You are the benevolent ruler of an island economy, which cannot trade with other countries. You have complete control of the islands workforce. The workers can either produce goods to be consumed, or capital (in this case, tools and machinery).

a) Assume that in year 1, you decide to direct all production effect into goods. Also assume diminishing marginal product of labour. Sketch your initial production function, with hours worked per person per day on the x-axis, and total output of goods on the y-axis. Turn this into a feasible set. Show your optimal choice of how workers spend their time in year 1, by sketching in indifference curves for a representative worker.

b) You decide that, in year 2, you will tell your workers to spend half of their time making capital, and half making goods. Show the impact on your total goods production in year 2. Why might you do this?

c) Assume that the capital you have produced lasts forever. Now explain what you would choose to produce in year 3. Sketch the new feasible frontier and optimal choice.