiences a natural disaster. A hurricane destroys
50% of the economy’s population and 75% of its capital stock. Show the path of the following
variables (Note: your answer should consist of a graph of a variable or the log of a variable on
the vertical axis, and time on the horizontal axis) and explain the changes over time to the following variables.
A) Capital and production per worker (k and y)
B) Employment N
C) Capital stock K
D) Output Y

Answer 1

Considering that there is no other factor in economy which effects output

Output (Y) = Capital Stock (K) X Total Labor (L)

Let us consider before disaster, total capital stock was 100, while total populaion was 200.

So Capital per worker before disaster was 100/200 = 0.5,

After disaster Total Capital stock will be (1-75%) X 100 = 25% X 100 = 25,

After Disaster total population will be (1-50%) X 200 = 50% X 200 = 100

So Capital Pre worker will be 25/ 100 = 0.25

Same way production per worker will get lower from 0.5 to .0.25 as capital and labor are only two factors responsible for production.

Employment (N): Since population has become half, competition for employment also becomes half. So employment rate must get doubled

Capital Stock: Since, 75% of capital stock is destroyed, it will become 1/4th

Output: Population is halved and capital stock has become 1/4th, then output will become 1/8th

Following are charts:

Thanks