Question

An island economy has no government and is a no storage economy. There is fixed amount of land in the island. The aggregate production function requires land and labour inputs as following: Y=zf(L,N). Population growth rate N'/N is depending on living standards C/N as following N'/N=g(C/N). If there is a positive technology shock, analyse the short run and long run effects on output, consumption, output per worker, consumption per worker and population.

Answer 1

With no storage economy, we can assume that there are no savings. So, there must be no investment as well, since it is also a closed economy.

A positive technology shock shifts the production curve outwards. It menas that with given resources , we can produce more. So, given fixed quantity of land and population, output increases. Since, consumption is positively related to output, increased output also increases consumption. since, workers are fixed in short run, there is an increase inoutput per worker and consumption per worker as well. Taking C as consumption in the question, an increase in C/N also increases growth rate of population, but in the longer term.

Since population has increased due to technology shock, an increase in one of factors of production(N) further raises output and consumption in the long run. However, there is no growth in output per worker and consumption per worker since denominator has also increased. Further, population growth rate may also stabilise due to no change in C/N