You are the sole survivor of a shipwreck on a desert island. You do not expect to be rescued.

You can either use your time to grow food to consume immediately, or to build new tools and

buildings (capital) which will increase your supply of food in future years.

a) Sketch your initial production function (total output of food + capital in terms of your

labour input), and show how to turn this into a feasible set. Show your optimal choice

of how you spend your time, assuming you initially consume everything you produce.

b) You discover a more efficient way of harvesting coconuts, that increases your food

production by 50%, taking labour input and other inputs as given. Show the impact on

your total production and labour supply

(i) in the short run and

(ii) in the longer term,if this allows you to spend some of your time producing capital.