Pooh is a country with only two occupations. You can work as a laborer or you can become an entrepreneur, who hires labor and makes profits. To become an entrepreneur, you need a loan of 20,000 pahs (a pah is the unit of currency in Pooh). With 20,000 pahs you can set up a factory that hires ten workers, each of whom you must pay an income of w pahs over the year. Together, the workers produce for you an output of 30,000 pahs. At the end of the year, you must sell your factory (for 20,000 pahs) and repay the loan. The rate of interest in Pooh is 10% per year.
(a) Suppose you were to contemplate running away instead. Imagine you would be caught, fined 5000 pah, and 20% of your business profits would be seized. You would also lose whatever collateral you put up with the bank (plus interest), but you would get to keep the 20,000 pah (plus interest that you also owe). Find a formula that describes how much collateral the bank should ask for (in pah units) before it would advance you a loan. Examine this required collateral for different levels of the wage income: w = 1000, 2000, and 2, 500. Does the required collateral go up or down with the wage? Explain your answer.
(b) Let’s suppose that the minimum wage in Pooh is fixed by law at 500 pah. Find the collateral required to get a loan if w is at the minimum wage. Consider the following statement: “If more than x% of Pooh inhabitants are unable to put up this collateral, then some people are unable to get employment, whether as laborers or entrepreneurs.” Calculate x.