# Consider a simple economy, with just three occupations

November 24, 2016

Consider a simple economy, with just three occupations: subsistence producer, industrial worker, and entrepreneur. Subsistence producers can produce some fixed amount valued \$2,000 with their labor. An industrial worker can earn a wage w. An entrepreneur runs the business that hires the industrial worker, but the business requires a start-up capital of \$200,000. With \$200,000 you can set up a factory that hires 10 workers, paying w dollars to each worker over the year. Together the workers generate a revenue of \$300,000 for you. So the gross profit is \$(300,000 – 10 w). At the end of the year, you must sell the factory (for \$200,000) and repay the loan. The rate of interest is 10% per year. Hence the net profit is: \$[(300,000 – 10 w) – (1.1 × 200,000)]. You put your wealth A up as collateral to borrow the start-up capital \$200,000. Suppose you try defaulting on the loan. Imagine you would be caught, fined \$50,000, and 20% of your business profits (gross) would be seized. You would also lose the collateral plus interest. But you would get to keep the borrowed money plus the interest. (i) What is the benefit from defaulting? (ii) What is the cost of defaulting? (iii) Using (i) and (ii), find out the condition so that the worker will not choose to default. (iv) Rearranging this condition, find a formula that describes how much collateral (A) the bank should ask for before it would advance you a loan. (v) There is a high enough wage, call it w , such that the net profit from running a business becomes exactly same as the earning of an industrial worker. Calculate w . (Note that for wages higher than w , net profit from business is less than wage, so that no one wants to be entrepreneur)

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