Suppose the country of Pooh has only two occupations. You can work as a laborer or you can become an entrepreneur. The entrepreneur hires labor and makes profits. However, to become an entrepreneur one must take out a loan of I = 20,000 pahs (a pah is the unit of currency in Pooh) in order to set up a factory. Each entrepreneur will hire m=10 workers and pay them a wage of w pahs. The total value of your output is g = 30,000 pahs. The interest rate on the loan is r= 10% per year. If an entrepreneur is caught defaulting on their loan, they must pay a fine of F = 5,000 pahs and a percentage of business profits A = 20%, in addition to the wealth put up for collateral valued at the rate of interest W (1+r). a) Set up the formula to determine the minimum amount of collateral W needed to be granted a loan (Note, you are not given a value for w yet). 5 marks) b) Examine the required collateral for different levels of wage rate: w = 10, 20, 30 and 40. How does the collateral requirement go up or down with the wage rate? Explain your