1. Suppose you own a piece of land on which you need 800 units of work to be performed using labour. You can hire all the workers you want, but you are told that each worker has an S-Shaped capacity curve. Specifically, capacity is zero for the first $10 of income, it increases by 2 units for each additional unit of income up to a total income of $ 50. After this point capacity increases by 1 unit for each unit of additional income up to a total income of $ 100. Any additional income above $ 100 does not generate additional capacity. Assume that all income you pay to the workers is spent on nutrition.
a) Draw the capacity curve for one worker with capacity in units of work on the vertical axis and income on the horizontal axis.
b) Assume that you want to minimize your total cost of completing 1000 units of work. How many workers would you hire and how much would you pay each of them.
c) Suppose that you find a complementary technology that enables workers to deliver 2 additional units of capacity for each additional unit of income paid above $10. Capacity is zero for income up to $10 and becomes constant at $100 of income. How many workers would you hire and how much would you pay each of them. Interpret you answer.
d) Repeat b) assuming that capacity is zero for the first $20 of income. All other rules remain the same. How does your answer change and why?