1) Consider a simple economy, with just three occupations: subsistence producer, industrialworker, and entrepreneur. Subsistence producers can produce some fixed amount valued $2,000with their labor. An industrial worker can earn a wage w. An entrepreneur runs the business thathires 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 eachworker over the year. Together the workers generate a revenue of $300,000 for you. So thegross profit is $(300,000 â 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 â 10 w) â (1.1 Ã 200,000)].You put your wealth A up as collateral to borrow the start-up capital $200,000. Suppose youtry defaulting on the loan. Imagine you would be caught, fined $50,000, and 20% of yourbusiness profits (gross) would be seized. You would also lose the collateral plus interest. Butyou would get to keep the borrowed money plus the interest.(i)(ii) What is the benefit from defaulting?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 businessbecomes exactly same as the earning of an industrial worker. Calculate w . (Note that forwages higher than w , net profit from business is less than wage, so that no one wants to beentrepreneur) 2.(You will want to use a spreadsheet for this problemâfor example, Microsoft Excel.) Maya is arecent high school graduate considering three careers that involve flowing water. She can beginwork immediately at the municipal Water Department, which would pay her (in real terms)$10,000 each year for the next 45 years. A second choice is to spend five years in college, with anannual tuition of $25,000 per year, and become a civil engineer; this would allow her to earn$55,000 per year for the 40 years after she graduates. The final option is to get the same civilengineering degree (just as before), spend the following 5 years getting a Ph.D. in hydrology(with no tuition and a $15,000 annual fellowship), and then work for 35 years as a groundwaterspecialist who earns $75,000 per year.a. If the interest rate were 7 percent, which option would Maya choose? Use aspreadsheet program (your choiceâExcel, or some other program) to perform yourcalculations, and attach the output of that exercise. The top line of your output shouldlook like the following. Remember to start in Year 0 (i.e., the first payments are madeand/or received immediately, not one year from today) and end in Year 44.Option 1Option 2YearEarningsValueEarnings Option 1Option 2Option 3Option 3Present Value EarningsPresent Value Present b. Would Maya change her mind if a new act of Congress limited fellowships forgraduate students to $9000 per year?c. How would that decision change if the interest rate rose to 8 percent? (Use the original$15,000 fellowship value here.) Write at least 2 or 3 sentences to explain why thechange in Mayaâs decision makes intuitive sense from a financial point of view.Mention what else Maya might do with the money she had saved for tuition payments.3.Consider the following graph of private and social returns to and costs of education,then answer the following questions: a. What is the optimal amount of education from the viewpoint of the privateindividual?b. What is the optimal amount of education from the viewpoint of society?4. Education is said to promote economic growth. Explain how this might be the case. Discussany possible limitations on the ability of education to help a country develop. (See EasterlyReading)
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