Pooh is a country with only two occupations. You can work as a laborer or you ca
ID: 2776030 • Letter: P
Question
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.
Explanation / Answer
(a) Suppose you were to contemplate a loan default. 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?
Suppose that the required minimum collateral size is given by Wm. If you repay the loan, you pay up 20,000 pay plus an interest rate of 10%, which makes for 22,000 pah in all. If you do not pay, you lose the collateral (plus interest), you are fined 5,000 pah, and you lose 20% of business profits. The collateral plus interest is worth W(1 + r) = (1.1)W. Business profits are 30, 000 10w, where w is the wage rate. So if you do not repay, your total losses are (1.1)W + 5, 000 + (0.2)[30, 000 10w]. You will repay, therefore, of this last expression is at least as great as 22,000 pah, which is the amount you give up if you do decide to repay. This means that the minimum necessary collateral is given by
Wm = 17, 000 (0.2)[30, 000 10w]
1.1
Now you can calculate what happens to Wm for different values of the wage rate w. As discussed in class, the minimum required collateral increases with the wage rate, because business profits are lower and therefore less valuable to the creditor in the event of non repayment. Thus a larger collateral is asked for the begin with.
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.
Just use the above formula to calculate Wm if the wage rate is fixed at 500 pah. Now let us go on to the second part. Let N be the total population and let p the fraction of people who cannot put up this kind of collateral. Then p × N people get into the labor market. The remainder become entrepreneurs: each of them demands 10 workers, so the total demand for labor is 10 × (1 p) × N. If the total supply exceeds the total demand, then some people will be unable to get employment, whether as laborers or as entrepreneurs (in terms of our model in class, they would have to go into subsistence farming). The requirement for this is 7 the condition pN 10(1 p)N, which means that the value of p should exceed 10/11. Translate this to percentages to find x.